The usual theory of inflation breaks down in eternal inflation. We derive a
dual description of eternal inflation in terms of a deformed Euclidean CFT located at the
threshold of eternal inflation. The partition function gives the amplitude of different geometries
of the threshold surface in the no-boundary state. Its local and global behavior
in dual toy models shows that the amplitude is low for surfaces which are not nearly conformal
to the round three-sphere and essentially zero for surfaces with negative curvature.
Based on this we conjecture that the exit from eternal inflation does not produce an infinite
fractal-like multiverse, but is finite and reasonably smooth
A smooth-exit the-phase-transition-to-slow-roll-eternal-inflationmirgytoo
This document summarizes research on the phase transition to eternal inflation. It begins by introducing the concept of eternal inflation occurring when quantum fluctuations dominate over classical drift. The authors argue that even in the eternal inflation regime, perturbations of the geometry and interactions remain perturbative, allowing quantitative analysis. They aim to precisely define the critical condition for eternal inflation and calculate statistics of the reheating volume to understand the phase transition.
This presentation is based on an exhibition of Einstein's manuscripts on General Relativity that was organized during the Einstein centenary in Berlin in November 2015.
Large scale mass_distribution_in_the_illustris_simulationSérgio Sacani
Observations at low redshifts thus far fail to account for all of the baryons expected in the
Universe according to cosmological constraints. A large fraction of the baryons presumably
resides in a thin and warm–hot medium between the galaxies, where they are difficult to observe
due to their low densities and high temperatures. Cosmological simulations of structure
formation can be used to verify this picture and provide quantitative predictions for the distribution
of mass in different large-scale structure components. Here we study the distribution
of baryons and dark matter at different epochs using data from the Illustris simulation. We
identify regions of different dark matter density with the primary constituents of large-scale
structure, allowing us to measure mass and volume of haloes, filaments and voids. At redshift
zero, we find that 49 per cent of the dark matter and 23 per cent of the baryons are within
haloes more massive than the resolution limit of 2 × 108 M⊙. The filaments of the cosmic
web host a further 45 per cent of the dark matter and 46 per cent of the baryons. The remaining
31 per cent of the baryons reside in voids. The majority of these baryons have been transported
there through active galactic nuclei feedback. We note that the feedback model of Illustris
is too strong for heavy haloes, therefore it is likely that we are overestimating this amount.
Categorizing the baryons according to their density and temperature, we find that 17.8 per cent
of them are in a condensed state, 21.6 per cent are present as cold, diffuse gas, and 53.9 per cent
are found in the state of a warm–hot intergalactic medium.
E. Sefusatti, Tests of the Initial Conditions of the Universe after PlanckSEENET-MTP
This document outlines Emiliano Sefusatti's presentation on testing the initial conditions of the universe using data from the Planck satellite. The presentation covers predictions from inflation like a flat, homogeneous universe with a nearly scale-invariant power spectrum. It discusses how Planck improved constraints on non-Gaussianity parameters like fNL compared to WMAP. For example, Planck reduced errors on the local fNL parameter by a factor of 2-4 depending on the shape. The implications of Planck's results are explored through the example of constraints on a DBI inflation model.
This document discusses classical and quantum dynamics of inflation. It summarizes the horizon problem in standard cosmology and how slow-roll inflation solves it by providing more expansion between the early universe and recombination. Quantum fluctuations during inflation are discussed, along with canonical quantization and vacuum fluctuations. Minimal coupling of inflation fields is introduced. The standard model Higgs boson and its potential as the inflaton field are considered. Specific Higgs portal inflation models are analyzed. Key inflation parameters are defined and their allowed ranges from observational data are shown. Unitary issues with Higgs inflation models are noted.
This document describes 9 numerical calculation methods for analyzing piled rafts, ranging from simple to more complex models. The simplest is the linear contact pressure method (Method 1), which assumes a linear distribution of contact pressures without interaction between the foundation and soil. Winkler's model (Methods 2-3) represents the soil as elastic springs, with pile reactions proportional to settlement. The continuum model (Methods 4-9) considers interaction between all foundation elements and layered soil, represented as a continuum. The most complex method is the modulus of compressibility method for layered soil (Methods 6-9). Finite element analysis is used except for one rigid raft method. The key equations for each method are presented.
1) John Nash presents an equation that is a 4th order covariant tensor partial differential equation applicable to the metric tensor of spacetime. This equation is formally divergence free like the Einstein vacuum equation.
2) The equation can be derived from a specific Lagrangian involving terms quadratic in the scalar curvature and Ricci tensor. Previous theorists had considered such Lagrangians in attempts at quantum gravity theories but had not focused on this specific choice.
3) The equation may allow a wider variety of gravitational waves, including compressional waves not excluded in electromagnetic theory. Standard GR only allows transverse gravitational waves.
A smooth-exit the-phase-transition-to-slow-roll-eternal-inflationmirgytoo
This document summarizes research on the phase transition to eternal inflation. It begins by introducing the concept of eternal inflation occurring when quantum fluctuations dominate over classical drift. The authors argue that even in the eternal inflation regime, perturbations of the geometry and interactions remain perturbative, allowing quantitative analysis. They aim to precisely define the critical condition for eternal inflation and calculate statistics of the reheating volume to understand the phase transition.
This presentation is based on an exhibition of Einstein's manuscripts on General Relativity that was organized during the Einstein centenary in Berlin in November 2015.
Large scale mass_distribution_in_the_illustris_simulationSérgio Sacani
Observations at low redshifts thus far fail to account for all of the baryons expected in the
Universe according to cosmological constraints. A large fraction of the baryons presumably
resides in a thin and warm–hot medium between the galaxies, where they are difficult to observe
due to their low densities and high temperatures. Cosmological simulations of structure
formation can be used to verify this picture and provide quantitative predictions for the distribution
of mass in different large-scale structure components. Here we study the distribution
of baryons and dark matter at different epochs using data from the Illustris simulation. We
identify regions of different dark matter density with the primary constituents of large-scale
structure, allowing us to measure mass and volume of haloes, filaments and voids. At redshift
zero, we find that 49 per cent of the dark matter and 23 per cent of the baryons are within
haloes more massive than the resolution limit of 2 × 108 M⊙. The filaments of the cosmic
web host a further 45 per cent of the dark matter and 46 per cent of the baryons. The remaining
31 per cent of the baryons reside in voids. The majority of these baryons have been transported
there through active galactic nuclei feedback. We note that the feedback model of Illustris
is too strong for heavy haloes, therefore it is likely that we are overestimating this amount.
Categorizing the baryons according to their density and temperature, we find that 17.8 per cent
of them are in a condensed state, 21.6 per cent are present as cold, diffuse gas, and 53.9 per cent
are found in the state of a warm–hot intergalactic medium.
E. Sefusatti, Tests of the Initial Conditions of the Universe after PlanckSEENET-MTP
This document outlines Emiliano Sefusatti's presentation on testing the initial conditions of the universe using data from the Planck satellite. The presentation covers predictions from inflation like a flat, homogeneous universe with a nearly scale-invariant power spectrum. It discusses how Planck improved constraints on non-Gaussianity parameters like fNL compared to WMAP. For example, Planck reduced errors on the local fNL parameter by a factor of 2-4 depending on the shape. The implications of Planck's results are explored through the example of constraints on a DBI inflation model.
This document discusses classical and quantum dynamics of inflation. It summarizes the horizon problem in standard cosmology and how slow-roll inflation solves it by providing more expansion between the early universe and recombination. Quantum fluctuations during inflation are discussed, along with canonical quantization and vacuum fluctuations. Minimal coupling of inflation fields is introduced. The standard model Higgs boson and its potential as the inflaton field are considered. Specific Higgs portal inflation models are analyzed. Key inflation parameters are defined and their allowed ranges from observational data are shown. Unitary issues with Higgs inflation models are noted.
This document describes 9 numerical calculation methods for analyzing piled rafts, ranging from simple to more complex models. The simplest is the linear contact pressure method (Method 1), which assumes a linear distribution of contact pressures without interaction between the foundation and soil. Winkler's model (Methods 2-3) represents the soil as elastic springs, with pile reactions proportional to settlement. The continuum model (Methods 4-9) considers interaction between all foundation elements and layered soil, represented as a continuum. The most complex method is the modulus of compressibility method for layered soil (Methods 6-9). Finite element analysis is used except for one rigid raft method. The key equations for each method are presented.
1) John Nash presents an equation that is a 4th order covariant tensor partial differential equation applicable to the metric tensor of spacetime. This equation is formally divergence free like the Einstein vacuum equation.
2) The equation can be derived from a specific Lagrangian involving terms quadratic in the scalar curvature and Ricci tensor. Previous theorists had considered such Lagrangians in attempts at quantum gravity theories but had not focused on this specific choice.
3) The equation may allow a wider variety of gravitational waves, including compressional waves not excluded in electromagnetic theory. Standard GR only allows transverse gravitational waves.
1. Conformal cyclic cosmology (CCC) predicts the existence of concentric circles of anomalously low temperature variance in the cosmic microwave background (CMB) that would provide evidence of violent events prior to the Big Bang.
2. Analysis of WMAP and BOOMERANG CMB data reveals families of concentric circles up to 6 standard deviations below the mean temperature variance, consistent with CCC predictions.
3. These circles are not easily explained by standard inflationary cosmology, as the events that could cause some of the largest circles observed would need to occur before the end of inflation in the previous aeon.
On Semi-Invariant Submanifolds of a Nearly Hyperbolic Kenmotsu Manifold with ...IJERA Editor
We consider a nearly hyperbolic Kenmotsu manifold admitting a semi-symmetric metric connection and study semi-invariant submanifolds of a nearly hyperbolic Kenmotsu manifold with semi-symmetric metric connection. We also find the integrability conditions of some distributions on nearly hyperbolic Kenmotsu manifold andstudy parallel distributions on nearly hyperbolic Kenmotsu manifold.
A relationship between mass as a geometric concept and motion associated with a closed curve in spacetime (a notion taken from differential geometry) is investigated. We show that the 4-dimensional exterior Schwarzschild solution of the General Theory of Relativity can be mapped to a 4-dimensional Euclidean spacetime manifold. As a consequence of this mapping, the quantity M in the exterior Schwarzschild solution which is usually attributed to a massive central object is shown to correspond to a geometric property of spacetime. An additional outcome of this analysis is the discovery that, because M is a property of spacetime geometry, an anisotropy with respect to its spacetime components measured in a Minkowski tangent space defined with respect to a spacetime event P by an observer O who is stationary with respect to the spacetime event P, may be a sensitive measure of an anisotropic cosmic accelerated expansion. The presence of anisotropy in the cosmic accelerated expansion may contribute to the reason that there are currently two prevailing measured estimates of this quantity
Some Notes on Self-similar Axisymmetric Force-free Magnetic Fields and Rotati...Premier Publishers
An axisymmetric force-free magnetic field in spherical coordinates has a relationship between its azimuthal component to its poloidal flux-function. A power law dependence for the connection admits separable field solutions but poses a nonlinear eigenvalue boundary-value problem for the separation parameter (Low and Lou, Astrophys. J. 352, 343 (1990)).When the atmosphere of a star is rotating the problem complexity increases. These Notes consider the nonlinear eigenvalue spectrum, providing an understanding of the eigen functions and relationship between the field's degree of multi-polarity, the rotation and rate of radial decay as illustrated through a polytropic equation of state. The Notes are restricted to uniform rotation and to axisymmetric fields. Dominant effects are presented of rotation in changing the spatial patterns of the magnetic field from those without rotation. For differential rotation and non-axisymmetric force-free fields there may be field solutions of even richer topological structure but the governing equations have remained intractable to date. Perhaps the methods and discussion given here for the uniformly rotating situation indicate a possible procedure for such problems that need to be solved urgently for a more complete understanding of force-free magnetic fields in stellar atmospheres.
Application of Gauss,Green and Stokes TheoremSamiul Ehsan
Gauss' law, Stokes' theorem, and Green's theorem are used to relate line integrals, surface integrals, and volume integrals. Gauss' law relates the electric flux through a closed surface to the enclosed charge. Stokes' theorem converts a line integral around a closed curve into a surface integral over the enclosed surface. Green's theorem converts a line integral around a closed curve into a double integral over the enclosed area. These theorems have applications in electrostatics, electrodynamics, calculating mass and momentum, and deriving Kepler's laws of planetary motion.
Lambda, the cosmological constant, is considered the fifth foundational constant in physics along with the speed of light c, Planck's constant h, gravitational constant G, and Boltzmann's constant k. Einstein, de Sitter, Lemaitre, and others originally considered Lambda in their early formulations of cosmology. Lambda represents the energy density of empty space and is related to the curvature of spacetime. Its observed value plays a key role in the current Lambda-CDM model of cosmology, which describes our flat, expanding universe containing dark matter, dark energy, and other components.
A young astronomer’s by now ten years old
results are re-told and put in perspective. The implications are
far-reaching. Angular-momentum shows its clout not only in
quantum mechanics where this is well known, but is also a
major player in the space-time theory of the equivalence
principle and its ramifications. In general relativity, its
fundamental role was largely neglected for the better part of a
century. A children’s device – a friction-free rotating bicycle
wheel suspended from its hub that can be lowered and pulled
up reversibly – serves as an eye-opener. The consequences are
embarrassingly far-reaching in reviving Einstein’s original
dream
The peculiar shapes of Saturn’s small inner moons as evidence of mergers of s...Sérgio Sacani
The Cassini spacecraft revealed the spectacular, highly irregular
shapes of the small inner moons of Saturn1
, ranging from
the unique 'ravioli-like' forms of Pan and Atlas2,3
to the highly
elongated structure of Prometheus. Closest to Saturn, these
bodies provide important clues regarding the formation process
of small moons in close orbits around their host planet4,
but their range of irregular shapes has not been explained yet.
Here, we show that the spectrum of shapes among Saturn’s
small moons is a natural outcome of merging collisions among
similar-sized moonlets possessing physical properties and
orbits that are consistent with those of the current moons.
A significant fraction of such merging collisions take place
either at the first encounter or after 1–2 hit-and-run events,
with impact velocities in the range of 1–5 times the mutual
escape velocity. Close to head-on mergers result in flattened
objects with large equatorial ridges, as observed on Atlas and
Pan. With slightly more oblique impact angles, collisions lead
to elongated, Prometheus-like shapes. These results suggest
that the current forms of the small moons provide direct
evidence of the processes at the final stages of their formation,
involving pairwise encounters of moonlets of comparable
size4–6. Finally, we show that this mechanism may also
explain the formation of Iapetus’ equatorial ridge7
, as well as
its oblate shape8.
The document is a report submitted by three students on surface and volume integrals and linear systems in real world problems. It discusses line, surface, and volume integrals and defines linear systems. It provides examples of applying integrals in electrostatics, magnetism, and gravity. It also discusses applications of linear systems and integrals in areas like fluid dynamics, mass continuity, and conservation of momentum. The conclusion reiterates that linear systems can have zero, one, or infinite solutions depending on consistency and independence, and methods for solving systems like graphing, substitution, and addition/subtraction are introduced.
Quantum Theory of Spin and Anomalous Hall effects in Graphene Mirco Milletari'
1) The document discusses quantum theories of spin and anomalous Hall effects in graphene, focusing on developing a full quantum mechanical approach rather than semiclassical approximations.
2) It presents a model of adatom-decorated graphene to induce intrinsic spin-orbit coupling and explores resonant skew scattering and the crossover between quantum side-jump and skew scattering dominated regimes.
3) The document develops a diagrammatic approach to calculate the spin Hall conductivity beyond the Gaussian approximation, taking into account correlated disorder effects, and finds that coherent processes may dominate the anomalous contribution.
Pratik Tarafdar is investigating the application of analogue gravity techniques to model primordial black hole accretion. He plans to apply these techniques used to model astrophysical black hole accretion to primordial black holes. This will help understand primordial black hole accretion phenomena from the perspective of analogue gravity. He has focused on calculating the analogue surface gravity and has obtained expressions for it in both adiabatic and isothermal cases for different accretion disk models. Future work will extend this to model radiation accretion onto primordial black holes and study effects of fluid dispersion on the analogue Hawking temperature.
Numerical Simulations on Flux Tube Tectonic Model for Solar Coronal HeatingRSIS International
This document discusses numerical simulations of the flux tube tectonic model for solar coronal heating. It begins with an introduction to the sun's corona and mechanisms for coronal heating. It then describes the 3D MHD code used to model the interaction and reconnection of magnetic flux tubes in the photosphere. The simulations show the formation of current sheets where flux tubes of opposite polarity come into contact. An analytical 1D model is also presented that can predict the behavior observed in the simulations, such as the outward migration of current sheets over time as photospheric shearing increases.
The document discusses Michael Faraday's experiments with static electric fields and induced electromotive forces using concentric metallic spheres. It then summarizes Gauss's law and how it can be applied to determine the electric flux density D for various charge distributions like a point charge or line charge. It shows that a cylindrical surface is suitable for applying Gauss's law to a line charge, as the radial component of D is the only non-zero component and it is everywhere normal to the cylindrical surface. Finally, it derives one of Maxwell's equations from Gauss's law by taking the divergence of the electric flux density D.
This document summarizes research on inflation in the context of string theory landscapes. It discusses how string theory can stabilize moduli fields like the dilaton and volume to allow for inflation. The KKLT construction is described as stabilizing the volume through non-perturbative effects and uplifting the minimum with an anti-D3 brane. Inflation models in string theory like brane inflation and modular inflation are mentioned. The document also discusses how the string theory landscape of vacua can address anthropic arguments and the cosmological constant problem through the distribution of probabilities in an eternally inflating multiverse.
End point of_black_ring_instabilities_and_the_weak_cosmic_censorship_conjectureSérgio Sacani
We produce the first concrete evidence that violation of the weak cosmic censorship conjecture can occur
in asymptotically flat spaces of five dimensions by numerically evolving perturbed black rings. For certain
thin rings, we identify a new, elastic-type instability dominating the evolution, causing the system to settle to
a spherical black hole. However, for sufficiently thin rings the Gregory-Laflamme mode is dominant, and the
instability unfolds similarly to that of black strings, where the horizon develops a structure of bulges connected
by necks which become ever thinner over time.
Lens history and physics.
For comments please contact me on solo.hermelin@gmail.com.
For more presentations visit my website at http://www.solohermelin.com.
This presentation is in the Optics folder.
Within the framework of the general theory of relativity (GR) the modeling of the central symmetrical
gravitational field is considered. The mapping of the geodesic motion of the Lemetr and Tolman basis on
their motion in the Minkowski space on the world lines is determined. The expression for the field intensity
and energy where these bases move is obtained. The advantage coordinate system is found, the coordinates
and the time of the system coincide with the Galilean coordinates and the time in the Minkowski space.
membranes2015_Attractive Planar Panelization using Dynamic Relaxation Princip...Florian Gauss
The document proposes an Attractive Planar Relaxation method to approximate a target surface with a planar quad mesh. The method starts with a planar quad mesh in the target surface footprint. Iteratively, vertices are attracted towards the surface, introducing non-planarities. A dynamic relaxation algorithm then planarizes the mesh faces. This attraction-planarization process continues until the mesh is close to the target surface. The method is demonstrated on a shopping center roof, starting with a subdivision of principal curvature lines to guide the initial mesh, which is optimized over 30 iterations to closely match the double curved roof geometry.
A smooth-exit-from-eternal-inflation (hawking-hertog-2018)mirgytoo
This document discusses a holographic approach to modeling eternal inflation. It proposes that eternal inflation can be described by a dual conformal field theory defined on the boundary of the inflating region. The partition function of this CFT provides a "holographic measure" on the geometry of the boundary. For small perturbations, the round sphere geometry is favored, contrary to standard predictions. For large deformations using a toy vector model dual, highly squashed sphere geometries are disfavored. This suggests the exit from eternal inflation may be finite and smooth, rather than producing an infinite fractal multiverse.
This document describes the identification of a new supercluster of galaxies called Laniakea. The researchers used a catalog of peculiar galaxy velocities to map large-scale structure and identify locations where velocity flows diverge, tracing the surface that surrounds the local volume with inward motions after removing the cosmic expansion. They define this volume, which encompasses over 100,000 galaxies including the Virgo cluster, as the Laniakea supercluster. It has a diameter of 160 million parsecs and a mass of around 1017 solar masses. The researchers analyze velocity and density fields within this volume to further characterize its structure and flows.
Quantum-Gravity Thermodynamics, Incorporating the Theory of Exactly Soluble Active Stochastic Processes, with Applications
by Daley, K.
Published in IJTP in 2009. http://adsabs.harvard.edu/abs/2009IJTP..tmp...67D
Extracting linear information from nonlinear large-scale structure observationsMarcel Schmittfull
This document discusses methods for extracting linear cosmological information from observations of nonlinear large-scale structure. It describes four paradigms for doing reconstruction to reduce nonlinear effects: 1) Lagrangian reconstruction, 2) forward modeling and sampling, 3) forward modeling and optimization, and 4) machine learning approaches. Two specific reconstruction algorithms are outlined: 1) an isobaric/nonlinear method using a moving mesh code, and 2) an iterative method applying Zeldovich displacements from large to small scales. Results show the iterative method better correlates reconstructed densities to initial conditions over a wider range of scales compared to standard reconstruction.
1. Conformal cyclic cosmology (CCC) predicts the existence of concentric circles of anomalously low temperature variance in the cosmic microwave background (CMB) that would provide evidence of violent events prior to the Big Bang.
2. Analysis of WMAP and BOOMERANG CMB data reveals families of concentric circles up to 6 standard deviations below the mean temperature variance, consistent with CCC predictions.
3. These circles are not easily explained by standard inflationary cosmology, as the events that could cause some of the largest circles observed would need to occur before the end of inflation in the previous aeon.
On Semi-Invariant Submanifolds of a Nearly Hyperbolic Kenmotsu Manifold with ...IJERA Editor
We consider a nearly hyperbolic Kenmotsu manifold admitting a semi-symmetric metric connection and study semi-invariant submanifolds of a nearly hyperbolic Kenmotsu manifold with semi-symmetric metric connection. We also find the integrability conditions of some distributions on nearly hyperbolic Kenmotsu manifold andstudy parallel distributions on nearly hyperbolic Kenmotsu manifold.
A relationship between mass as a geometric concept and motion associated with a closed curve in spacetime (a notion taken from differential geometry) is investigated. We show that the 4-dimensional exterior Schwarzschild solution of the General Theory of Relativity can be mapped to a 4-dimensional Euclidean spacetime manifold. As a consequence of this mapping, the quantity M in the exterior Schwarzschild solution which is usually attributed to a massive central object is shown to correspond to a geometric property of spacetime. An additional outcome of this analysis is the discovery that, because M is a property of spacetime geometry, an anisotropy with respect to its spacetime components measured in a Minkowski tangent space defined with respect to a spacetime event P by an observer O who is stationary with respect to the spacetime event P, may be a sensitive measure of an anisotropic cosmic accelerated expansion. The presence of anisotropy in the cosmic accelerated expansion may contribute to the reason that there are currently two prevailing measured estimates of this quantity
Some Notes on Self-similar Axisymmetric Force-free Magnetic Fields and Rotati...Premier Publishers
An axisymmetric force-free magnetic field in spherical coordinates has a relationship between its azimuthal component to its poloidal flux-function. A power law dependence for the connection admits separable field solutions but poses a nonlinear eigenvalue boundary-value problem for the separation parameter (Low and Lou, Astrophys. J. 352, 343 (1990)).When the atmosphere of a star is rotating the problem complexity increases. These Notes consider the nonlinear eigenvalue spectrum, providing an understanding of the eigen functions and relationship between the field's degree of multi-polarity, the rotation and rate of radial decay as illustrated through a polytropic equation of state. The Notes are restricted to uniform rotation and to axisymmetric fields. Dominant effects are presented of rotation in changing the spatial patterns of the magnetic field from those without rotation. For differential rotation and non-axisymmetric force-free fields there may be field solutions of even richer topological structure but the governing equations have remained intractable to date. Perhaps the methods and discussion given here for the uniformly rotating situation indicate a possible procedure for such problems that need to be solved urgently for a more complete understanding of force-free magnetic fields in stellar atmospheres.
Application of Gauss,Green and Stokes TheoremSamiul Ehsan
Gauss' law, Stokes' theorem, and Green's theorem are used to relate line integrals, surface integrals, and volume integrals. Gauss' law relates the electric flux through a closed surface to the enclosed charge. Stokes' theorem converts a line integral around a closed curve into a surface integral over the enclosed surface. Green's theorem converts a line integral around a closed curve into a double integral over the enclosed area. These theorems have applications in electrostatics, electrodynamics, calculating mass and momentum, and deriving Kepler's laws of planetary motion.
Lambda, the cosmological constant, is considered the fifth foundational constant in physics along with the speed of light c, Planck's constant h, gravitational constant G, and Boltzmann's constant k. Einstein, de Sitter, Lemaitre, and others originally considered Lambda in their early formulations of cosmology. Lambda represents the energy density of empty space and is related to the curvature of spacetime. Its observed value plays a key role in the current Lambda-CDM model of cosmology, which describes our flat, expanding universe containing dark matter, dark energy, and other components.
A young astronomer’s by now ten years old
results are re-told and put in perspective. The implications are
far-reaching. Angular-momentum shows its clout not only in
quantum mechanics where this is well known, but is also a
major player in the space-time theory of the equivalence
principle and its ramifications. In general relativity, its
fundamental role was largely neglected for the better part of a
century. A children’s device – a friction-free rotating bicycle
wheel suspended from its hub that can be lowered and pulled
up reversibly – serves as an eye-opener. The consequences are
embarrassingly far-reaching in reviving Einstein’s original
dream
The peculiar shapes of Saturn’s small inner moons as evidence of mergers of s...Sérgio Sacani
The Cassini spacecraft revealed the spectacular, highly irregular
shapes of the small inner moons of Saturn1
, ranging from
the unique 'ravioli-like' forms of Pan and Atlas2,3
to the highly
elongated structure of Prometheus. Closest to Saturn, these
bodies provide important clues regarding the formation process
of small moons in close orbits around their host planet4,
but their range of irregular shapes has not been explained yet.
Here, we show that the spectrum of shapes among Saturn’s
small moons is a natural outcome of merging collisions among
similar-sized moonlets possessing physical properties and
orbits that are consistent with those of the current moons.
A significant fraction of such merging collisions take place
either at the first encounter or after 1–2 hit-and-run events,
with impact velocities in the range of 1–5 times the mutual
escape velocity. Close to head-on mergers result in flattened
objects with large equatorial ridges, as observed on Atlas and
Pan. With slightly more oblique impact angles, collisions lead
to elongated, Prometheus-like shapes. These results suggest
that the current forms of the small moons provide direct
evidence of the processes at the final stages of their formation,
involving pairwise encounters of moonlets of comparable
size4–6. Finally, we show that this mechanism may also
explain the formation of Iapetus’ equatorial ridge7
, as well as
its oblate shape8.
The document is a report submitted by three students on surface and volume integrals and linear systems in real world problems. It discusses line, surface, and volume integrals and defines linear systems. It provides examples of applying integrals in electrostatics, magnetism, and gravity. It also discusses applications of linear systems and integrals in areas like fluid dynamics, mass continuity, and conservation of momentum. The conclusion reiterates that linear systems can have zero, one, or infinite solutions depending on consistency and independence, and methods for solving systems like graphing, substitution, and addition/subtraction are introduced.
Quantum Theory of Spin and Anomalous Hall effects in Graphene Mirco Milletari'
1) The document discusses quantum theories of spin and anomalous Hall effects in graphene, focusing on developing a full quantum mechanical approach rather than semiclassical approximations.
2) It presents a model of adatom-decorated graphene to induce intrinsic spin-orbit coupling and explores resonant skew scattering and the crossover between quantum side-jump and skew scattering dominated regimes.
3) The document develops a diagrammatic approach to calculate the spin Hall conductivity beyond the Gaussian approximation, taking into account correlated disorder effects, and finds that coherent processes may dominate the anomalous contribution.
Pratik Tarafdar is investigating the application of analogue gravity techniques to model primordial black hole accretion. He plans to apply these techniques used to model astrophysical black hole accretion to primordial black holes. This will help understand primordial black hole accretion phenomena from the perspective of analogue gravity. He has focused on calculating the analogue surface gravity and has obtained expressions for it in both adiabatic and isothermal cases for different accretion disk models. Future work will extend this to model radiation accretion onto primordial black holes and study effects of fluid dispersion on the analogue Hawking temperature.
Numerical Simulations on Flux Tube Tectonic Model for Solar Coronal HeatingRSIS International
This document discusses numerical simulations of the flux tube tectonic model for solar coronal heating. It begins with an introduction to the sun's corona and mechanisms for coronal heating. It then describes the 3D MHD code used to model the interaction and reconnection of magnetic flux tubes in the photosphere. The simulations show the formation of current sheets where flux tubes of opposite polarity come into contact. An analytical 1D model is also presented that can predict the behavior observed in the simulations, such as the outward migration of current sheets over time as photospheric shearing increases.
The document discusses Michael Faraday's experiments with static electric fields and induced electromotive forces using concentric metallic spheres. It then summarizes Gauss's law and how it can be applied to determine the electric flux density D for various charge distributions like a point charge or line charge. It shows that a cylindrical surface is suitable for applying Gauss's law to a line charge, as the radial component of D is the only non-zero component and it is everywhere normal to the cylindrical surface. Finally, it derives one of Maxwell's equations from Gauss's law by taking the divergence of the electric flux density D.
This document summarizes research on inflation in the context of string theory landscapes. It discusses how string theory can stabilize moduli fields like the dilaton and volume to allow for inflation. The KKLT construction is described as stabilizing the volume through non-perturbative effects and uplifting the minimum with an anti-D3 brane. Inflation models in string theory like brane inflation and modular inflation are mentioned. The document also discusses how the string theory landscape of vacua can address anthropic arguments and the cosmological constant problem through the distribution of probabilities in an eternally inflating multiverse.
End point of_black_ring_instabilities_and_the_weak_cosmic_censorship_conjectureSérgio Sacani
We produce the first concrete evidence that violation of the weak cosmic censorship conjecture can occur
in asymptotically flat spaces of five dimensions by numerically evolving perturbed black rings. For certain
thin rings, we identify a new, elastic-type instability dominating the evolution, causing the system to settle to
a spherical black hole. However, for sufficiently thin rings the Gregory-Laflamme mode is dominant, and the
instability unfolds similarly to that of black strings, where the horizon develops a structure of bulges connected
by necks which become ever thinner over time.
Lens history and physics.
For comments please contact me on solo.hermelin@gmail.com.
For more presentations visit my website at http://www.solohermelin.com.
This presentation is in the Optics folder.
Within the framework of the general theory of relativity (GR) the modeling of the central symmetrical
gravitational field is considered. The mapping of the geodesic motion of the Lemetr and Tolman basis on
their motion in the Minkowski space on the world lines is determined. The expression for the field intensity
and energy where these bases move is obtained. The advantage coordinate system is found, the coordinates
and the time of the system coincide with the Galilean coordinates and the time in the Minkowski space.
membranes2015_Attractive Planar Panelization using Dynamic Relaxation Princip...Florian Gauss
The document proposes an Attractive Planar Relaxation method to approximate a target surface with a planar quad mesh. The method starts with a planar quad mesh in the target surface footprint. Iteratively, vertices are attracted towards the surface, introducing non-planarities. A dynamic relaxation algorithm then planarizes the mesh faces. This attraction-planarization process continues until the mesh is close to the target surface. The method is demonstrated on a shopping center roof, starting with a subdivision of principal curvature lines to guide the initial mesh, which is optimized over 30 iterations to closely match the double curved roof geometry.
A smooth-exit-from-eternal-inflation (hawking-hertog-2018)mirgytoo
This document discusses a holographic approach to modeling eternal inflation. It proposes that eternal inflation can be described by a dual conformal field theory defined on the boundary of the inflating region. The partition function of this CFT provides a "holographic measure" on the geometry of the boundary. For small perturbations, the round sphere geometry is favored, contrary to standard predictions. For large deformations using a toy vector model dual, highly squashed sphere geometries are disfavored. This suggests the exit from eternal inflation may be finite and smooth, rather than producing an infinite fractal multiverse.
This document describes the identification of a new supercluster of galaxies called Laniakea. The researchers used a catalog of peculiar galaxy velocities to map large-scale structure and identify locations where velocity flows diverge, tracing the surface that surrounds the local volume with inward motions after removing the cosmic expansion. They define this volume, which encompasses over 100,000 galaxies including the Virgo cluster, as the Laniakea supercluster. It has a diameter of 160 million parsecs and a mass of around 1017 solar masses. The researchers analyze velocity and density fields within this volume to further characterize its structure and flows.
Quantum-Gravity Thermodynamics, Incorporating the Theory of Exactly Soluble Active Stochastic Processes, with Applications
by Daley, K.
Published in IJTP in 2009. http://adsabs.harvard.edu/abs/2009IJTP..tmp...67D
Extracting linear information from nonlinear large-scale structure observationsMarcel Schmittfull
This document discusses methods for extracting linear cosmological information from observations of nonlinear large-scale structure. It describes four paradigms for doing reconstruction to reduce nonlinear effects: 1) Lagrangian reconstruction, 2) forward modeling and sampling, 3) forward modeling and optimization, and 4) machine learning approaches. Two specific reconstruction algorithms are outlined: 1) an isobaric/nonlinear method using a moving mesh code, and 2) an iterative method applying Zeldovich displacements from large to small scales. Results show the iterative method better correlates reconstructed densities to initial conditions over a wider range of scales compared to standard reconstruction.
This document discusses Bose-Einstein condensation controlled by a combination of trapping potentials, including a harmonic oscillator potential (HOP) along the x-axis and an optical lattice potential (OLP) along the y-axis. It analyzes how parameters in the HOP and OLP, such as the anisotropy parameter and q parameter, affect properties of the trapping potential, initial and final wave functions, and chemical potential. The study uses the Gross-Pitaevskii equation and Crank-Nicolson numerical method to solve for the wave function under different trapping conditions. Results show relationships between the chemical potential and the HOP anisotropy/OLP q parameter, as well as the distribution of
This document numerically analyzes the wave function of atoms under the combined effects of an optical lattice trapping potential and a harmonic oscillator potential, as used in Bose-Einstein condensation experiments. It employs the Crank-Nicolson scheme to solve the Gross-Pitaevskii equation. The results show that the wave function distribution responds to parameters like the trapping frequencies ratio, optical lattice intensity, chemical potential, and energy. Careful adjustment of the time step and grid spacing is needed to satisfy conservation of norms and energy as required by the physical system. Distributions of the overlapping potentials for different q-factors are presented.
1) The document discusses modeling gravitational fields within general relativity by mapping geodesic motion in curved spacetime to motion along worldlines in Minkowski spacetime.
2) It presents equations showing the equivalence between motion in a gravitational field described by a metric and motion in flat spacetime under the influence of a force field.
3) As an example, it models the Schwarzschild metric by considering dust moving radially in Minkowski spacetime, recovering the Schwarzschild solution from Einstein's field equations in vacuum.
Outgoing ingoingkleingordon spvmforminit1 - copy - copyfoxtrot jp R
This document summarizes the solutions to the Klein-Gordon equation of motion for a scalar field in the background of a Schwarzschild spacetime metric near a black hole. Very near the event horizon, the radial equation is approximated as an oscillatory solution in the Regge-Wheeler coordinate. These solutions are then expressed as outgoing and ingoing waves using Eddington-Finkelstein coordinates. While the outgoing waves have regular behavior at the future event horizon, the ingoing waves hit the future event horizon in finite coordinate time as the radial coordinate approaches negative infinity.
The multiverse interpretation of quantum mechanicsSérgio Sacani
This document discusses the relationship between the many-worlds interpretation of quantum mechanics and the multiverse theory of eternal inflation. It argues that:
1) Decoherence in quantum mechanics, which explains the appearance of definite outcomes, is subjective because it depends on the choice of environment.
2) In an eternally inflating multiverse, decoherence cannot occur globally because there is no complete environment.
3) However, within a "causal diamond" region bounded by light cones, the boundary acts as a natural environment, allowing for objective decoherence into many distinct worlds or histories.
4) By considering the causal diamonds as fundamental, the global multiverse picture can be reconstructed as a single
Outgoing ingoingkleingordon 8th_jun19sqrdfoxtrot jp R
This document discusses solutions to the Klein-Gordon equation in Schwarzschild spacetime near a black hole's event horizon. The radial equation is approximated in the Regge-Wheeler coordinate, leading to oscillatory solutions. These solutions are then expressed as outgoing and ingoing waves, which have different properties in the future and past horizons. Near the horizon, the radial equation simplifies to an oscillatory form, allowing solutions describing outgoing and ingoing waves.
This document provides an introduction to photonic crystals, including:
- Photonic crystals are periodic electromagnetic structures that can possess photonic band gaps where light cannot propagate, analogous to electronic band gaps in solids.
- The propagation of electromagnetic waves in periodic media is governed by Bloch's theorem and results in photonic band structures and gaps similar to electronic band structures.
- Introducing defects in photonic crystals allows for localized electromagnetic states like waveguides and cavities, allowing the crystal to confine and control light.
Quantization of the Orbital Motion of a Mass In The Presence Of Einstein’s Gr...IOSR Journals
This document presents a theoretical model to explain the quantized nature of planetary orbits around the sun based on Einstein's general theory of relativity. It derives expressions for the Lagrangian and Hamiltonian of a unit mass moving in the curved spacetime around a massive body. Using these, it writes a Schrodinger-like quantum equation that includes variation of the wavefunction with respect to a curve parameter representing spacetime curvature. The solutions reveal the quantized energy levels and orbits determined by quantum numbers. When applied to planetary orbits, the model estimates distances from the sun in good agreement with observed values.
This document discusses outgoing and ingoing Klein-Gordon waves near the event horizons of black holes. It first presents the Klein-Gordon equation of motion in the background of the Schwarzschild spacetime metric. Near the event horizon, the radial equation is approximated in the Regge-Wheeler coordinate, leading to oscillatory solutions. The time and radial solutions are then expressed in outgoing and ingoing coordinates, resulting in outgoing and ingoing waves with different analytic properties in the future and past event horizons.
Outgoing ingoingkleingordon spvmforminit_proceedfrom12dec18foxtrot jp R
This document discusses outgoing and ingoing Klein-Gordon waves near the event horizons of a black hole. It begins by introducing the Klein-Gordon equation of motion in the background of the Schwarzschild spacetime metric. It then presents the solution to this equation in product form and discusses the radial and time component equations. Finally, it recasts the radial equation using the Regge-Wheeler coordinate and shows that very near the horizon, the equation can be approximated as a simple oscillatory solution. The goal is to obtain outgoing and ingoing wave solutions that have different properties on either side of the black hole's event horizons.
Outgoing ingoingkleingordon spvmforminit_proceedfromfoxtrot jp R
This document discusses outgoing and ingoing Klein-Gordon waves near the event horizons of a black hole. It begins by introducing the Klein-Gordon equation of motion in the background of the Schwarzschild spacetime metric. It then presents the solution to this equation in product form and discusses the radial and time component equations. Finally, it recasts the radial equation using the Regge-Wheeler coordinate and shows that very near the horizon, the equation can be approximated as a simple oscillatory solution. The goal is to obtain outgoing and ingoing wave solutions that have different properties on either side of the black hole's event horizons.
The enhancement of sub-barrier fusion has been interpreted due to coupling between the relative motion and other degrees of freedom. The coupling gives rise to the distribution of fusion barriers and passage over the lowest barrier which is responsible for fusion enhancement at energies below the barrier. There are several orders of magnitude could be considered due to the tunneling through the barrier. The barrier height could be deduced from the measured cross section data for different energies, as well as using many empirical forms for incomplete and complete fusion of two massive nuclei. Firstly, we present a formula for barrier height (ODEFF) and check, over wide ranges of interacting pairs the percentage agreement with those calculated or measured values for all pairs within ZP ZT ≤ 3000. Secondly, the more recently measured excitation functions are studied using four models of nuclear forces, indicating that most of them can be used for wide energy range while the others failed to do so .We refer this notice to the theory deducing the model . For this, the 14 undertaken pairs recover the range18 ≤ ZP ZT ≤ 1320
The caustic that occur in geodesics in space-times which are solutions to the gravitational field equations with the energy-momentum tensor satisfying the dominant energy condition can be circumvented if quantum variations are allowed. An action is developed such that the variation yields the field equations
and the geodesic condition, and its quantization provides a method for determining the extent of the wave packet around the classical path.
The caustic that occur in geodesics in space-times which are solutions to the gravitational field equations
with the energy-momentum tensor satisfying the dominant energy condition can be circumvented if
quantum variations are allowed. An action is developed such that the variation yields the field equations
and the geodesic condition, and its quantization provides a method for determining the extent of the wave
packet around the classical path.
The caustic that occur in geodesics in space-times which are solutions to the gravitational field equations with the energy-momentum tensor satisfying the dominant energy condition can be circumvented if quantum variations are allowed. An action is developed such that the variation yields the field equations
and the geodesic condition, and its quantization provides a method for determining the extent of the wave packet around the classical path.
The caustic that occur in geodesics in space-times which are solutions to the gravitational field equations
with the energy-momentum tensor satisfying the dominant energy condition can be circumvented if
quantum variations are allowed. An action is developed such that the variation yields the field equations
and the geodesic condition, and its quantization provides a method for determining the extent of the wave
packet around the classical path.
Similar to A smooth exit from eternal inflation? (20)
The binding of cosmological structures by massless topological defectsSérgio Sacani
Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field
equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational
field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin
spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling
concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect
light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is
mitigated, at least in part.
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...Sérgio Sacani
Context. With a mass exceeding several 104 M⊙ and a rich and dense population of massive stars, supermassive young star clusters
represent the most massive star-forming environment that is dominated by the feedback from massive stars and gravitational interactions
among stars.
Aims. In this paper we present the Extended Westerlund 1 and 2 Open Clusters Survey (EWOCS) project, which aims to investigate
the influence of the starburst environment on the formation of stars and planets, and on the evolution of both low and high mass stars.
The primary targets of this project are Westerlund 1 and 2, the closest supermassive star clusters to the Sun.
Methods. The project is based primarily on recent observations conducted with the Chandra and JWST observatories. Specifically,
the Chandra survey of Westerlund 1 consists of 36 new ACIS-I observations, nearly co-pointed, for a total exposure time of 1 Msec.
Additionally, we included 8 archival Chandra/ACIS-S observations. This paper presents the resulting catalog of X-ray sources within
and around Westerlund 1. Sources were detected by combining various existing methods, and photon extraction and source validation
were carried out using the ACIS-Extract software.
Results. The EWOCS X-ray catalog comprises 5963 validated sources out of the 9420 initially provided to ACIS-Extract, reaching a
photon flux threshold of approximately 2 × 10−8 photons cm−2
s
−1
. The X-ray sources exhibit a highly concentrated spatial distribution,
with 1075 sources located within the central 1 arcmin. We have successfully detected X-ray emissions from 126 out of the 166 known
massive stars of the cluster, and we have collected over 71 000 photons from the magnetar CXO J164710.20-455217.
The debris of the ‘last major merger’ is dynamically youngSérgio Sacani
The Milky Way’s (MW) inner stellar halo contains an [Fe/H]-rich component with highly eccentric orbits, often referred to as the
‘last major merger.’ Hypotheses for the origin of this component include Gaia-Sausage/Enceladus (GSE), where the progenitor
collided with the MW proto-disc 8–11 Gyr ago, and the Virgo Radial Merger (VRM), where the progenitor collided with the
MW disc within the last 3 Gyr. These two scenarios make different predictions about observable structure in local phase space,
because the morphology of debris depends on how long it has had to phase mix. The recently identified phase-space folds in Gaia
DR3 have positive caustic velocities, making them fundamentally different than the phase-mixed chevrons found in simulations
at late times. Roughly 20 per cent of the stars in the prograde local stellar halo are associated with the observed caustics. Based
on a simple phase-mixing model, the observed number of caustics are consistent with a merger that occurred 1–2 Gyr ago.
We also compare the observed phase-space distribution to FIRE-2 Latte simulations of GSE-like mergers, using a quantitative
measurement of phase mixing (2D causticality). The observed local phase-space distribution best matches the simulated data
1–2 Gyr after collision, and certainly not later than 3 Gyr. This is further evidence that the progenitor of the ‘last major merger’
did not collide with the MW proto-disc at early times, as is thought for the GSE, but instead collided with the MW disc within
the last few Gyr, consistent with the body of work surrounding the VRM.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
THE IMPORTANCE OF MARTIAN ATMOSPHERE SAMPLE RETURN.Sérgio Sacani
The return of a sample of near-surface atmosphere from Mars would facilitate answers to several first-order science questions surrounding the formation and evolution of the planet. One of the important aspects of terrestrial planet formation in general is the role that primary atmospheres played in influencing the chemistry and structure of the planets and their antecedents. Studies of the martian atmosphere can be used to investigate the role of a primary atmosphere in its history. Atmosphere samples would also inform our understanding of the near-surface chemistry of the planet, and ultimately the prospects for life. High-precision isotopic analyses of constituent gases are needed to address these questions, requiring that the analyses are made on returned samples rather than in situ.
Multi-source connectivity as the driver of solar wind variability in the heli...Sérgio Sacani
The ambient solar wind that flls the heliosphere originates from multiple
sources in the solar corona and is highly structured. It is often described
as high-speed, relatively homogeneous, plasma streams from coronal
holes and slow-speed, highly variable, streams whose source regions are
under debate. A key goal of ESA/NASA’s Solar Orbiter mission is to identify
solar wind sources and understand what drives the complexity seen in the
heliosphere. By combining magnetic feld modelling and spectroscopic
techniques with high-resolution observations and measurements, we show
that the solar wind variability detected in situ by Solar Orbiter in March
2022 is driven by spatio-temporal changes in the magnetic connectivity to
multiple sources in the solar atmosphere. The magnetic feld footpoints
connected to the spacecraft moved from the boundaries of a coronal hole
to one active region (12961) and then across to another region (12957). This
is refected in the in situ measurements, which show the transition from fast
to highly Alfvénic then to slow solar wind that is disrupted by the arrival of
a coronal mass ejection. Our results describe solar wind variability at 0.5 au
but are applicable to near-Earth observatories.
Gliese 12 b: A Temperate Earth-sized Planet at 12 pc Ideal for Atmospheric Tr...Sérgio Sacani
Recent discoveries of Earth-sized planets transiting nearby M dwarfs have made it possible to characterize the
atmospheres of terrestrial planets via follow-up spectroscopic observations. However, the number of such planets
receiving low insolation is still small, limiting our ability to understand the diversity of the atmospheric
composition and climates of temperate terrestrial planets. We report the discovery of an Earth-sized planet
transiting the nearby (12 pc) inactive M3.0 dwarf Gliese 12 (TOI-6251) with an orbital period (Porb) of 12.76 days.
The planet, Gliese 12 b, was initially identified as a candidate with an ambiguous Porb from TESS data. We
confirmed the transit signal and Porb using ground-based photometry with MuSCAT2 and MuSCAT3, and
validated the planetary nature of the signal using high-resolution images from Gemini/NIRI and Keck/NIRC2 as
well as radial velocity (RV) measurements from the InfraRed Doppler instrument on the Subaru 8.2 m telescope
and from CARMENES on the CAHA 3.5 m telescope. X-ray observations with XMM-Newton showed the host
star is inactive, with an X-ray-to-bolometric luminosity ratio of log 5.7 L L X bol » - . Joint analysis of the light
curves and RV measurements revealed that Gliese 12 b has a radius of 0.96 ± 0.05 R⊕,a3σ mass upper limit of
3.9 M⊕, and an equilibrium temperature of 315 ± 6 K assuming zero albedo. The transmission spectroscopy metric
(TSM) value of Gliese 12 b is close to the TSM values of the TRAPPIST-1 planets, adding Gliese 12 b to the small
list of potentially terrestrial, temperate planets amenable to atmospheric characterization with JWST.
Gliese 12 b, a temperate Earth-sized planet at 12 parsecs discovered with TES...Sérgio Sacani
We report on the discovery of Gliese 12 b, the nearest transiting temperate, Earth-sized planet found to date. Gliese 12 is a
bright (V = 12.6 mag, K = 7.8 mag) metal-poor M4V star only 12.162 ± 0.005 pc away from the Solar system with one of the
lowest stellar activity levels known for M-dwarfs. A planet candidate was detected by TESS based on only 3 transits in sectors
42, 43, and 57, with an ambiguity in the orbital period due to observational gaps. We performed follow-up transit observations
with CHEOPS and ground-based photometry with MINERVA-Australis, SPECULOOS, and Purple Mountain Observatory,
as well as further TESS observations in sector 70. We statistically validate Gliese 12 b as a planet with an orbital period of
12.76144 ± 0.00006 d and a radius of 1.0 ± 0.1 R⊕, resulting in an equilibrium temperature of ∼315 K. Gliese 12 b has excellent
future prospects for precise mass measurement, which may inform how planetary internal structure is affected by the stellar
compositional environment. Gliese 12 b also represents one of the best targets to study whether Earth-like planets orbiting cool
stars can retain their atmospheres, a crucial step to advance our understanding of habitability on Earth and across the galaxy.
The importance of continents, oceans and plate tectonics for the evolution of...Sérgio Sacani
Within the uncertainties of involved astronomical and biological parameters, the Drake Equation
typically predicts that there should be many exoplanets in our galaxy hosting active, communicative
civilizations (ACCs). These optimistic calculations are however not supported by evidence, which is
often referred to as the Fermi Paradox. Here, we elaborate on this long-standing enigma by showing
the importance of planetary tectonic style for biological evolution. We summarize growing evidence
that a prolonged transition from Mesoproterozoic active single lid tectonics (1.6 to 1.0 Ga) to modern
plate tectonics occurred in the Neoproterozoic Era (1.0 to 0.541 Ga), which dramatically accelerated
emergence and evolution of complex species. We further suggest that both continents and oceans
are required for ACCs because early evolution of simple life must happen in water but late evolution
of advanced life capable of creating technology must happen on land. We resolve the Fermi Paradox
(1) by adding two additional terms to the Drake Equation: foc
(the fraction of habitable exoplanets
with significant continents and oceans) and fpt
(the fraction of habitable exoplanets with significant
continents and oceans that have had plate tectonics operating for at least 0.5 Ga); and (2) by
demonstrating that the product of foc
and fpt
is very small (< 0.00003–0.002). We propose that the lack
of evidence for ACCs reflects the scarcity of long-lived plate tectonics and/or continents and oceans on
exoplanets with primitive life.
A Giant Impact Origin for the First Subduction on EarthSérgio Sacani
Hadean zircons provide a potential record of Earth's earliest subduction 4.3 billion years ago. Itremains enigmatic how subduction could be initiated so soon after the presumably Moon‐forming giant impact(MGI). Earlier studies found an increase in Earth's core‐mantle boundary (CMB) temperature due to theaccumulation of the impactor's core, and our recent work shows Earth's lower mantle remains largely solid, withsome of the impactor's mantle potentially surviving as the large low‐shear velocity provinces (LLSVPs). Here,we show that a hot post‐impact CMB drives the initiation of strong mantle plumes that can induce subductioninitiation ∼200 Myr after the MGI. 2D and 3D thermomechanical computations show that a high CMBtemperature is the primary factor triggering early subduction, with enrichment of heat‐producing elements inLLSVPs as another potential factor. The models link the earliest subduction to the MGI with implications forunderstanding the diverse tectonic regimes of rocky planets.
Climate extremes likely to drive land mammal extinction during next supercont...Sérgio Sacani
Mammals have dominated Earth for approximately 55 Myr thanks to their
adaptations and resilience to warming and cooling during the Cenozoic. All
life will eventually perish in a runaway greenhouse once absorbed solar
radiation exceeds the emission of thermal radiation in several billions of
years. However, conditions rendering the Earth naturally inhospitable to
mammals may develop sooner because of long-term processes linked to
plate tectonics (short-term perturbations are not considered here). In
~250 Myr, all continents will converge to form Earth’s next supercontinent,
Pangea Ultima. A natural consequence of the creation and decay of Pangea
Ultima will be extremes in pCO2 due to changes in volcanic rifting and
outgassing. Here we show that increased pCO2, solar energy (F⨀;
approximately +2.5% W m−2 greater than today) and continentality (larger
range in temperatures away from the ocean) lead to increasing warming
hostile to mammalian life. We assess their impact on mammalian
physiological limits (dry bulb, wet bulb and Humidex heat stress indicators)
as well as a planetary habitability index. Given mammals’ continued survival,
predicted background pCO2 levels of 410–816 ppm combined with increased
F⨀ will probably lead to a climate tipping point and their mass extinction.
The results also highlight how global landmass configuration, pCO2 and F⨀
play a critical role in planetary habitability.
Constraints on Neutrino Natal Kicks from Black-Hole Binary VFTS 243Sérgio Sacani
The recently reported observation of VFTS 243 is the first example of a massive black-hole binary
system with negligible binary interaction following black-hole formation. The black-hole mass (≈10M⊙)
and near-circular orbit (e ≈ 0.02) of VFTS 243 suggest that the progenitor star experienced complete
collapse, with energy-momentum being lost predominantly through neutrinos. VFTS 243 enables us to
constrain the natal kick and neutrino-emission asymmetry during black-hole formation. At 68% confidence
level, the natal kick velocity (mass decrement) is ≲10 km=s (≲1.0M⊙), with a full probability distribution
that peaks when ≈0.3M⊙ were ejected, presumably in neutrinos, and the black hole experienced a natal
kick of 4 km=s. The neutrino-emission asymmetry is ≲4%, with best fit values of ∼0–0.2%. Such a small
neutrino natal kick accompanying black-hole formation is in agreement with theoretical predictions.
Detectability of Solar Panels as a TechnosignatureSérgio Sacani
In this work, we assess the potential detectability of solar panels made of silicon on an Earth-like
exoplanet as a potential technosignature. Silicon-based photovoltaic cells have high reflectance in the
UV-VIS and in the near-IR, within the wavelength range of a space-based flagship mission concept
like the Habitable Worlds Observatory (HWO). Assuming that only solar energy is used to provide
the 2022 human energy needs with a land cover of ∼ 2.4%, and projecting the future energy demand
assuming various growth-rate scenarios, we assess the detectability with an 8 m HWO-like telescope.
Assuming the most favorable viewing orientation, and focusing on the strong absorption edge in the
ultraviolet-to-visible (0.34 − 0.52 µm), we find that several 100s of hours of observation time is needed
to reach a SNR of 5 for an Earth-like planet around a Sun-like star at 10pc, even with a solar panel
coverage of ∼ 23% land coverage of a future Earth. We discuss the necessity of concepts like Kardeshev
Type I/II civilizations and Dyson spheres, which would aim to harness vast amounts of energy. Even
with much larger populations than today, the total energy use of human civilization would be orders of
magnitude below the threshold for causing direct thermal heating or reaching the scale of a Kardashev
Type I civilization. Any extraterrrestrial civilization that likewise achieves sustainable population
levels may also find a limit on its need to expand, which suggests that a galaxy-spanning civilization
as imagined in the Fermi paradox may not exist.
Jet reorientation in central galaxies of clusters and groups: insights from V...Sérgio Sacani
Recent observations of galaxy clusters and groups with misalignments between their central AGN jets
and X-ray cavities, or with multiple misaligned cavities, have raised concerns about the jet – bubble
connection in cooling cores, and the processes responsible for jet realignment. To investigate the
frequency and causes of such misalignments, we construct a sample of 16 cool core galaxy clusters and
groups. Using VLBA radio data we measure the parsec-scale position angle of the jets, and compare
it with the position angle of the X-ray cavities detected in Chandra data. Using the overall sample
and selected subsets, we consistently find that there is a 30% – 38% chance to find a misalignment
larger than ∆Ψ = 45◦ when observing a cluster/group with a detected jet and at least one cavity. We
determine that projection may account for an apparently large ∆Ψ only in a fraction of objects (∼35%),
and given that gas dynamical disturbances (as sloshing) are found in both aligned and misaligned
systems, we exclude environmental perturbation as the main driver of cavity – jet misalignment.
Moreover, we find that large misalignments (up to ∼ 90◦
) are favored over smaller ones (45◦ ≤ ∆Ψ ≤
70◦
), and that the change in jet direction can occur on timescales between one and a few tens of Myr.
We conclude that misalignments are more likely related to actual reorientation of the jet axis, and we
discuss several engine-based mechanisms that may cause these dramatic changes.
The solar dynamo begins near the surfaceSérgio Sacani
The magnetic dynamo cycle of the Sun features a distinct pattern: a propagating
region of sunspot emergence appears around 30° latitude and vanishes near the
equator every 11 years (ref. 1). Moreover, longitudinal flows called torsional oscillations
closely shadow sunspot migration, undoubtedly sharing a common cause2. Contrary
to theories suggesting deep origins of these phenomena, helioseismology pinpoints
low-latitude torsional oscillations to the outer 5–10% of the Sun, the near-surface
shear layer3,4. Within this zone, inwardly increasing differential rotation coupled with
a poloidal magnetic field strongly implicates the magneto-rotational instability5,6,
prominent in accretion-disk theory and observed in laboratory experiments7.
Together, these two facts prompt the general question: whether the solar dynamo is
possibly a near-surface instability. Here we report strong affirmative evidence in stark
contrast to traditional models8 focusing on the deeper tachocline. Simple analytic
estimates show that the near-surface magneto-rotational instability better explains
the spatiotemporal scales of the torsional oscillations and inferred subsurface
magnetic field amplitudes9. State-of-the-art numerical simulations corroborate these
estimates and reproduce hemispherical magnetic current helicity laws10. The dynamo
resulting from a well-understood near-surface phenomenon improves prospects
for accurate predictions of full magnetic cycles and space weather, affecting the
electromagnetic infrastructure of Earth.
Extensive Pollution of Uranus and Neptune’s Atmospheres by Upsweep of Icy Mat...Sérgio Sacani
In the Nice model of solar system formation, Uranus and Neptune undergo an orbital upheaval,
sweeping through a planetesimal disk. The region of the disk from which material is accreted by
the ice giants during this phase of their evolution has not previously been identified. We perform
direct N-body orbital simulations of the four giant planets to determine the amount and origin of solid
accretion during this orbital upheaval. We find that the ice giants undergo an extreme bombardment
event, with collision rates as much as ∼3 per hour assuming km-sized planetesimals, increasing the
total planet mass by up to ∼0.35%. In all cases, the initially outermost ice giant experiences the
largest total enhancement. We determine that for some plausible planetesimal properties, the resulting
atmospheric enrichment could potentially produce sufficient latent heat to alter the planetary cooling
timescale according to existing models. Our findings suggest that substantial accretion during this
phase of planetary evolution may have been sufficient to impact the atmospheric composition and
thermal evolution of the ice giants, motivating future work on the fate of deposited solid material.
Exomoons & Exorings with the Habitable Worlds Observatory I: On the Detection...Sérgio Sacani
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was the construction of an observatory capable of characterizing habitable worlds. In this paper series
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the detectability of Moon analogs with HWO. We determine that Earth-Moon analogs are detectable
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water band where large moons can outshine their host planet, will aid in differentiating exomoon signals
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to our Moon are more likely to be detected in younger systems, where shorter orbital periods and
favorable geometry enhance the probability and frequency of mutual events.
Emergent ribozyme behaviors in oxychlorine brines indicate a unique niche for...Sérgio Sacani
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Continuum emission from within the plunging region of black hole discsSérgio Sacani
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sourced from within the plunging region, utilizing new analytical models that reproduce the properties of numerical accretion
simulations. We show that in general the neglected intra-ISCO emission produces a hot-and-small quasi-blackbody component,
but can also produce a weak power-law tail for more extreme parameter regions. A similar hot-and-small blackbody component
has been added in by hand in an ad hoc manner to previous analyses of X-ray binary spectra. We show that the X-ray spectrum
of MAXI J1820+070 in a soft-state outburst is extremely well described by a full Kerr black hole disc, while conventional
models that neglect intra-ISCO emission are unable to reproduce the data. We believe this represents the first robust detection of
intra-ISCO emission in the literature, and allows additional constraints to be placed on the MAXI J1820 + 070 black hole spin
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continuum fitting model is made publicly available.
ANAMOLOUS SECONDARY GROWTH IN DICOT ROOTS.pptxRASHMI M G
Abnormal or anomalous secondary growth in plants. It defines secondary growth as an increase in plant girth due to vascular cambium or cork cambium. Anomalous secondary growth does not follow the normal pattern of a single vascular cambium producing xylem internally and phloem externally.
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Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
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A smooth exit from eternal inflation?
1. JHEP04(2018)147
Published for SISSA by Springer
Received: April 20, 2018
Accepted: April 20, 2018
Published: April 27, 2018
A smooth exit from eternal inflation?
S.W. Hawkinga and Thomas Hertogb
a
DAMTP, CMS,
Wilberforce Road, CB3 0WA Cambridge, U.K.
b
Institute for Theoretical Physics, University of Leuven,
Celestijnenlaan 200D, 3001 Leuven, Belgium
E-mail: S.W.Hawking@damtp.cam.ac.uk, Thomas.Hertog@kuleuven.be
Abstract: The usual theory of inflation breaks down in eternal inflation. We derive a
dual description of eternal inflation in terms of a deformed Euclidean CFT located at the
threshold of eternal inflation. The partition function gives the amplitude of different ge-
ometries of the threshold surface in the no-boundary state. Its local and global behavior
in dual toy models shows that the amplitude is low for surfaces which are not nearly con-
formal to the round three-sphere and essentially zero for surfaces with negative curvature.
Based on this we conjecture that the exit from eternal inflation does not produce an infinite
fractal-like multiverse, but is finite and reasonably smooth.
Keywords: AdS-CFT Correspondence, Gauge-gravity correspondence, Models of Quan-
tum Gravity, Spacetime Singularities
ArXiv ePrint: 1707.07702
Open Access, c The Authors.
Article funded by SCOAP3
.
https://doi.org/10.1007/JHEP04(2018)147
2. JHEP04(2018)147
Contents
1 Introduction 1
2 A holographic measure on eternal inflation 3
2.1 Setup 3
2.2 Local measure: perturbations around S3 5
2.3 Global measure: squashed three-spheres 5
2.4 Global measure: general metric deformations 8
3 Discussion 10
1 Introduction
Eternal inflation [1] refers to the near de Sitter (dS) regime deep into the phase of inflation in
which the quantum fluctuations in the energy density of the inflaton are large. In the usual
account of eternal inflation the quantum diffusion dynamics of the fluctuations is modeled as
stochastic effects around a classical slow roll background. Since the stochastic effects domi-
nate the classical slow roll it is argued eternal inflation produces universes that are typically
globally highly irregular, with exceedingly large or infinite constant density surfaces [2–5].
However this account is questionable, because the dynamics of eternal inflation wipes
out the separation into classical backgrounds and quantum fluctuations that is assumed.
A proper treatment of eternal inflation must be based on quantum cosmology. In this
paper we put forward a new quantum cosmological model of scalar field driven eternal
inflation by using gauge-gravity duality [6–8]. We define the Euclidean dual theory on
the threshold surface of eternal inflation, which therefore describes the transition from the
quantum realm of eternal inflation towards a classical universe, in line with the original
vision behind inflation [9]. The subsequent evolution is assumed to be classical.
A reliable theory of eternal inflation is important to sharpen the predictions of slow
roll inflation. This is because the physics of eternal inflation specifies initial conditions for
classical cosmology. In particular a quantum model of eternal inflation specifies a prior
over the so-called zero modes, or classical slow roll backgrounds, in the theory. This in
turn determines its predictions for the precise spectral properties of CMB fluctuations on
observable scales.
Our starting point remains the no-boundary quantum state of the universe [10]. This
gives the ground state and is heavily biased towards universes with a low amount of in-
flation [11]. However we do not observe the entire universe. Instead our observations are
limited to a small patch mostly along part of our past light cone. Probabilities for local ob-
servations in the no-boundary state are weighted by the volume of a surface Σf of constant
measured density, to account for the different possible locations of our past light cone [12].
– 1 –
3. JHEP04(2018)147
Figure 1. Two representations in the complex time-plane of the same no-boundary saddle point
associated with an inflationary universe. The saddle point action includes an integral over time τ
from the no-boundary origin or South Pole (SP) to its endpoint υ on Σf . Different contours for
this give different geometric representations of the saddle point, each giving the same amplitude
for the final real configuration (hij(x), φ(x)) on Σf . The interior saddle point geometry along the
nearly vertical contour going upwards from the SP consists of a regular, Euclidean, locally AdS
domain wall with a complex scalar profile. Its regularized action specifies the tree-level probability
in the no-boundary state of the associated inflationary, asymptotically de Sitter history. Euclidean
AdS/CFT relates this to the partition function of a dual field theory yielding (1.1).
This transforms the probability distribution for the amount of inflation and leads to the
prediction that our universe emerged from a regime of eternal inflation [12, 13]. Thus we
must understand eternal inflation in order to understand the observational implications of
the no-boundary wave function.
However the standard saddle point approximation of the no-boundary wave func-
tion breaks down in eternal inflation. We therefore turn to gauge-gravity duality or
dS/CFT [6–8], which gives an alternative form of the wave function evaluated on a sur-
face Σf in the large three-volume limit. In this, the wave function is specified in terms of
the partition function of certain deformations of a Euclidean CFT defined directly on Σf .
Euclidean AdS/CFT generalized to complex relevant deformations implies an approximate
realisation of dS/CFT [14–19]. This follows from the observation [18] that all no-boundary
saddle points in low energy gravity theories with a positive scalar potential V admit a
geometric representation in which their weighting is fully specified by an interior, locally
AdS, domain wall region governed by an effective negative scalar potential −V . We illus-
trate this in figure 1. Quantum cosmology thus lends support to the view that Euclidean
AdS/CFT and dS/CFT are two real domains of a single complexified theory [6, 14, 20–23].
In the large three-volume limit this has led to the following proposal for a holographic form
of the semiclassical no-boundary wave function [18] in Einstein gravity,
ΨNB[hij, φ] = Z−1
QFT [˜hij, ˜α] exp(iSst[hij, φ]/ ) . (1.1)
Here the sources (˜hij, ˜α) are conformally related to the argument (hij, φ) of the wave
function, Sst are the usual surface terms, and ZQFT in this form of dS/CFT are partition
functions of (complex) deformations of Euclidean AdS/CFT duals. The boundary metric
˜hij stands for background and fluctuations.
– 2 –
4. JHEP04(2018)147
The holographic form (1.1) has led to a fruitful and promising application of holo-
graphic techniques to early universe cosmology (see e.g. [15, 24–28]). No field theories have
been identified that correspond to top-down models of realistic cosmologies where inflation
transitions to a decelerating phase. However we find that many of the known AdS/CFT
duals are ideally suited to study eternal inflation from a holographic viewpoint. This is
because supergravity theories in AdS4 typically contain scalars of mass m2 = −2l2
AdS with
a negative potential for large φ. In the context of (1.1) such scalars give rise to (slow roll)
eternal inflation in the dS domain of the theory that is governed effectively by −V . In
fact the Breitenlohner-Freedman bound in AdS corresponds precisely to the condition for
eternal inflation in dS.
Here we use (1.1) to study eternal inflation holographically in toy-model cosmologies
of this kind in which a single bulk scalar drives slow roll eternal inflation. We take the
dual to be defined on a global constant density surface Σf at the threshold (or exit) of the
regime of scalar field driven eternal inflation. The bulk scalar driving inflation corresponds
to a source ˜α that turns on a low dimension scalar operator in the dual. Hence we use
holography to excise the bulk regime of eternal inflation and replace this by field theory
degrees of freedom on a kind of ‘end-of-the-world’ brane. This is somewhat analogous to
the holographic description of vacuum decay in AdS [29], although the interpretation here
is different.
Conventional wisdom based on semiclassical gravity asserts that surfaces of constant
scalar field in eternal inflation typically become highly irregular on the largest scales, de-
veloping a configuration of bubble-like regions with locally negative curvature. Holography
provides a new perspective on this: the dependence of the partition function on the confor-
mal geometry hij of Σf in the presence of a constant source ˜α = 0 specifies a holographic
measure on the global structure of constant density surfaces in eternal inflation. We analyse
various properties of this measure and find that the amplitude of surfaces with conformal
structures far from the round one is exponentially small, in contrast with expectations
based on semiclassical gravity. We also argue on general grounds that the amplitude is
zero for all highly deformed conformal boundaries with a negative Yamabe invariant. This
raises doubt about the widespread idea that eternal inflation produces a highly irregular
universe with a mosaic structure of bubble like patches separated by inflationary domains.
2 A holographic measure on eternal inflation
2.1 Setup
For definiteness we start with the well known consistent truncation of M-theory on AdS4 ×
S7 down to Einstein gravity coupled to a single scalar φ with potential
V (φ) = −2 − cosh(
√
2φ) , (2.1)
in units where Λ = −3 and hence l2
AdS = 1. The scalar has mass m2 = −2. Therefore in
the large three-volume regime it behaves as
φ(x, r) = α(x)e−r
+ β(x)e−2r
+ · · · (2.2)
– 3 –
5. JHEP04(2018)147
where r is the overall radial coordinate in Euclidean AdS, with scale factor er. The
Fefferman-Graham expansion implies that in terms of the variable r the asymptotically
(Lorentzian) dS domain of the theory is to be found along the vertical line τ = r + iπ/2
in the complex τ-plane [18]. This is illustrated in figure 1 where r changes from real to
imaginary values along the horizontal branch of the AdS contour from xA to xTP . This
also means that in the dS domain the original potential (2.1) acts as a positive effective
potential
˜V (φ) = −V = 2 + cosh(
√
2φ) . (2.3)
This is a potential for which the conditions for inflation and eternal inflation ≤ ˜V hold,
where ≡ ˜V 2
,φ/ ˜V 2, for a reasonably broad range of field values around its minimum. This
close connection between AdS supergravity truncations and eternal inflation in the frame-
work of the no-boundary wave function (1.1) stems from the fact that the Breitenlohner-
Freedman stability bound on the mass of scalars in AdS corresponds precisely to the con-
dition for eternal inflation in the de Sitter domain of the theory.
Bulk solutions with φ 1 initially are at all times dominated by the cosmological
constant Λ and eternally inflate in a trivial manner. By contrast, solutions with φ ≥ 1 ini-
tially have a regime of scalar field driven eternal inflation, which eventually transitions into
a Λ-dominated phase. The wave function (1.1) contains both classes of histories. We are
mostly interested in the latter class and in particular in the amplitude of different (confor-
mal) shapes of the constant scalar field transition surface1 Σf between these two regimes.
The variance of the semiclassical wave function of inhomogeneous fluctuation modes in
the bulk is of order ∼ ˜V / , evaluated at horizon crossing. In eternal inflation ≤ ˜V . Hence
the fluctuation wave function spreads out and becomes broadly distributed [5]. This is a
manifestation of the fact that the universe’s evolution, according to semiclassical gravity,
is governed by the quantum diffusion dynamics of the fluctuations and their backreaction
on the geometry rather than the classical slow roll [2–5]. It is usually argued that the
typical individual histories described by this wave function develop highly irregular constant
density surfaces with a configuration of bubble-like regions with locally negative curvature.
Below we revisit this from a holographic viewpoint.
We conclude this discussion of our setup with a few technical remarks. The argument
(hij, φ) of the wave function evaluated at υ in figure 1 is real. This means that in saddle
points associated with inflationary universes, the scalar field must become real along the
vertical dS line in the τ-plane. The expansion (2.2) shows this requires its leading coeffi-
cient α to be imaginary, which in turn means that the scalar profile is complex along the
entire interior AdS domain wall part of the saddle points. But the bulk scalar sources a
deformation by an operator O of dimension one with coupling α in the dual ABJM theory.
Hence the holographic measure in this model involves the AdS dual partition function on
deformed three-spheres in the presence of an imaginary mass deformation α ≡ i˜α. We
are primarily interested in the probability distribution over ˜hij for sufficiently large defor-
1
A realistic cosmology of course involves an intermediate radiation and matter dominated phase before
the cosmological constant takes over. However since we are concerned with the structure of the universe at
the exit from scalar field eternal inflation this toy-model setup suffices.
– 4 –
6. JHEP04(2018)147
mations α, since these correspond to histories with a scalar field driven regime of eternal
inflation. Finally whilst we formally define our dual on the exit surface Σf from scalar
field eternal inflation, at υ in figure 1, we might as well take υ → ∞ because the classical,
asymptotic Λ-phase amounts to an overall volume rescaling of the boundary surface which
preserves the relative probabilities of different conformal bopundary geometries [18].
2.2 Local measure: perturbations around S3
We first recall the general behavior of partition functions for small perturbations away
from the round S3. Locally around the round sphere, the F-theorem and its extension to
spin-2 deformations provide a general argument that the round sphere is a local minimum
of the partition function. The F-theorem for three-dimensional CFTs [30, 31] states that
the free energy of a CFT on S3 decreases along an RG flow triggered by a relevant de-
formation. A similar result was recently proved for metric perturbations of the conformal
S3 background [32, 33]. The coupling of the energy-momentum tensor of the CFT to the
curved background metric triggers a spin-2 deformation. The fact that the free energy
is a local maximum for the round sphere is essentially equivalent to the positive definite-
ness of the stress tensor two-point function. Applied to the holographic no-boundary wave
function (1.1) these results imply that the pure de Sitter history in the bulk is a local
maximum of the holographic probability distribution, in contrast with expectations based
on semiclassical bulk gravity in eternal inflation.
2.3 Global measure: squashed three-spheres
We now turn to large deformations. The dual of our bulk model is the ABJM SCFT.
Hence to evaluate (1.1) we are faced with the problem of evaluating the partition function of
supersymmetry breaking deformations of this theory. We do not attempt this here. Instead
we first focus on a simplified model of this setup where we consider an O(N) vector model.
This is conjectured to be dual to higher-spin Vassiliev gravity in four dimensions [34].
Higher-spin theories are very different from Einstein gravity. However, ample evidence
indicates that the behavior of the free energy of vector models qualitatively captures that of
duals to Einstein gravity when one restricts to scalar, vector or spin 2 deformations [35–37].
This includes a remarkable qualitative agreement of the relation between the vev and the
source for the particular scalar potential (2.1) [38]. We therefore view these vector models
in this section as dual toy models of eternal inflation and proceed to evaluate their partition
functions for a specific class of large deformations. We return to Einstein gravity and a
general argument in support of our conjecture below in section 2.4.
Specifically we consider the O(N) vector model on squashed deformations of the
three-sphere,
ds2
=
r2
0
4
(σ1)2
+
1
1 + A
(σ2)2
+
1
1 + B
(σ3)2
, (2.4)
where r0 is an overall scale and σi, with i = 1, 2, 3, are the left-invariant one-forms of SU(2).
Note that the Ricci scalar R(A, B) < 0 for large squashings [36]. We further turn on a mass
deformation O with coupling α. This is a relevant deformation which in our dual O(N)
vector toy model induces a flow from the free to the critical O(N) model. The coefficient
– 5 –
7. JHEP04(2018)147
α is imaginary in the dS domain of the wave function as discussed above. Hence we are led
to evaluate the partition function, or free energy, of the critical O(N) model as a function
of the squashing parameters A and B and an imaginary mass deformation α ≡ ˜m2. The
key question of interest is whether or not the resulting holographic measure (1.1) favors
large deformations as semiclassical gravity would lead one to believe.
The deformed critical O(N) model is obtained from a double trace deformation
f(φ · φ)2/(2N) of the free model with an additional source ρf ˜m2 turned on for the single
trace operator O ≡ (φ · φ). By taking f → ∞ the theory flows from its unstable UV
fixed point, where the source has dimension one, to its critical fixed point with a source of
dimension two [34]. To see this we write the mass deformed free model partition function as
Zfree[m2
] = Dφe−Ifree+ d3x
√
gm2O(x)
, (2.5)
where Ifree is the action of the free O(N) model
Ifree =
1
2
d3
x
√
g ∂µφa∂µ
φa
+
1
8
Rφaφa
. (2.6)
Here φa is an N-component field transforming as a vector under O(N) rotations and R
is the Ricci scalar of the squashed boundary geometry. Introducing an auxiliary variable
˜m2 = m2
ρf + O
ρ yields
Zfree[m2
] = DφD ˜m2
e
−Ifree+N d3x
√
g ρf ˜m2O− f
2
O2− 1
2f
(m2−ρf ˜m2)2
, (2.7)
which can be written as
Zfree[m2
] = D ˜m2
e
− N
2f
d3x
√
g(m2−ρf ˜m2)2
Zcrit[ ˜m2
] , (2.8)
with
Zcrit[ ˜m2
] = Dφe−Ifree+N d3x
√
g[ρf ˜m2O− f
2
O2
] . (2.9)
Inverting (2.8) gives Zcrit as a function of Zfree:
Zcrit[ ˜m2
] = e
Nfρ2
2
d3x
√
g ˜m4
Dm2
e
N d3x
√
g m4
2f
−ρ ˜m2m2
Zfree[m2
] . (2.10)
The value of ρ can be determined by comparing two point functions in the bulk with those
in the boundary theory [37]. For the O(N) model this implies ρ = 1, which agrees with
the transformation from critical to free in [39].
We compute Zcrit for a single squashing A = 0 and ˜m2 = 0 by first calculating the
partition function of the free mass deformed O(N) vector model on a squashed sphere and
then evaluate (2.10) in a large N saddle point approximation.2 Evaluating the Gaussian
integral in (2.5) amounts to computing the following determinant
− log Zfree = F =
N
2
log det
− 2 + m2 + R
8
Λ2
, (2.11)
2
The generalization to double squashings A, B = 0 yields qualitatively similar results but requires
extensive numerical work and is discussed in [38].
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8. JHEP04(2018)147
-0.4 -0.2 0.2 0.4
im
2
-0.5
0.5
Rem2
-0.4 -0.2 0.2 0.4
im
2
-0.6
-0.4
-0.2
0.2
0.4
0.6
Imm2
Figure 2. The real and imaginary parts of the solutions m2
of the saddle point equation (2.13)
are shown for three different values of a single squashing, i.e. A = −0.8 (blue), A = 0 (red) and
A = 2.06 (green). For large i ˜m2
we have Re(m2
) → −R/8.
where Λ is a cutoff that we use to regularize the UV divergences in this theory. The
eigenvalues of the operator in (2.11) can be found in closed analytic form [40],
λn,q = n2
+ A(n − 1 − 2q)2
−
1
4(1 + A)
+ m2
, q = 0, 1, . . . , n − 1, n = 1, 2, . . . (2.12)
To regularize the infinite sum in (2.11) we follow [36, 37] and use a heat-kernel type
regularization. Using a heat-kernel the sum over eigenvalues divides in a UV and an IR
part. The latter converges and can readily be done numerically. By contrast the former
contains all the divergences and should be treated with care. We regularize this numerically
by verifying how the sum over high energy modes changes when we vary the energy cutoff.
From a numerical fit we then deduce its non-divergent part which we add to the sum over
the low energy modes to give the total renormalized free energy. The resulting determinant
after heat-kernel regularization captures all modes with energies lower than the cutoff Λ.
The contribution of modes with eigenvalues above the cutoff is exponentially small. For
more details on this procedure we refer to [36, 38].
To evaluate the holographic measure we must substitute our result for Zfree[A, m2]
in (2.10) and compute the integral in a large N saddle point approximation. The factor
outside the path integral in (2.10) diverges in the large f limit. We cancel this by adding
the appropriate counterterms. The saddle point equation then becomes
2π2
(1 + A)(1 + B)
m2
f
− ˜m2
= −
∂ log Zfree[m2]
∂m2
. (2.13)
We are interested in imaginary ˜m2 as discussed above. This means we need Zfree[A, m2]
for complex deformations m2. Numerically inverting (2.13) in the large f limit we find a
saddle point relation m2( ˜m2). This is shown in figure 2, where the real and imaginary
parts of m2 are plotted as a function of i ˜m2 for three different values of A.
Notice that Re(m2) ≥ −R(A)/8. This reflects the fact that the determinant (2.11),
which is a product over all eigenvalues of the operator − 2 +m2 +R/8, vanishes when the
operator has a zero eigenvalue. Since the lowest eigenvalue of the Laplacian 2 is always
zero, the first eigenvalue λ1 of the operator in (2.11) is zero when R/8 + m2 = 0. In the
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9. JHEP04(2018)147
Figure 3. The holographic probability distribution in a dual toy model of eternal inflation as
a function of the coupling of the mass deformation ˜m2
that is dual to the bulk scalar, and the
squashing A of the future boundary that parameterizes the amount of asymptotic anisotropy. The
distribution is smooth and normalizable over the entire configuration space and suppresses strongly
anisotropic future boundaries.
region of configuration space where the operator has one or more negative eigenvalues the
Gaussian integral (2.5) does not converge, and (2.11) does not apply. This in turn means
that the holographic measure Z−1
crit[A, ˜m2] is zero on such boundary configurations, as we
now see.
Inserting the relation m2( ˜m2) in (2.10) yields the partition function Zcrit[A, ˜m2]. We
show the resulting two-dimensional holographic measure in figure 3. The distribution
is well behaved and normalizable with a global maximum at zero squashing and zero
deformation corresponding to the pure de Sitter history, in agreement with the F-theorem
and its spin-2 extensions. When the scalar is turned on the local maximum shifts slightly
towards positive values of A. However the total probability of highly deformed boundary
geometries is exponentially small as anticipated.3 We illustrate this in figure 4 where we
plot two one-dimensional slices of the distribution for two different values of ˜m2.
2.4 Global measure: general metric deformations
It is beyond the current state-of-the-art to evaluate partition functions, be it of vector
models or ABJM or duals to other models, for general large metric deformations. However,
the above calculation implies a general argument suggesting that the amplitude of large
deformations of the conformal boundary geometry is highly suppressed in the holographic
measure both in higher-spin and in Einstein gravity. This is because the action of any dual
CFT includes a conformal coupling term of the form Rφ2. For geometries that are close to
the round sphere this is positive and prevents the partition function from diverging. On
3
The distribution has an exponentially small tail in the region of configuration space where the Ricci
scalar R(A) is negative and Zfree diverges. We attribute this to our saddle point approximation of (2.10).
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10. JHEP04(2018)147
0 5 10 15 20 25 30
A
0.5
1.0
1.5
2.0
1
Z2
0 10 20 30 40
A
0.02
0.04
0.06
0.08
0.10
0.12
1
Z2
Figure 4. Two slices of the probability distribution for ˜m2
= 0.0 (left) and ˜m2
= 0.05i (right).
the other hand the same argument suggests that the conformal coupling likely causes the
partition function to diverge on boundary geometries that are far from the round conformal
structure [41]. These include in particular geometries with patches of negative curvature
or, more accurately, a negative Yamabe invariant.
The Yamabe invariant Y (˜h) is a property of conformal classes. It is essentially the
infimum of the total scalar curvature in the conformal class of ˜h, normalized with respect
to the overall volume. It is defined as
Y (˜h) ≡ infω I(ω1/4˜h) (2.14)
where the infimum is taken over conformal transformations ω(x) and I(ω˜h) is the normal-
ized average scalar curvature of ω1/4˜h,
I(ω1/4˜h) =
M ω2R(˜h) + 8(∂ω)2 ˜h d3x
M ω6 ˜h d3x
1/3
. (2.15)
There always exists a conformal transformation ω(x) such that the metric ˜h = ω1/4˜h has
constant scalar curvature [42]. The infimum defining Y is obtained for this metric ˜h .
The Yamabe invariant is negative in conformal classes containing a metric of con-
stant R < 0. Since the lowest eigenvalue of the conformal Laplacian is negative on such
backgrounds one expects that the partition function of a CFT does not converge, thereby
strongly suppressing the amplitude of such conformal classes in the measure (1.1). This is
born out by the holographic measure specified by the partition function of the deformed
O(N) model on squashed spheres evaluated in section 2.3. There the probabilities of large
squashings for which R < 0 are exponentially small, which can be traced in the calculation
to the divergence of Zfree on such backgrounds.
Conformal classes with negative Y (˜h) precisely include the highly irregular constant
density surfaces featuring in a semiclassical gravity analysis of eternal inflation. This
general argument therefore suggests their amplitude will be low in a holographic measure.
We interpret this as evidence against the idea that eternal inflation typically leads to
– 9 –
11. JHEP04(2018)147
a highly irregular universe with a mosaic structure of bubble like patches separated by
inflationary domains.4 Instead we conjecture that the exit from eternal inflation produces
classical universes that are reasonably smooth on the largest scales.
3 Discussion
We have used gauge-gravity duality to describe the quantum dynamics of scalar field driven
eternal inflation in the no-boundary state in terms of a dual field theory defined on a global
constant density surface at the exit from (scalar field) eternal inflation. Working with the
semiclassical form (1.1) of dS/CFT the dual field theories involved are Euclidean AdS/CFT
duals deformed by a complex low dimension scalar operator sourced by the bulk scalar
driving eternal inflation.
The inverse of the partition function specifies the amplitude of different shapes of the
conformal boundary at the exit from scalar field eternal inflation. This yields a holographic
measure on the global structure of such eternally inflating universes. We have computed
this explicitly in a toy model consisting of a mass deformed interacting O(N) vector theory
defined on squashed spheres. In this model we find that the amplitude is low for geometries
far from the round conformal structure. Second, building on this result we have argued
on general grounds that exit surfaces with significant patches of negative scalar curvature
are strongly suppressed in a holographic measure in Einstein gravity too. Based on this
we conjecture that eternal inflation produces universes that are relatively regular on the
largest scales. This is radically different from the usual picture of eternal inflation arising
from a semiclassical gravity treatment.
We have considered toy model cosmologies in which a scalar field driven regime of eter-
nal inflation transitions directly to a Λ-dominated phase. The application of our ideas to
more realistic cosmologies that include a decelerating phase requires further development
of holographic cosmology (as is the case for all current applications of holographic tech-
niques to early universe cosmology, e.g. [15, 24–28]). It has been suggested that in realistic
cosmologies, inflation corresponds to an IR fixed point of the dual theory [24] in which case
the partition function of the IR theory might specify the amplitude of exit surfaces.
Our conjecture strengthens the intuition that holographic cosmology implies a signifi-
cant reduction of the multiverse to a much more limited set of possible universes. This has
important implications for anthropic reasoning. In a significantly constrained multiverse
discrete parameters are determined by the theory. Anthropic arguments apply only to a
subset of continuously varying parameters, such as the amount of slow roll inflation.
The dual Euclidean description of eternal inflation we put forward amounts to a sig-
nificant departure from the original no-boundary idea. In our description, histories with a
regime of eternal inflation have an inner boundary in the past, at the threshold for (scalar
field) eternal inflation. The field theory on this inner boundary gives an approximate de-
4
This resonates with [13] where we argued that probabilities for local observations in eternal inflation can
be obtained by coarse-graining over the large-scale fluctuations associated with eternal inflation, thereby
effectively restoring smoothness. Our holographic analysis suggests that the dual description implements
some of this coarse-graining automatically.
– 10 –
12. JHEP04(2018)147
scription of the transition from the quantum realm of eternal inflation, to a universe in
the semiclassical domain. For simplicity we have assumed a sharp inner boundary, but of
course one can imagine models where this is fuzzy. The detailed exit from eternal inflation
is encoded in the coupling between the field theory degrees of freedom on the exit surface
and the classical bulk dynamics.
Acknowledgments
We thank Dio Anninos, Nikolay Bobev, Frederik Denef, Jim Hartle, Kostas Skenderis and
Yannick Vreys for stimulating discussions over many years. SWH thanks the Institute for
Theoretical Physics in Leuven for its hospitality. TH thanks Trinity College and the CTC
in Cambridge for their hospitality. This work is supported in part by the ERC grant no.
ERC-2013-CoG 616732 HoloQosmos.
Open Access. This article is distributed under the terms of the Creative Commons
Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in
any medium, provided the original author(s) and source are credited.
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