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.
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
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.
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
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.
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.
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.
Numerical Simulations on Flux Tube Tectonic Model for Solar Coronal HeatingRSIS International
The sun is a G-type main sequence star. Corona is an
aura of Plasma that Surrounds the Sun and other Stars. The
heating of solar Corona is one of most important problem in
Astrophysics. There are several mechanism of Coronal heating.
In this paper we discuss Numerical Simulation on Flux tube
Tectonic Model For Solar Coronal Heating .
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.
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
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.
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.
Numerical Simulations on Flux Tube Tectonic Model for Solar Coronal HeatingRSIS International
The sun is a G-type main sequence star. Corona is an
aura of Plasma that Surrounds the Sun and other Stars. The
heating of solar Corona is one of most important problem in
Astrophysics. There are several mechanism of Coronal heating.
In this paper we discuss Numerical Simulation on Flux tube
Tectonic Model For Solar Coronal Heating .
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.
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
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.
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)
Também conhecido como o “Time Lock Puzzle”, o LCS35 é um desafio em forma de criptografia projetado em 1999 pelo pesquisador Ron Rivest, do Instituto de Tecnologia de Massachusetts (MIT). Quando este problema matemático for resolvido, uma cápsula do tempo de chumbo será aberta no MIT.
O puzzle envolve a divisão de um número incrivelmente enorme, por um número que é apenas um pouco menor que o da conta (mas ainda com mais de 600 dígitos).
Ninguém sabe o que está dentro da capsula e, segundo os dados de Rivest, estima-se que levaria cerca de 35 anos para que o enigma seja resolvido. Os interessados ainda terão de esperar para descobrir o que de fato tem na capsula.
Wow! Signal Decoded as Foundations of Theory of EverythingXequeMateShannon
The Wow! signal was a strong narrowband radio signal received on August 15, 1977, by Ohio State University's Big Ear radio telescope in the United States, then used to support the search for extraterrestrial intelligence. The signal appeared to come from the constellation Sagittarius and bore the expected hallmarks of extraterrestrial origin.
Em Matemática, um número normal é um número real cujos algarismos são distribuídos de maneira aleatória no seu desenvolvimento decimal, isto é, os algarismos aparecem todos com a mesma freqüência. Os "algarismos" se referem aos algarismos antes da vírgula e a seqüência infinita de algarismos após a vírgula.
Um algoritmo genético é uma técnica de busca utilizada na ciência da computação para achar soluções aproximadas em problemas de otimização e busca, fundamentado principalmente pelo americano John Henry Holland.
Hamiltonian design in readout from room-temperature Raman atomic memory XequeMateShannon
We present an experimental demonstration of the Hamiltonian manipulation in light-atom interface in Raman-type warm rubidium-87 vapor atomic memory. By adjusting the detuning of the driving beam we varied the relative contributions of the Stokes and anti-Stokes scattering to the process of four-wave mixing which reads out a spatially multimode state of atomic memory. We measured the temporal evolution of the readout fields and the spatial intensity correlations between write-in and readout as a function of detuning with the use of an intensified camera. The correlation maps enabled us to resolve between the anti-Stokes and the Stokes scattering and to quantify their contributions. Our experimental results agree quantitatively with a simple, plane-wave theoretical model we provide. They allow for a simple interpretation of the coaction of the anti-Stokes and the Stokes scattering at the readout stage. The Stokes contribution yields additional, adjustable gain at the readout stage, albeit with inevitable extra noise. Here we provide a simple and useful framework to trace it and the results can be utilized in the existing atomic memories setups. Furthermore, the shown Hamiltonian manipulation offers a broad range of atom-light interfaces readily applicable in current and future quantum protocols with atomic ensembles.
Good cryptography requires good random numbers. This paper evaluates the hardwarebased Intel Random Number Generator (RNG) for use in cryptographic applications.
Almost all cryptographic protocols require the generation and use of secret values that must be unknown to attackers. For example, random number generators are required to generate public/private keypairs for asymmetric (public key) algorithms including RSA, DSA, and Diffie-Hellman. Keys for symmetric and hybrid cryptosystems are also generated randomly. RNGs are also used to create challenges, nonces (salts), padding bytes, and blinding values. The one time pad – the only provably-secure encryption system – uses as much key material as ciphertext and requires that the keystream be generated from a truly random process.
A palavra aleatoriedade exprime quebra de ordem, propósito, causa, ou imprevisibilidade em uma terminologia não científica. Um processo aleatório é o processo repetitivo cujo resultado não descreve um padrão determinístico, mas segue uma distribuição de probabilidade.
Quantum cryptography can, in principle, provide unconditional security guaranteed by the law of physics only. Here, we survey the theory and practice of the subject and highlight some recent developments.
The Security of Practical Quantum Key DistributionXequeMateShannon
Quantum key distribution (QKD) is the first quantum information task to reach the level of mature technology, already fit for commercialization. It aims at the creation of a secret key between authorized partners connected by a quantum channel and a classical authenticated channel. The security of the key can in principle be guaranteed without putting any restriction on the eavesdropper's power.
The first two sections provide a concise up-to-date review of QKD, biased toward the practical side. The rest of the paper presents the essential theoretical tools that have been developed to assess the security of the main experimental platforms (discrete variables, continuous variables and distributed-phase-reference protocols).
Experimental realisation of Shor's quantum factoring algorithm using qubit r...XequeMateShannon
Quantum computational algorithms exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms. Shor's quantum algorithm for fast number factoring is a key example and the prime motivator in the international effort to realise a quantum computer. However, due to the substantial resource requirement, to date, there have been only four small-scale demonstrations. Here we address this resource demand and demonstrate a scalable version of Shor's algorithm in which the n qubit control register is replaced by a single qubit that is recycled n times: the total number of qubits is one third of that required in the standard protocol. Encoding the work register in higher-dimensional states, we implement a two-photon compiled algorithm to factor N=21. The algorithmic output is distinguishable from noise, in contrast to previous demonstrations. These results point to larger-scale implementations of Shor's algorithm by harnessing scalable resource reductions applicable to all physical architectures.
The different faces of mass action in virus assemblyXequeMateShannon
The spontaneous encapsulation of genomic and non-genomic polyanions by coat proteins of simple icosahedral viruses is driven, in the first instance, by electrostatic interactions with polycationic RNA binding domains on these proteins. The efficiency with which the polyanions can be encapsulated in vitro, and presumably also in vivo, must in addition be governed by the loss of translational and mixing entropy associated with co-assembly, at least if this co-assembly constitutes a reversible process. These forms of entropy counteract the impact of attractive interactions between the constituents and hence they counteract complexation. By invoking mass action-type arguments and a simple model describing electrostatic interactions, we show how these forms of entropy might settle the competition between negatively charged polymers of different molecular weights for co-assembly with the coat proteins. In direct competition, mass action turns out to strongly work against the encapsulation of RNAs that are significantly shorter, which is typically the case for non-viral (host) RNAs. We also find that coat proteins favor forming virus particles over nonspecific binding to other proteins in the cytosol even if these are present in vast excess. Our results rationalize a number of recent in vitro co-assembly experiments showing that short polyanions are less effective at attracting virus coat proteins to form virus-like particles than long ones do, even if both are present at equal weight concentrations in the assembly mixture.
A Digital Signature Based on a Conventional Encryption FunctionXequeMateShannon
A new digital signature based only on a conventional encryption function (such as DES) is described which is as secure as the underlying encryption function -- the security does not depend on the difficulty of factoring and the high computational costs of modular arithmetic are avoided. The signature system can sign an unlimited number of messages, and the signature size increases logarithmically as a function of the number of messages signed. Signature size in a ‘typical’ system might range from a few hundred bytes to a few kilobytes, and generation of a signature might require a few hundred to a few thousand computations of the underlying conventional encryption function.
Quantum algorithm for solving linear systems of equationsXequeMateShannon
Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need to know the solution x itself, but rather an approximation of the expectation value of some operator associated with x, e.g., x'Mx for some matrix M. In this case, when A is sparse, N by N and has condition number kappa, classical algorithms can find x and estimate x'Mx in O(N sqrt(kappa)) time. Here, we exhibit a quantum algorithm for this task that runs in poly(log N, kappa) time, an exponential improvement over the best classical algorithm.
Countermeasures Against High-Order Fault-Injection Attacks on CRT-RSAXequeMateShannon
In this paper we study the existing CRT-RSA countermeasures against fault-injection at-tacks. In an attempt to classify them we get to achieve deep understanding of how they work. We show that the many countermeasures that we study (and their variations) actually share a number of common features, but optimize them in different ways. We also show that there is no conceptual distinction between test-based and infective countermeasures and how either one can be transformed into the other. Furthermore, we show that faults on the code (skipping instructions) can be captured by considering only faults on the data. These intermediate results allow us to improve the state of the art in several ways: (a) we fix an existing and that was known to be broken countermeasure (namely the one from Shamir); (b) we drastically optimize an existing countermeasure (namely the one from Vigilant) which we reduce to 3 tests instead of 9 in its original version, and prove that it resists not only one fault but also an arbitrary number of randomizing faults; (c) we also show how to upgrade countermeasures to resist any given number of faults: given a correct first-order countermeasure, we present a way to design a prov-able high-order countermeasure (for a well-defined and reasonable fault model). Finally, we pave the way for a generic approach against fault attacks for any modular arithmetic computations, and thus for the automatic insertion of countermeasures.
The complexity of promise problems with applications to public-key cryptographyXequeMateShannon
A “promise problem” is a formulation of partial decision problem. Complexity issues about promise problems arise from considerations about cracking problems for public-key cryptosystems. Using a notion of Turing reducibility between promise problems, this paper disproves a conjecture made by Even and Yacobi (1980), that would imply nonexistence of public-key cryptosystems with NP-hard cracking problems. In its place a new conjecture is raised having the same consequence. In addition, the new conjecture implies that NP-complete sets cannot be accepted by Turing machines that have at most one accepting computation for each input word.
The ability to recreate computational results with minimal effort and actionable metrics provides a solid foundation for scientific research and software development. When people can replicate an analysis at the touch of a button using open-source software, open data, and methods to assess and compare proposals, it significantly eases verification of results, engagement with a diverse range of contributors, and progress. However, we have yet to fully achieve this; there are still many sociotechnical frictions.
Inspired by David Donoho's vision, this talk aims to revisit the three crucial pillars of frictionless reproducibility (data sharing, code sharing, and competitive challenges) with the perspective of deep software variability.
Our observation is that multiple layers — hardware, operating systems, third-party libraries, software versions, input data, compile-time options, and parameters — are subject to variability that exacerbates frictions but is also essential for achieving robust, generalizable results and fostering innovation. I will first review the literature, providing evidence of how the complex variability interactions across these layers affect qualitative and quantitative software properties, thereby complicating the reproduction and replication of scientific studies in various fields.
I will then present some software engineering and AI techniques that can support the strategic exploration of variability spaces. These include the use of abstractions and models (e.g., feature models), sampling strategies (e.g., uniform, random), cost-effective measurements (e.g., incremental build of software configurations), and dimensionality reduction methods (e.g., transfer learning, feature selection, software debloating).
I will finally argue that deep variability is both the problem and solution of frictionless reproducibility, calling the software science community to develop new methods and tools to manage variability and foster reproducibility in software systems.
Exposé invité Journées Nationales du GDR GPL 2024
This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.
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.
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...University of Maribor
Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
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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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].
– 6 –
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
– 7 –
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).
– 8 –
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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