The document discusses evidence for dark energy and the Lambda Cold Dark Matter (Lambda-CDM) model of cosmology. It notes that:
1) Evidence from COBE and age constraints provides evidence for a cosmological constant.
2) Type Ia supernovae provide independent confirmation of dark energy.
3) Observations are consistent with a flat Lambda-CDM model, known as the "concordance cosmology".
However, the cosmological constant poses theoretical problems, such as a discrepancy of 30 orders of magnitude between observed and predicted vacuum energy densities. Alternatives to Lambda-CDM that could still be consistent with observations are also discussed.
Detailing Coherent, Minimum Uncertainty States of Gravitons, as Semi Classical Components of Gravity Waves, and How Squeezed States Affect Upper Limits to Graviton Mass /• We present what is relevant to squeezed states of initial space time and how that affects both the composition of relic GW and also gravitons. A side issue to consider is if gravitons can be configured as semi classical “particles”, which is akin to the Pilot particles model of Quantum Mechanics as embedded in a larger non linear “deterministic” background.
First Presented Saturday, September 3, 2011 at the G999 Conference, Philadelphia, PA http://ggg999.org/
Next Presentation : Friday, September 9, SAN MARINO WORKSHOP ON ASTROPHYSICS AND COSMOLOGY
FOR MATTER AND ANTIMATTER
http://www.workshops-hadronic-mechanics.org/
San Marino, N. Italy
Discussion: The Nature of Semi-classical Nature of Gravity Reviewed; And Can We Use a Graviton Entanglement Version of the EPR System to Answer if The Graviton is Classical or Quantum in Origin?
Publisher’s note: Dr. Beckwith: I am honored that you have seen fit to acknowledge me in your presentations of today, September 3, 2011 at the G999 Conference in Philadelphia, and Friday, September 9, at the San Marino Workshop on Astrophysics and Cosmology For Matter and Antimatter, in San Marino, N. Italy.
In my view, these are rather extraordinary postulations, especially the probability of extra-universal black hole gravitational origins, along with expansion beyond Hawking of Quantum Wave theory and the “quantizing” of gravity. The latter may very well lead to a thorough reexamination of our concept of space and time, and that the latter might not be so unidirectional afterall. The potential is breathtaking, as it represents steps forward in proving the existence of subspace, the possibility of concomitant multi-universiality and 5D dimensionality of black holes.
Can time manipulation and Biefeld-Brown suggested electro-gravitics as a spacecraft propulsive methodology be far behind? I think not…
1) A new cosmological model is proposed where the universe is spontaneously created from nothing via quantum tunneling into a de Sitter space.
2) After tunneling, the model evolves according to the inflationary scenario, avoiding the big bang singularity and not requiring initial conditions.
3) The model suggests that the universe was created via quantum tunneling from a state of literally nothing into a de Sitter space, which then evolved into the expanding universe we observe according to known physics.
The document discusses string theory, extra dimensions, and cosmology. It notes that inflation and dark energy require new physics beyond general relativity and quantum field theory. Most string cosmology models invoke string theory, branes, or extra dimensions as approximations of string theory solutions. However, reliably anchoring cosmology in string theory has proven difficult, with success being rare. While cosmological observations can't determine the nature of dark energy, understanding fundamental physics through experiments like the LHC remains a key hope.
Current knowledge of the transversity quark distribution function, or how transversely polarized quarks are distributed in a transversely polarized proton?
Detailing Coherent, Minimum Uncertainty States of Gravitons, as Semi Classical Components of Gravity Waves, and How Squeezed States Affect Upper Limits to Graviton Mass /• We present what is relevant to squeezed states of initial space time and how that affects both the composition of relic GW and also gravitons. A side issue to consider is if gravitons can be configured as semi classical “particles”, which is akin to the Pilot particles model of Quantum Mechanics as embedded in a larger non linear “deterministic” background.
First Presented Saturday, September 3, 2011 at the G999 Conference, Philadelphia, PA http://ggg999.org/
Next Presentation : Friday, September 9, SAN MARINO WORKSHOP ON ASTROPHYSICS AND COSMOLOGY
FOR MATTER AND ANTIMATTER
http://www.workshops-hadronic-mechanics.org/
San Marino, N. Italy
Discussion: The Nature of Semi-classical Nature of Gravity Reviewed; And Can We Use a Graviton Entanglement Version of the EPR System to Answer if The Graviton is Classical or Quantum in Origin?
Publisher’s note: Dr. Beckwith: I am honored that you have seen fit to acknowledge me in your presentations of today, September 3, 2011 at the G999 Conference in Philadelphia, and Friday, September 9, at the San Marino Workshop on Astrophysics and Cosmology For Matter and Antimatter, in San Marino, N. Italy.
In my view, these are rather extraordinary postulations, especially the probability of extra-universal black hole gravitational origins, along with expansion beyond Hawking of Quantum Wave theory and the “quantizing” of gravity. The latter may very well lead to a thorough reexamination of our concept of space and time, and that the latter might not be so unidirectional afterall. The potential is breathtaking, as it represents steps forward in proving the existence of subspace, the possibility of concomitant multi-universiality and 5D dimensionality of black holes.
Can time manipulation and Biefeld-Brown suggested electro-gravitics as a spacecraft propulsive methodology be far behind? I think not…
This document analyzes extensions of the Standard Model that naturally accommodate tiny neutrino masses through the exchange of heavy particles. It discusses how neutrino masses are generated at tree-level by seesaw mechanisms involving fermionic singlets/triplets or scalar triplets. Dimension-six operators are also explored, as they may allow observable low-energy effects even with suppressed dimension-five operators. Phenomenological consequences are then analyzed, with a focus on charged lepton flavor violating processes and constraints from rare decays.
Detailing Coherent, Minimum Uncertainty States of Gravitons, as Semi Classical Components of Gravity Waves, and How Squeezed States Affect Upper Limits to Graviton Mass /• We present what is relevant to squeezed states of initial space time and how that affects both the composition of relic GW and also gravitons. A side issue to consider is if gravitons can be configured as semi classical “particles”, which is akin to the Pilot particles model of Quantum Mechanics as embedded in a larger non linear “deterministic” background.
First Presented Saturday, September 3, 2011 at the G999 Conference, Philadelphia, PA http://ggg999.org/
Next Presentation : Friday, September 9, SAN MARINO WORKSHOP ON ASTROPHYSICS AND COSMOLOGY
FOR MATTER AND ANTIMATTER
http://www.workshops-hadronic-mechanics.org/
San Marino, N. Italy
Discussion: The Nature of Semi-classical Nature of Gravity Reviewed; And Can We Use a Graviton Entanglement Version of the EPR System to Answer if The Graviton is Classical or Quantum in Origin?
Publisher’s note: Dr. Beckwith: I am honored that you have seen fit to acknowledge me in your presentations of today, September 3, 2011 at the G999 Conference in Philadelphia, and Friday, September 9, at the San Marino Workshop on Astrophysics and Cosmology For Matter and Antimatter, in San Marino, N. Italy.
In my view, these are rather extraordinary postulations, especially the probability of extra-universal black hole gravitational origins, along with expansion beyond Hawking of Quantum Wave theory and the “quantizing” of gravity. The latter may very well lead to a thorough reexamination of our concept of space and time, and that the latter might not be so unidirectional afterall. The potential is breathtaking, as it represents steps forward in proving the existence of subspace, the possibility of concomitant multi-universiality and 5D dimensionality of black holes.
Can time manipulation and Biefeld-Brown suggested electro-gravitics as a spacecraft propulsive methodology be far behind? I think not…
1) A new cosmological model is proposed where the universe is spontaneously created from nothing via quantum tunneling into a de Sitter space.
2) After tunneling, the model evolves according to the inflationary scenario, avoiding the big bang singularity and not requiring initial conditions.
3) The model suggests that the universe was created via quantum tunneling from a state of literally nothing into a de Sitter space, which then evolved into the expanding universe we observe according to known physics.
The document discusses string theory, extra dimensions, and cosmology. It notes that inflation and dark energy require new physics beyond general relativity and quantum field theory. Most string cosmology models invoke string theory, branes, or extra dimensions as approximations of string theory solutions. However, reliably anchoring cosmology in string theory has proven difficult, with success being rare. While cosmological observations can't determine the nature of dark energy, understanding fundamental physics through experiments like the LHC remains a key hope.
Current knowledge of the transversity quark distribution function, or how transversely polarized quarks are distributed in a transversely polarized proton?
Detailing Coherent, Minimum Uncertainty States of Gravitons, as Semi Classical Components of Gravity Waves, and How Squeezed States Affect Upper Limits to Graviton Mass /• We present what is relevant to squeezed states of initial space time and how that affects both the composition of relic GW and also gravitons. A side issue to consider is if gravitons can be configured as semi classical “particles”, which is akin to the Pilot particles model of Quantum Mechanics as embedded in a larger non linear “deterministic” background.
First Presented Saturday, September 3, 2011 at the G999 Conference, Philadelphia, PA http://ggg999.org/
Next Presentation : Friday, September 9, SAN MARINO WORKSHOP ON ASTROPHYSICS AND COSMOLOGY
FOR MATTER AND ANTIMATTER
http://www.workshops-hadronic-mechanics.org/
San Marino, N. Italy
Discussion: The Nature of Semi-classical Nature of Gravity Reviewed; And Can We Use a Graviton Entanglement Version of the EPR System to Answer if The Graviton is Classical or Quantum in Origin?
Publisher’s note: Dr. Beckwith: I am honored that you have seen fit to acknowledge me in your presentations of today, September 3, 2011 at the G999 Conference in Philadelphia, and Friday, September 9, at the San Marino Workshop on Astrophysics and Cosmology For Matter and Antimatter, in San Marino, N. Italy.
In my view, these are rather extraordinary postulations, especially the probability of extra-universal black hole gravitational origins, along with expansion beyond Hawking of Quantum Wave theory and the “quantizing” of gravity. The latter may very well lead to a thorough reexamination of our concept of space and time, and that the latter might not be so unidirectional afterall. The potential is breathtaking, as it represents steps forward in proving the existence of subspace, the possibility of concomitant multi-universiality and 5D dimensionality of black holes.
Can time manipulation and Biefeld-Brown suggested electro-gravitics as a spacecraft propulsive methodology be far behind? I think not…
This document analyzes extensions of the Standard Model that naturally accommodate tiny neutrino masses through the exchange of heavy particles. It discusses how neutrino masses are generated at tree-level by seesaw mechanisms involving fermionic singlets/triplets or scalar triplets. Dimension-six operators are also explored, as they may allow observable low-energy effects even with suppressed dimension-five operators. Phenomenological consequences are then analyzed, with a focus on charged lepton flavor violating processes and constraints from rare decays.
This document provides an overview of modified gravity theories as alternatives to dark energy and dark matter. It discusses that while general relativity is well-tested, there are theoretical motivations to consider modifications such as to address mysteries like dark energy. It reviews several examples of modified gravity theories involving additional fields, higher derivatives, or extra dimensions. Theories are constrained by solar system and laboratory tests but can be made compatible through screening mechanisms. Modified gravity can drive cosmic acceleration and affects the growth of structure, tested by cosmological observations of large-scale structure, peculiar velocities, and clusters.
This document summarizes a lecture on modified gravity theories. It discusses scalar-tensor theories as a framework for modifying general relativity, and mentions specific theories like DGP and f(R) gravity. It outlines two screening mechanisms - chameleon screening, where the scalar field acquires an environment-dependent mass, and Vainshtein screening, where derivative interactions lead to a scale-dependent suppression of the scalar force. Tests of modified gravity theories are discussed at both large cosmological and small solar system scales.
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.
In this talk, I looked at three theorems due to Poincaré concerning the long-term behavior of dynamical systems, namely, the Poincaré–Perron Theorem, the Poincaré–Bendixson Theorem and the rather counterintuitive Poincaré Recurrence Theorem, along with their proofs. Certain aspects of ergodic theory and topological dynamics, for instance, their applications in number theory and analysis (Green–Tao Theorem and Szemerédi’s Theorem), were also touched upon.
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 provides an outline of string theory. It begins with background on reductionism in physics and the unification of forces. String theory emerged as a way to address difficulties in quantizing gravity. There are five consistent string theories in 10 dimensions: type I open superstring theory with oriented strings; type IIA closed superstring theory with two independent sets of supersymmetry; heterotic string theories that combine bosonic and supersymmetric strings. String theory led to the discovery of supersymmetry and relates fundamental forces and particles to vibrational modes of strings.
This document provides an overview of quantum electrodynamics (QED). It begins by discussing cross sections and the scattering matrix, defining cross section as the effective size of target particles. It then derives an expression for cross section in terms of the transition rate and flux of incident particles. Next, it summarizes the derivation of the differential cross section and decay rate formulas in QED using relativistic quantum field theory and Feynman diagrams. It concludes by briefly reviewing the historical development of QED and the equivalence of the propagator approach and other formulations.
A Calabi-Yau manifold is a smooth space that represents a deformation which smooths out an orbifold singularity. This document discusses superstring theory and fermions in string theories. It introduces the spinning string action and shows that the Neveu-Schwarz model contains a tachyon ground state while the Ramond model contains massless fermions. Combining the two sectors using the Gliozzi-Scherk-Olive projection results in a model with N=1 supersymmetry in ten dimensions.
- The document derives the second order Friedmann equations from the quantum corrected Raychaudhuri equation (QRE), which includes quantum corrections terms.
- One correction term can be interpreted as dark energy/cosmological constant with the observed density value, providing an explanation for the coincidence problem.
- The other correction term can be interpreted as a radiation term in the early universe that prevents the formation of a big bang singularity and predicts an infinite age for the universe by avoiding a divergence in the Hubble parameter or its derivative at any finite time in the past.
- The document discusses a braneworld model where a 3-brane moves in a 5-dimensional anti-de Sitter bulk. The brane behaves effectively as a tachyon field with an inverse quartic potential.
- When the backreaction of the radion field (related to fluctuations of the brane position) is included, the tachyon Lagrangian is modified by its interaction with the radion. This results in an effective equation of state at large scales that describes "warm dark matter".
- The model extends the second Randall-Sundrum braneworld model to include nonlinear effects from the radion field, which distorts the anti-de Sitter geometry.
The document summarizes key concepts from quantum mechanics and symmetries. It states that physical states are represented by rays in a Hilbert space, with observables represented by Hermitian operators. The probability of measuring a state is given by the inner product of the state vectors. Symmetries are represented by either unitary or antiunitary operators on the Hilbert space. Symmetries that can be continuously connected to the identity must be represented by unitary operators. Symmetries form a group, with transformations combining according to the group multiplication rule.
The mp-quantales were introduced in a previous paper as an abstraction of the lattices of ideals in mp-rings and the lattices of ideals in conormal lattices. Several properties of m-rings and conormal lattices were generalized to mp-quantales. In this paper we shall prove new characterization theorems for mp-quantales and for semiprime mp-quantales (these last structures coincide with the P F-quantales). Some proofs reflect the way in which the reticulation functor (from coherent quantales to bounded distributive lattices) allows us to export some properties from conormal lattices to mp-quantales.
This document discusses whether quantum mechanics is involved in the early evolution of the universe and if a Machian relationship between gravitons and gravitinos can help answer this question. It proposes that:
1) Gravitons and gravitinos carry information and their relationship, described as a Mach's principle, conserves this information from the electroweak era to today. This suggests quantum mechanics may not be essential in early universe formation.
2) A minimum amount of initial information, such as a small value for Planck's constant, is needed to set fundamental cosmological parameters and could be transferred from a prior universe.
3) Early spacetime may have had a pre-quantum state with low entropy and degrees of freedom
This document provides an overview of string theory and superstring theory. It discusses the following key points:
1) A Calabi-Yau manifold is a smooth space that is Ricci flat and represents a deformation that smooths out an orbifold singularity from a space-time perspective.
2) In the 1960s, particle physics was dominated by S-matrix theory, which focused on scattering matrix properties rather than fundamental fields. S-matrix theory assumed analyticity, crossing, and unitarity of scattering amplitudes.
3) Early string theory models treated particles as vibrating strings to address limitations of S-matrix theory for high spin particles. This led to the development of bosonic string theory and super
The optimal cosmic_epoch_for_precision_cosmologySérgio Sacani
The document discusses the optimal epoch for precision cosmology measurements based on the number of independent Fourier modes available. It finds that the best constraints on the primordial power spectrum are accessible at redshifts around z=10 through instruments like 21-cm intensity mapping. The ability to constrain the initial cosmological conditions will deteriorate rapidly in our cosmic future as the exponential expansion erases information beyond 100 Hubble times from now.
This document provides an introduction to the concept of wave turbulence. It discusses how waves interact nonlinearly at finite amplitudes to produce a statistical, non-equilibrium dynamics. Key points:
- Wave turbulence involves dispersive waves that are excited and damped by external processes, leading to interactions between many degrees of freedom.
- The nonlinear interactions can be modeled using a Hamiltonian approach by including higher-order terms that couple different Fourier modes.
- A central goal is developing a statistical description of the system using correlation functions and obtaining a closed kinetic equation for the wave spectrum.
- In the weak turbulence regime, this kinetic equation can be solved perturbatively to obtain scaling laws for the wave spectrum in both physical and
1. The document discusses nonadiabatic transitions in chemical systems using path integral representations.
2. It introduces a nonadiabatic path integral approach based on overlap integrals between nuclear configurations on different electronic surfaces, as an alternative to the traditional derivative coupling approach.
3. A nonadiabatic beads model is presented for calculating nonadiabatic partition functions using a quantum-classical mapping, where the Boltzmann operator is divided among discrete nuclear coordinates on different surfaces connected by overlap integrals.
Understanding the experimental and mathematical derivation of Heisenberg's Uncertainty Principle. Simple application for estimating single degree of freedom particle in a potential free environment is also discussed.
Extra dimensions beyond the usual 3 dimensions are motivated by theories of grand unification and string theory. If extra dimensions exist, they would appear as Kaluza-Klein towers of increasingly massive copies of standard model particles. Some theories propose our universe is confined to a 3D brane embedded in higher dimensions accessible only to gravity. Large or warped extra dimensions could lower the true Planck scale to within reach of experiments like the LHC, solving the hierarchy problem and providing a test of theories of quantum gravity.
The Cosmic Microwave (CMB), and Infra-Red (CIRB) Backgrounds are Simple Effec...David Harding
In Continuous Quantum Iteration (CQI) theory, a new approximation of the universal engagement is explored. Science, as of yet, cannot define infinity; the absolute beginning. Yet it is only natural that science should ask the question....How did the local Universe get started? And where does this energy keep coming from? And what is the quantum vacuum really doing? Aspects of virtual quantum iteration are examined considering the plausibility of this new approximation. The Cosmic Microwave (CMB), and the Infra-Red Background (CIRB) are shown to be simple effects of Continual Quantum Vacuum Iterations occurring through Planck-Stoney scale interactions with the universal equilibrium event - horizon background.
This document provides an overview of modified gravity theories as alternatives to dark energy and dark matter. It discusses that while general relativity is well-tested, there are theoretical motivations to consider modifications such as to address mysteries like dark energy. It reviews several examples of modified gravity theories involving additional fields, higher derivatives, or extra dimensions. Theories are constrained by solar system and laboratory tests but can be made compatible through screening mechanisms. Modified gravity can drive cosmic acceleration and affects the growth of structure, tested by cosmological observations of large-scale structure, peculiar velocities, and clusters.
This document summarizes a lecture on modified gravity theories. It discusses scalar-tensor theories as a framework for modifying general relativity, and mentions specific theories like DGP and f(R) gravity. It outlines two screening mechanisms - chameleon screening, where the scalar field acquires an environment-dependent mass, and Vainshtein screening, where derivative interactions lead to a scale-dependent suppression of the scalar force. Tests of modified gravity theories are discussed at both large cosmological and small solar system scales.
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.
In this talk, I looked at three theorems due to Poincaré concerning the long-term behavior of dynamical systems, namely, the Poincaré–Perron Theorem, the Poincaré–Bendixson Theorem and the rather counterintuitive Poincaré Recurrence Theorem, along with their proofs. Certain aspects of ergodic theory and topological dynamics, for instance, their applications in number theory and analysis (Green–Tao Theorem and Szemerédi’s Theorem), were also touched upon.
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 provides an outline of string theory. It begins with background on reductionism in physics and the unification of forces. String theory emerged as a way to address difficulties in quantizing gravity. There are five consistent string theories in 10 dimensions: type I open superstring theory with oriented strings; type IIA closed superstring theory with two independent sets of supersymmetry; heterotic string theories that combine bosonic and supersymmetric strings. String theory led to the discovery of supersymmetry and relates fundamental forces and particles to vibrational modes of strings.
This document provides an overview of quantum electrodynamics (QED). It begins by discussing cross sections and the scattering matrix, defining cross section as the effective size of target particles. It then derives an expression for cross section in terms of the transition rate and flux of incident particles. Next, it summarizes the derivation of the differential cross section and decay rate formulas in QED using relativistic quantum field theory and Feynman diagrams. It concludes by briefly reviewing the historical development of QED and the equivalence of the propagator approach and other formulations.
A Calabi-Yau manifold is a smooth space that represents a deformation which smooths out an orbifold singularity. This document discusses superstring theory and fermions in string theories. It introduces the spinning string action and shows that the Neveu-Schwarz model contains a tachyon ground state while the Ramond model contains massless fermions. Combining the two sectors using the Gliozzi-Scherk-Olive projection results in a model with N=1 supersymmetry in ten dimensions.
- The document derives the second order Friedmann equations from the quantum corrected Raychaudhuri equation (QRE), which includes quantum corrections terms.
- One correction term can be interpreted as dark energy/cosmological constant with the observed density value, providing an explanation for the coincidence problem.
- The other correction term can be interpreted as a radiation term in the early universe that prevents the formation of a big bang singularity and predicts an infinite age for the universe by avoiding a divergence in the Hubble parameter or its derivative at any finite time in the past.
- The document discusses a braneworld model where a 3-brane moves in a 5-dimensional anti-de Sitter bulk. The brane behaves effectively as a tachyon field with an inverse quartic potential.
- When the backreaction of the radion field (related to fluctuations of the brane position) is included, the tachyon Lagrangian is modified by its interaction with the radion. This results in an effective equation of state at large scales that describes "warm dark matter".
- The model extends the second Randall-Sundrum braneworld model to include nonlinear effects from the radion field, which distorts the anti-de Sitter geometry.
The document summarizes key concepts from quantum mechanics and symmetries. It states that physical states are represented by rays in a Hilbert space, with observables represented by Hermitian operators. The probability of measuring a state is given by the inner product of the state vectors. Symmetries are represented by either unitary or antiunitary operators on the Hilbert space. Symmetries that can be continuously connected to the identity must be represented by unitary operators. Symmetries form a group, with transformations combining according to the group multiplication rule.
The mp-quantales were introduced in a previous paper as an abstraction of the lattices of ideals in mp-rings and the lattices of ideals in conormal lattices. Several properties of m-rings and conormal lattices were generalized to mp-quantales. In this paper we shall prove new characterization theorems for mp-quantales and for semiprime mp-quantales (these last structures coincide with the P F-quantales). Some proofs reflect the way in which the reticulation functor (from coherent quantales to bounded distributive lattices) allows us to export some properties from conormal lattices to mp-quantales.
This document discusses whether quantum mechanics is involved in the early evolution of the universe and if a Machian relationship between gravitons and gravitinos can help answer this question. It proposes that:
1) Gravitons and gravitinos carry information and their relationship, described as a Mach's principle, conserves this information from the electroweak era to today. This suggests quantum mechanics may not be essential in early universe formation.
2) A minimum amount of initial information, such as a small value for Planck's constant, is needed to set fundamental cosmological parameters and could be transferred from a prior universe.
3) Early spacetime may have had a pre-quantum state with low entropy and degrees of freedom
This document provides an overview of string theory and superstring theory. It discusses the following key points:
1) A Calabi-Yau manifold is a smooth space that is Ricci flat and represents a deformation that smooths out an orbifold singularity from a space-time perspective.
2) In the 1960s, particle physics was dominated by S-matrix theory, which focused on scattering matrix properties rather than fundamental fields. S-matrix theory assumed analyticity, crossing, and unitarity of scattering amplitudes.
3) Early string theory models treated particles as vibrating strings to address limitations of S-matrix theory for high spin particles. This led to the development of bosonic string theory and super
The optimal cosmic_epoch_for_precision_cosmologySérgio Sacani
The document discusses the optimal epoch for precision cosmology measurements based on the number of independent Fourier modes available. It finds that the best constraints on the primordial power spectrum are accessible at redshifts around z=10 through instruments like 21-cm intensity mapping. The ability to constrain the initial cosmological conditions will deteriorate rapidly in our cosmic future as the exponential expansion erases information beyond 100 Hubble times from now.
This document provides an introduction to the concept of wave turbulence. It discusses how waves interact nonlinearly at finite amplitudes to produce a statistical, non-equilibrium dynamics. Key points:
- Wave turbulence involves dispersive waves that are excited and damped by external processes, leading to interactions between many degrees of freedom.
- The nonlinear interactions can be modeled using a Hamiltonian approach by including higher-order terms that couple different Fourier modes.
- A central goal is developing a statistical description of the system using correlation functions and obtaining a closed kinetic equation for the wave spectrum.
- In the weak turbulence regime, this kinetic equation can be solved perturbatively to obtain scaling laws for the wave spectrum in both physical and
1. The document discusses nonadiabatic transitions in chemical systems using path integral representations.
2. It introduces a nonadiabatic path integral approach based on overlap integrals between nuclear configurations on different electronic surfaces, as an alternative to the traditional derivative coupling approach.
3. A nonadiabatic beads model is presented for calculating nonadiabatic partition functions using a quantum-classical mapping, where the Boltzmann operator is divided among discrete nuclear coordinates on different surfaces connected by overlap integrals.
Understanding the experimental and mathematical derivation of Heisenberg's Uncertainty Principle. Simple application for estimating single degree of freedom particle in a potential free environment is also discussed.
Extra dimensions beyond the usual 3 dimensions are motivated by theories of grand unification and string theory. If extra dimensions exist, they would appear as Kaluza-Klein towers of increasingly massive copies of standard model particles. Some theories propose our universe is confined to a 3D brane embedded in higher dimensions accessible only to gravity. Large or warped extra dimensions could lower the true Planck scale to within reach of experiments like the LHC, solving the hierarchy problem and providing a test of theories of quantum gravity.
The Cosmic Microwave (CMB), and Infra-Red (CIRB) Backgrounds are Simple Effec...David Harding
In Continuous Quantum Iteration (CQI) theory, a new approximation of the universal engagement is explored. Science, as of yet, cannot define infinity; the absolute beginning. Yet it is only natural that science should ask the question....How did the local Universe get started? And where does this energy keep coming from? And what is the quantum vacuum really doing? Aspects of virtual quantum iteration are examined considering the plausibility of this new approximation. The Cosmic Microwave (CMB), and the Infra-Red Background (CIRB) are shown to be simple effects of Continual Quantum Vacuum Iterations occurring through Planck-Stoney scale interactions with the universal equilibrium event - horizon background.
This document discusses potentials and fields in electrostatics and electrodynamics. It introduces vector and scalar potentials, gauge transformations, and Maxwell's equations in potential form. It then covers plane wave solutions to Maxwell's equations using potentials. Retarded potentials are defined using the retarded time, and it is shown that the retarded potentials satisfy Maxwell's equations in the Lorentz gauge. Finally, it discusses Lienard-Wiechert potentials for point charges and approaches to deriving length contraction and other relativistic effects from potentials and fields.
This document summarizes key concepts in electrostatics including Laplace's equation, Poisson's equation, and boundary value problems. It discusses:
1) Boundary value problems where the potential over a boundary is known but not the charge distribution, requiring boundary conditions to solve.
2) Laplace's equation and Poisson's equation, important for solving boundary value problems. Laplace's equation describes the electric potential in static systems with no charges while Poisson's equation includes the charge density.
3) Methods for solving problems involving different charge distributions and geometries like parallel plates, cylindrical shells, and spherical shells using Laplace's equation and appropriate coordinate systems.
Artigo que descreve o trabalho feito com o Chandra nos aglomerados de galáxias de Perseus e Virgo sobre a descoberta de uma turbulência cósmica que impede a formação de novas estrelas.
1. The document discusses causality and relativity of simultaneity using spacetime diagrams. It explains that nothing can travel faster than the speed of light based on analyses of pole-barn paradox scenarios and Lorentz transformations.
2. Key concepts from special relativity are reviewed, including Lorentz transformations, 4-vectors like 4-displacement and 4-velocity, proper time, rest mass, 4-momentum, and conservation of 4-momentum. Collisions are also discussed in relation to conservation of 4-momentum.
3. Causality is maintained in special relativity because the order of events cannot be reversed between reference frames if they are causally connected within or on each other's light cones. Faster-
This document discusses calculating the frequencies of quasinormal modes of black holes using semi-analytical methods. It summarizes that quasinormal modes are oscillations of black holes that emit gravitational waves. The WKB approximation and continued fractions method are used to calculate the frequencies. Results from the WKB method match other semi-analytic results for lower modes. The continued fractions method is also shown to work as another semi-analytic technique.
This document summarizes research on quantum turbulence in superfluids like helium-4. Key points include:
- Turbulence involves a tangle of quantized vortex filaments. Dissipation occurs through reconnections and kelvin wave cascades.
- Numerical simulations show fluctuations in vortex line density follow a f^-5/3 scaling, matching experiments.
- Velocity statistics are non-Gaussian at small scales due to the quantum nature of vortices, but become Gaussian at larger scales.
- The decay of quantum turbulence can follow either a quasiclassical t^-3/2 or ultraquantum t^-1 scaling depending on conditions.
This document discusses Bayesian model comparison in cosmology using population Monte Carlo methods. It provides background on key questions in cosmology that can be addressed using cosmic microwave background data from experiments like WMAP and Planck. Population Monte Carlo and adaptive importance sampling methods are introduced to help approximate Bayesian evidence for different cosmological models given the immense computational challenges of working with this cosmological data.
Oxford graduate lectures on "Quantum Chromodynamics and LHC phenomenology" Pa...juanrojochacon
The document discusses the historical motivation for quantum chromodynamics (QCD). It describes how the discovery of many new strongly interacting particles in the mid-20th century led to the proposal of quarks as fundamental constituents. Quarks were proposed to have a new quantum number called color to explain experimental observations. Deep inelastic scattering experiments provided evidence that quarks are real particles and not just mathematical entities. The document outlines the basic properties of QCD, including its SU(3) symmetry and how this allows color-singlet hadrons to form from quarks.
General Relativity is inconsistent with quantum theory which
leaves our understanding of nature incomplete and unsatisfactory. The now 80 years old quest for a consistent theory of quantum gravity has so far almost entirely focused on mathematical consistency. But as of recently the possibility to look for observational evidence has received an increased amount of attention, as a tool to provide guidance for the construction of of the theory.
Here, I summarize recent developments in the search for
experimental signatures for quantum gravitational effects and how these help to put constraints on the theory-construction. Some of the topics that I will cover are the prospects of finding Planck scale effects in gamma ray bursts, in neutral Kaon oscillations, or with massive quantum oscillators. If time allows, I will also comment on the search for holographic noise and how to find evidence for space-time discreteness.
1) The document proposes an alternative cosmological model where dark matter and dark energy are described as forms of ether, analogous to Mach's principle of inertia.
2) In this model, dark matter arises from the QCD vacuum or "sea" of quark-antiquark pairs and gluons at the confinement scale, while dark energy corresponds to the zero-point energy of the QCD vacuum.
3) The model aims to replace the standard LambdaCDM model, treating the expanding universe as a dynamically stable "biking" Einstein universe where the running cosmological constant compensates for the effect of gravity at all epochs.
This document discusses the nature of gravity and its relationship to other forces and fields. It provides evidence that gravity is an emergent phenomenon that arises from an underlying non-gravitational theory. Specifically:
1) Gravity behaves differently than other forces in that it curves spacetime itself rather than being mediated by particle exchanges. However, quantum gravity theories propose gravitons as force-carrying particles.
2) Holographic duality theories from the 1990s demonstrated that gravitational theories in higher dimensions are equivalent to non-gravitational theories in lower dimensions.
3) Modern developments like string theory and the AdS/CFT correspondence provide concrete examples of holography and establish gravity as an emer
This is a pdf file on the topic Gamow theory of alpha decay which gives description about how the scientist Gamow had solved the theory of the alpha decay via tunneling .
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.
This document discusses machine learning concepts including supervised vs. unsupervised learning, clustering algorithms, and specific clustering methods like k-means and k-nearest neighbors. It provides examples of how clustering can be used for applications such as market segmentation and astronomical data analysis. Key clustering algorithms covered are hierarchy methods, partitioning methods, k-means which groups data by assigning objects to the closest cluster center, and k-nearest neighbors which classifies new data based on its closest training examples.
- The document discusses methods for characterizing dark energy and modified gravity models in a model-independent way using cosmological observations.
- Due to the "dark degeneracy" between dark matter and dark energy, it is not possible to separately measure the properties of dark matter and dark energy without assuming a specific model class.
- Observables like the Hubble parameter H(z) and gravitational potentials can be reconstructed from the data, but this does not break the degeneracy between dark matter and dark energy contributions.
- The scale-dependence of quantities like the gravitational potentials and growth rate can be used to test and constrain broad classes of dark energy and modified gravity models in a more model-independent way.
Seminar by Prof Bruce Bassett at IAP, Paris, October 2013CosmoAIMS Bassett
This document discusses the rise of machine learning and artificial intelligence in astronomy due to a massive increase in data from upcoming surveys. It will produce around an exabyte of data per day, far more than has been produced throughout human history. This raises issues around preparing students, and how science may be done. The document discusses using machine learning for tasks like supernova identification and classification. It also discusses challenges like ensuring machine learning results are trustworthy, and whether this can truly replace human genius. It explores the idea of a universal language for scientific theories that could be searched algorithmically.
The 21cm line from neutral hydrogen can be used to study cosmology during the first billion years of the universe. This includes the Dark Ages when no structures formed, the Cosmic Dawn when the first luminous objects formed, and the Epoch of Reionization when these objects reionized the intergalactic medium. Current and future 21cm experiments like LOFAR, MWA, PAPER, and HERA aim to detect the signal from these eras but face challenges in calibrating the instruments and subtracting bright foreground sources. Some progress has been made in placing upper limits on the signal and constraining the heating of the intergalactic medium by X-rays, but a clear detection of the signal is still needed
The document discusses the cosmic dawn and reionization period in the early universe. It describes the evolution from the dark ages after recombination to the epoch of reionization around z=6-20. Key aspects discussed include understanding the sources and sinks of ionizing photons that drove reionization, and challenges in modeling this period due to the large parameter space and scales involved, from single stars to the entire universe. Seminumerical simulations are presented as an efficient method to model reionization and predict 21cm signals.
A short introduction to massive gravity... or ... Can one give a mass to the ...CosmoAIMS Bassett
1. The document discusses massive gravity and proposes that giving the graviton a small mass could potentially explain dark matter and dark energy without needing to introduce those concepts.
2. It reviews several models of massive gravity, including the Dvali-Gabadadze-Porrati model, which produces cosmic acceleration similar to dark energy. Kaluza-Klein theory is also discussed as producing massive gravitons.
3. Nonlinear extensions of the Pauli-Fierz theory are examined, finding solutions only with singularities. The "Goldstone" description of massive gravity is introduced as a way to better understand nonlinear effects like the Vainshtein mechanism.
This document summarizes recent research on how the sizes and densities of galaxies have changed over time. Studies have found that galaxies at high redshift had smaller sizes than present-day galaxies of the same mass, often by a factor of 2-3 within 1 kpc and over 100 times within the effective radius. Various mechanisms are discussed for how galaxies could have grown, including minor mergers which could increase size more than mass over time. The document also examines constraints on the amount of growth massive galaxies could have experienced through mergers between redshifts of 0.8 to 0.1 based on the luminosity and stellar mass functions remaining largely unchanged over this period.
Cluster abundances and clustering Can theory step up to precision cosmology?CosmoAIMS Bassett
This document discusses improvements to the Press-Schechter theory for modeling the abundances and clustering of dark matter halos. It proposes that modeling halo collapse as requiring the density to "step up" above a critical density threshold at progressively larger spatial scales provides a better approximation than assuming fully correlated or uncorrelated densities. This "stepping up" approach requires only 2-point statistics and can be applied to non-Gaussian fields. The document also suggests that modeling the distribution of density slopes at peak positions provides a way to match halo counts through an Excursion Set Peaks model.
This document discusses gravitational lensing and some of the challenges involved in measuring it. Gravitational lensing causes the apparent deflection of light from distant background sources as it passes massive foreground objects. Precise measurements of lensing effects can provide information about dark matter distributions and the geometry and growth of the universe. However, there are three main problems: accurately measuring galaxy shapes used to detect lensing distortions, determining reliable photometric redshifts for galaxies, and accounting for intrinsic alignments of galaxy orientations unrelated to lensing.
Testing cosmology with galaxy clusters, the CMB and galaxy clusteringCosmoAIMS Bassett
This document summarizes a presentation on testing cosmology using galaxy clusters, the cosmic microwave background, and galaxy clustering. It discusses combining measurements of cosmic growth and expansion from these sources to constrain departures from general relativity. Models are presented for linear, time-dependent departures from GR. Constraints on parameters like the growth index γ are shown from combinations of clusters, CMB, and galaxy data. Tightening constraints are achieved by adding baryon acoustic oscillation, supernova, and Hubble constant data. The document also briefly discusses using cluster counts to constrain primordial non-Gaussianity.
This document discusses galaxy formation and evolution from cosmological simulations and models. It summarizes that galaxy formation is driven by the hierarchical growth of dark matter halos, gas accretion via cold filamentary streams or hot spherical halos, and feedback regulating star formation. Galaxy properties like star formation rates and metallicities are set by the balance between gas inflow and outflow.
Spit, Duct Tape, Baling Wire & Oral Tradition: Dealing With Radio DataCosmoAIMS Bassett
The document discusses the process of creating radio interferometers and summarizing data from them. It begins with an overview of how a normal reflector telescope can be broken up and transformed into an interferometer by replacing the optical path with electronics and correlating signals between antenna elements. It then discusses some of the challenges in summarizing interferometer data, including missing information due to an incomplete coverage of the uv-plane, measurement errors that distort the signals, and direction-dependent effects that vary with time, antenna, and direction. The document introduces the concept of the Radio Interferometer Measurement Equation (RIME) to formally describe these direction-dependent distortions.
The document summarizes the MeerKAT radio telescope project in South Africa, including:
- MeerKAT will be the largest radio telescope in the southern hemisphere and one of the largest in the world, establishing a legacy for Africa. It is an SKA precursor project.
- The specifications for MeerKAT including the number of antennas, maximum baseline, bandwidth, frequency range, and survey plans.
- MeerKAT will initially consist of 64 antennas in 2016, expanding over time. It aims to carry out a number of surveys for HI, pulsars, galaxies, and fast/slow transients.
- Opportunities are outlined for students and faculty to get involved in radio astronomy research
This document provides guidance on reducing interferometric radio astronomy data from the Karoo Array Telescope (KAT-7) using the Common Astronomy Software Applications (CASA). It describes the multi-step process of calibration and imaging required to produce an image from the visibility measurements made by an interferometer. The key steps involve: 1) converting the raw data from HDF5 format to a measurement set, 2) loading and inspecting the data, 3) flagging bad or corrupted data, 4) solving for the complex gain calibration terms using calibrator sources, 5) splitting the data for source and calibrator, 6) deconvolving the dirty image using CLEAN to account for incomplete uv-coverage. Trouble
From Darkness, Light: Computing Cosmological ReionizationCosmoAIMS Bassett
1) Reionization occurred between redshifts of 10-6, beginning around 10 billion years ago and ending around 1 billion years ago.
2) Observations of the CMB and galaxies at z>6 provide constraints but questions remain about the sources and topology of reionization.
3) Cosmological simulations of reionization must model structure formation, radiation transport, and non-equilibrium chemistry and physics to help address open questions.
WHAT CAN WE DEDUCE FROM STUDIES OF NEARBY GALAXY POPULATIONS?CosmoAIMS Bassett
Studies of nearby galaxy populations using large optical surveys like SDSS have provided insights into galaxy formation and evolution. Key findings include identifying characteristic scales where baryon conversion peaks at halo masses of ~10^12 solar masses and galaxies transition from blue to red at stellar masses of ~10^10 solar masses. While surveys have constrained stellar populations and traced dark matter halos, they have not well constrained gas accretion onto galaxies, gas outflows, or the influence of black holes on galaxy evolution.
Binary pulsars provide an excellent tool to test theories of gravity. The document describes several binary pulsar systems and how measurements of their orbital parameters over time have allowed for high-precision tests of general relativity in strong gravitational fields. Specifically, the double pulsar system PSR J0737-3039A/B has enabled measurements that agree with general relativity predictions to within 0.05% precision by measuring parameters like periastron advance and gravitational redshift effects.
Cross Matching EUCLID and SKA using the Likelihood RatioCosmoAIMS Bassett
1) The document discusses using a likelihood ratio technique to identify counterparts between low-resolution radio data from surveys like SKA and optical/infrared data from surveys like Euclid.
2) The likelihood ratio technique calculates probabilities that potential counterparts are true matches versus random alignments based on positional offsets and magnitude distributions.
3) Applying the technique to simulated lower-resolution radio data shows a 3-5% loss in identified counterparts compared to high-resolution data, with the worst effects for faint radio sources. However, the vast majority of identified counterparts remain the same.
The document discusses using machine learning techniques to classify astronomical objects from large surveys. It notes that surveys are producing huge amounts of data that conventional methods cannot fully process. Machine learning can be used to help classify objects and sort candidates. Specifically, the document discusses using machine learning on photometric data from the Sloan Digital Sky Survey (SDSS) to identify low-redshift quasars. It notes challenges including the large size and dimensionality of the data, and proposes using a boosted ensemble method to learn weights for different regions of feature space rather than trying to estimate probabilities. This would help classify objects from the SDSS into categories like quasars, stars or galaxies.
How to Interpret Trends in the Kalyan Rajdhani Mix Chart.pdfChart Kalyan
A Mix Chart displays historical data of numbers in a graphical or tabular form. The Kalyan Rajdhani Mix Chart specifically shows the results of a sequence of numbers over different periods.
Fueling AI with Great Data with Airbyte WebinarZilliz
This talk will focus on how to collect data from a variety of sources, leveraging this data for RAG and other GenAI use cases, and finally charting your course to productionalization.
Letter and Document Automation for Bonterra Impact Management (fka Social Sol...Jeffrey Haguewood
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Interested in deploying letter generation automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
Digital Marketing Trends in 2024 | Guide for Staying AheadWask
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Feeling lost in the digital marketing whirlwind of 2024? Technology is changing, consumer habits are evolving, and staying ahead of the curve feels like a never-ending pursuit. This e-book is your compass. Dive into actionable insights to handle the complexities of modern marketing. From hyper-personalization to the power of user-generated content, learn how to build long-term relationships with your audience and unlock the secrets to success in the ever-shifting digital landscape.
Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slackshyamraj55
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Main news related to the CCS TSI 2023 (2023/1695)Jakub Marek
An English 🇬🇧 translation of a presentation to the speech I gave about the main changes brought by CCS TSI 2023 at the biggest Czech conference on Communications and signalling systems on Railways, which was held in Clarion Hotel Olomouc from 7th to 9th November 2023 (konferenceszt.cz). Attended by around 500 participants and 200 on-line followers.
The original Czech 🇨🇿 version of the presentation can be found here: https://www.slideshare.net/slideshow/hlavni-novinky-souvisejici-s-ccs-tsi-2023-2023-1695/269688092 .
The videorecording (in Czech) from the presentation is available here: https://youtu.be/WzjJWm4IyPk?si=SImb06tuXGb30BEH .
Taking AI to the Next Level in Manufacturing.pdfssuserfac0301
Read Taking AI to the Next Level in Manufacturing to gain insights on AI adoption in the manufacturing industry, such as:
1. How quickly AI is being implemented in manufacturing.
2. Which barriers stand in the way of AI adoption.
3. How data quality and governance form the backbone of AI.
4. Organizational processes and structures that may inhibit effective AI adoption.
6. Ideas and approaches to help build your organization's AI strategy.
A Comprehensive Guide to DeFi Development Services in 2024Intelisync
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At Intelisync, we specialize in providing comprehensive DeFi development services tailored to meet the unique needs of our clients. From smart contract development to dApp creation and security audits, we ensure that your DeFi project is built with innovation, security, and scalability in mind. Trust Intelisync to guide you through the intricate landscape of decentralized finance and unlock the full potential of blockchain technology.
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Driving Business Innovation: Latest Generative AI Advancements & Success StorySafe Software
Are you ready to revolutionize how you handle data? Join us for a webinar where we’ll bring you up to speed with the latest advancements in Generative AI technology and discover how leveraging FME with tools from giants like Google Gemini, Amazon, and Microsoft OpenAI can supercharge your workflow efficiency.
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This webinar is ideal for professionals seeking to harness the power of AI within their data management systems while ensuring high levels of customization and security. Whether you're a novice or an expert, gain actionable insights and strategies to elevate your data processes. Join us to see how FME and AI can revolutionize how you work with data!
Programming Foundation Models with DSPy - Meetup SlidesZilliz
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Introduction of Cybersecurity with OSS at Code Europe 2024Hiroshi SHIBATA
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Chris Clarkson - Testing the Copernican Principle
1. testing the copernican principle in the light of dark energy
Chris Clarkson
Astrophysics, Cosmology & Gravitation Centre
University of Cape Town
Thursday, 26 January 12
2. Dark Energy Evidence
• evidence of cosmological
constant from COBE + age
constraints
• independent confirmation
from SNIa
• observations consistent
with flat Lambda-CDM
‘concordance cosmology’
Thursday, 26 January 12
3. Dark Energy Evidence
• evidence of cosmological
constant from COBE + age
constraints
• independent confirmation
from SNIa
• observations consistent
with flat Lambda-CDM
‘concordance cosmology’
Thursday, 26 January 12
4. Dark Energy Evidence
• evidence of cosmological
constant from COBE + age
constraints
• independent confirmation
from SNIa flat LCDM is it!
• observations consistent
with flat Lambda-CDM
‘concordance cosmology’
Thursday, 26 January 12
5. relativity is valid up to the Planck scale, w
4
vacuum energy in terms of a mass scale as ρvac = Mvac , in te
ρ(theory) ∼ MP10−3 eV, satisf
required to explain our observations vac Mvac ∼ .
is
(obs) 4
Problems with Λ Mvac ∼ 10 Mvac . (obs) −30 (theory)
(ob
Comparing this value to the value ρvac
obtain
Nevertheless, this discrepancy of 30 orders of magnitude in ener
• Lambda doesn’t make sense as by the cosmological(obs) ∼ 10−120 ρ(theory) ,
is what is meant vacuum energy: ρvac constant problem.
vac
One may add to this problem the following puzzling obser
• Why do we live at a specialmatter densities changes as the universe expands a
vacuum and time?
ΩΛ ρΛ
= ∝ a3 .
ΩM ρM
Thus, only during a brief epoch of cosmic history is it possible
• last modes are entering the Hubble radius ... we coincide with the largest
modes whichthe transition from matter domination to Λ domination, durin
will ever exist
of the same order of magnitude. This is known as the coinciden
The issue of reliably calculating the cosmological constant,
• Perhaps Landscape arguments can answer this ... one day ...
in which that calculation leads to a result dramatically differe
• in 10500 universesproven remarkably resistant to theoretical attack. It is fair t
has anything goes..?
currently any especially promising approaches. Nevertheless, t
lines of research that are worth mentioning in this context.
The first is supersymmetry (SUSY). Supersymmetry is a sp
Thursday, 26 January 12
6. relativity is valid up to the Planck scale, w
4
vacuum energy in terms of a mass scale as ρvac = Mvac , in te
ρ(theory) ∼ MP10−3 eV, satisf
required to explain our observations vac Mvac ∼ .
is
(obs) 4
Problems with Λ Mvac ∼ 10 Mvac . (obs) −30 (theory)
(ob
Comparing this value to the value ρvac
obtain
Nevertheless, this discrepancy of 30 orders of magnitude in ener
• Lambda doesn’t make sense as by the cosmological(obs) ∼ 10−120 ρ(theory) ,
is what is meant vacuum energy: ρvac constant problem.
vac
One may add to this problem the following puzzling obser
• Why do we live at a specialmatter densities changes as the universe expands a
vacuum and time?
ΩΛ ρΛ
= ∝ a3 .
ΩM ρM
Thus, only during a brief epoch of cosmic history is it possible
• last modes are entering the Hubble radius ... we coincide with the largest
modes whichthe transition from matter domination to Λ domination, durin
will ever exist
of the same order of magnitude. This is known as the coinciden
The issue of reliably calculating the cosmological constant,
• Perhaps Landscape arguments can answer this ... one day ...
in which that calculation leads to a result dramatically differe
• in 10500 universesproven remarkably resistant to theoretical attack. It is fair t
has anything goes..?
currently any especially promising approaches. Nevertheless, t
lines of research that are worth mentioning in this context.
The first is supersymmetry (SUSY). Supersymmetry is a sp
Thursday, 26 January 12
7. relativity is valid up to the Planck scale, w
4
vacuum energy in terms of a mass scale as ρvac = Mvac , in te
ρ(theory) ∼ MP10−3 eV, satisf
required to explain our observations vac Mvac ∼ .
is
(obs) 4
Problems with Λ Mvac ∼ 10 Mvac . (obs) −30 (theory)
(ob
Comparing this value to the value ρvac
obtain
Nevertheless, this discrepancy of 30 orders of magnitude in ener
• Lambda doesn’t make sense as by the cosmological(obs) ∼ 10−120 ρ(theory) ,
is what is meant vacuum energy: ρvac constant problem.
vac
One may add to this problem the following puzzling obser
• Why do we live at a specialmatter densities changes as the universe expands a
vacuum and time?
ΩΛ ρΛ
Lambda ρM larger
ΩM
=any∝ a3 .
Thus,and during a brief epoch of cosmic history is it possible
only we couldn’t exist
• last modes are entering the Hubble radius ... we coincide with the largest
modes whichthe transition from matter domination to Λ domination, durin
will ever exist
of the same order of magnitude. This is known as the coinciden
The issue of reliably calculating the cosmological constant,
• Perhaps Landscape arguments can answer this ... one day ...
in which that calculation leads to a result dramatically differe
• in 10500 universesproven remarkably resistant to theoretical attack. It is fair t
has anything goes..?
currently any especially promising approaches. Nevertheless, t
lines of research that are worth mentioning in this context.
The first is supersymmetry (SUSY). Supersymmetry is a sp
Thursday, 26 January 12
8. LCDM Denial
• if acceleration isn’t cosmological constant:
}
• ‘real’ dark energy - quintessence, k-essence ...
make things worse,
but help test LCDM
• modified gravity - gr wrong on Hubble scales
• inhomogeneous universe - backreaction?
• do we live at the centre of vast void? - copernican assumption wrong
• LCDM requires 2 phases of accelerated expansion - phenomenological
Thursday, 26 January 12
9. priors critical
• assumes FLRW background spacetime - spatial homogeneity
• can we demonstrate this observationally?
• or have we already? at what confidence level?
• what do we know if we don’t assume this?
• does dark energy necessarily exist?
Thursday, 26 January 12
18. Spherical Symmetry → void models
• within dust Lemaitre-Tolman-Bondi models - 2 free radial dof
• can fit distance-redshift data to any FLRW DE model
Mustapha, Hellaby, & Ellis
Thursday, 26 January 12
19. Spherical Symmetry → void models
• within dust Lemaitre-Tolman-Bondi models - 2 free radial dof
• can fit distance-redshift data to any FLRW DE model
Mustapha, Hellaby, & Ellis
Thursday, 26 January 12
20. Spherical Symmetry → void models
• within dust Lemaitre-Tolman-Bondi models - 2 free radial dof
• can fit distance-redshift data to any FLRW DE model
Mustapha, Hellaby, & Ellis
Thursday, 26 January 12
21. Spherical Symmetry → void models
• within dust Lemaitre-Tolman-Bondi models - 2 free radial dof
• can fit distance-redshift data to any FLRW DE model
Mustapha, Hellaby, & Ellis
Alnes, Amarzguioui, and Gron astro-ph/0512006
Thursday, 26 January 12
22. Spherical Symmetry → void models
• within dust Lemaitre-Tolman-Bondi models - 2 free radial dof
• can fit distance-redshift data to any FLRW DE model
Mustapha, Hellaby, & Ellis
Biswas, Monsouri and Notari, astro-ph/0606703
Thursday, 26 January 12
23. z jump =0.085 ; ∆CENTRE =-0.48
Spherical Symmetry → void models
0.75
0.5
0.25
• within dust Lemaitre-Tolman-Bondi models - 2 free radial dof
0
m
-0.25
• can fit distance-redshift data to any FLRW DE model
-0.5
-0.75 Mustapha, Hellaby, & Ellis
-1
0 0.25 0.5 0.75 1 1.25 1.5 1.75
z
1
0.75
0.5
0.25
∆Ρ
0
Ρ
-0.25
-0.5
-0.75
Biswas, Monsouri and Notari, astro-ph/0606703
0 0.02 0.04 0.06 0.08
z
FIG. 3: In the upper plot we show a fit of the Supernovae data (Riess et al. [28]) with an LTB model which has χ2 =
d.o.f. are 181). The inhomogeneous patch extends up to z 0.085 and the underdensity in the center is δCENTRE
Thursday, 26 January 12 We have shown ∆m ≡ m − mempty : the magnitude (m ≡ 5Log10 DL ) minus the magnitude of an empty open FLRW
24. Spherical Symmetry → void models
• within dust Lemaitre-Tolman-Bondi models - 2 free radial dof
• can fit distance-redshift data to any FLRW DE model
Mustapha, Hellaby, & Ellis
Biswas, Monsouri and Notari, astro-ph/0606703
Thursday, 26 January 12
25. Spherical Symmetry → void models
• within dust Lemaitre-Tolman-Bondi models - 2 free radial dof
• can fit distance-redshift data to any FLRW DE model
Mustapha, Hellaby, & Ellis
Thursday, 26 January 12
26. void profile today
Hubble scales ~ 5-10 Gpc
density inhomogeneity accompanied by curvature
gradients and anisotropic expansion
Thursday, 26 January 12
30. Fine tuned
Supernovae as seen by off-center observers in a local void 15
Figure 4. Magnitude dipole induced by moving the observer away from the void
center in the best fit on-center models. The curves show the difference in magnitude
for two SNe Ia with the same redshift but in opposite directions in the sky. Left panel:
A void with scale radius rs = 0.7 Gpc (z ≈ 0.18), preferred by the SDSS-II data
set. Right panel: A void with scale radius rs = 3.5 Gpc (z ≈ 1.02), preferred by the
Constitution data set.
6. Constraining the observer position with SNe Ia
Off-center observers will see an anisotropic relation between the luminosity distance
and the redshift for the SNe Ia. This means that a standard candle with the same
redshift but in different directions in the sky will have different observed magnitudes.
The isotropy of the data can be used to establish constraints on the observer position
Figure 6. The void. In this section, we will investigate how farIa as a functionin the local
inside the changes in the as values for theoff-center observers of a
Supernovae χ2 seen by fit to the SNe from the center the observer
observer’sbe located.
can position. The stars show the values when the static observer is displaced in
void
Sep 2009
the direction of the CMB dipole in the best fit on-center LTB model. The diamonds
show the values when anisotropy also has a peculiar velocity directed 2to accommodate
6.1. Maximum the observer
Michael Blomqvist1 and Edvard M¨rtsell o
the observed CMB dipole. The arrows indicate the direction of motion, either away
To get a sense for 1 The Oskarthe effect of being situated off-center has of Astronomy, Ia
how big Klein Centre for Cosmoparticle Physics, Department on the SN
from the void center or towards it. The vertical dotted line Center the position where
Stockholm University, AlbaNova University
shows
Thursday, 26 January 12 observations, we can calculate the maximum anisotropy in the form of the magnitude
the peculiar velocity is zero. The scale radius of the void is r = 5.0 Gpc for the
34. “Never let anyone tell
you you’re crazy”
Prof. Bob Nichol
Thursday, 26 January 12
35. Are void models ridiculous?
• being ‘at the centre of the
universe’ is crazy, but actually
only a coincidence of
1 in 10~9 in our Hubble volume
• possible selection effects?
• could high dark matter
density inhibit solar system
formation?
must be stable for ~5Gyr
• so, maybe not anti-
Copernican ?
Thursday, 26 January 12
37. Isn’t this a bit silly?
• Yes
Thursday, 26 January 12
38. Isn’t this a bit silly?
• Yes
• But:
• we should be able to rule all void models out observationally - tests CP
• helps make data ‘cosmology independent’ (eg, compare SNIa vs BAO)
• provides alternative probe of coincidence problem which can be tested
• unusual DE interpretation without LCDM as fixed point - only DE model
with known physics at late times
• can we construct a void which fits all observations? [v fine-tuned?]
Thursday, 26 January 12
39. Small scale CMB
Baumann, TASI lectures
Thursday, 26 January 12
40. Small scale CMB
• high-l CMB fixes only:
baryon-photon ratio
baryon fraction
distance to last
scattering
CC & Marco Regis
Thursday, 26 January 12
41. Small scale CMB
indistinguishable
from LCDM
Thursday, 26 January 12
43. Lithium problem → inhomogeneity at early times?
• a Gpc fluctuation in baryon-photon ratio solves Li problem
FIG. 1: Constraints on . Top left we estimate current constraints on 10 = 1010 from di erent
7 Do primordial Lithium abundances imply there’s no Dark Energy?
from Li observations [10] in Galactic globular clusters and Galactic halo are shown separately, alon
These agree with each other if 10 ⇠ 4. Local measurements of D are very uncertain [8] though they
Marco Regis and Chris Clarkson
assume the rather precise value we show (from Cosmology analyses inCentre,and an astration factor (i.e.
Astrophysics,
Bayesian & Gravity [11]) and,
Thursday, 26 January 12
formation in our Galaxy) of f ⇠ 2 3. (Or, alternatively, a smaller f [12] with a slightly di erent v
44. Lithium problem → inhomogeneity at early times?
• a Gpc fluctuation in baryon-photon ratio solves Li problem
FIG. 1: Constraints on . Top left we estimate current constraints on 10 = 1010 from di erent
7 Do primordial Lithium abundances imply there’s no Dark Energy?
from Li observations [10] in Galactic globular clusters and Galactic halo are shown separately, alon
These agree with each other if 10 ⇠ 4. Local measurements of D are very uncertain [8] though they
Marco Regis and Chris Clarkson
assume the rather precise value we show (from Cosmology analyses inCentre,and an astration factor (i.e.
Astrophysics,
Bayesian & Gravity [11]) and,
Thursday, 26 January 12
formation in our Galaxy) of f ⇠ 2 3. (Or, alternatively, a smaller f [12] with a slightly di erent v
45. Lithium problem → inhomogeneity at early times?
• a Gpc fluctuation in baryon-photon ratio solves Li problem
FIG. 1: Constraints on . Top left we estimate current constraints on 10 = 1010 from di erent
7 Do primordial Lithium abundances imply there’s no Dark Energy?
from Li observations [10] in Galactic globular clusters and Galactic halo are shown separately, alon
These agree with each other if 10 ⇠ 4. Local measurements of D are very uncertain [8] though they
Marco Regis and Chris Clarkson
assume the rather precise value we show (from Cosmology analyses inCentre,and an astration factor (i.e.
Astrophysics,
Bayesian & Gravity [11]) and,
Thursday, 26 January 12
formation in our Galaxy) of f ⇠ 2 3. (Or, alternatively, a smaller f [12] with a slightly di erent v
46. Lithium problem → inhomogeneity at early times?
• a Gpc fluctuation in baryon-photon ratio solves Li problem
FIG. 1: Constraints on . Top left we estimate current constraints on 10 = 1010 from di erent
7 Do primordial Lithium abundances imply there’s no Dark Energy?
from Li observations [10] in Galactic globular clusters and Galactic halo are shown separately, alon
These agree with each other if 10 ⇠ 4. Local measurements of D are very uncertain [8] though they
Marco Regis and Chris Clarkson
assume the rather precise value we show (from Cosmology analyses inCentre,and an astration factor (i.e.
Astrophysics,
Bayesian & Gravity [11]) and,
Thursday, 26 January 12
formation in our Galaxy) of f ⇠ 2 3. (Or, alternatively, a smaller f [12] with a slightly di erent v
47. CMB gives
expansion
rate here
Li determines
expansion rate here
Thursday, 26 January 12
50. infer expansion
rate here
CMB gives
sound horizon
rate here
assume sound
horizon here
Thursday, 26 January 12
51. e 2. Examples of the size of the dipole for different parameters of the constrained
model [19]. strong constraint left figure is the first order approximation
kSZ The dashed line in the
n [30].
• kSZ (and SZ) effect can look inside our past lightcone
!in=0.23, r0=1.8, H0=0.65, "r/r0=0.35
e void in90 eyes - the kSZ effect in LTB models
the 6
8
60
6
30 4
vP [1000 km/s]
2
0 -45 -90 -135
0
-2
-30
Figure 1. An off-centre cluster of galaxies in a void will “observe” CMB photons
-4
coming from the last scattering surface from all directions. Due to the higher expansion
rate inside the void, photons arriving through the centre (from the right in the figure)
will have a larger redshift (∆zin ), than photons arriving directly from the LSS (left,
-60
-6
with ∆zout ). There is a subdominant effect due to the time-dependent density profile
0.0
(the solid line corresponds to the current time, while the dot-dashed line to one tenth of 0.2 0.4 0.6
the present time). With a larger underdensity at later times, we have ∆z1 > ∆z4 , and
-90 Redshift
∆z2 + ∆z3 < 0, giving an overall difference ∆z1 > ∆z2 + ∆z3 + ∆z4 or, equivalently, a
Looking the void in the eyes - the kSZ effect in LTB
subdominant dipole with a blueshift towards the centre of the void. The overall effect
is a blueshift away from the centre.
models
e 3. The angular and redshift distribution of current observations together with
1 1,2
quently, in the ideal case Juan Garc´void, and a well embedded cluster, the
of a sphericalıa-Bellido , Troels Haugbølle
server will see an almost perfect dipole in the CMB, aligned along the radial parsec sized void model. Red triangles and
dicted dipoleInstituto de 28049 Madrid, UAM-CSIC, a gigaAut´noma de Madrid,
1
distribution for Universidad o
F´ısica Te´rica
o
008
Cantoblanco, Spain,
and with the blueshift pointing away from the centre of the void, where the
suares26 January 12 Department of Physics and Astronomy,negative peculiar C,
(see Fig. 1).represent of a spherical void and CMB sky of of Aarhus, DK-8000 Aarhus velocities respectively, with the
The detailed effect positive on the University an
2
Thursday,
52. e 2. Examples of the size of the dipole for different parameters of the constrained
model [19]. strong constraint left figure is the first order approximation
kSZ The dashed line in the
n [30].
• kSZ (and SZ) effect can look inside our past lightcone
!in=0.23, r0=1.8, H0=0.65, "r/r0=0.35
e void in90 eyes - the kSZ effect in LTB models
the 6
8
60
6
30 4
vP [1000 km/s]
2
0 -45 -90 -135
0
-2
-30
Figure 1. An off-centre cluster of galaxies in a void will “observe” CMB photons
-4
coming from the last scattering surface from all directions. Due to the higher expansion
rate inside the void, photons arriving through the centre (from the right in the figure)
will have a larger redshift (∆zin ), than photons arriving directly from the LSS (left,
-60
-6
with ∆zout ). There is a subdominant effect due to the time-dependent density profile
0.0
(the solid line corresponds to the current time, while the dot-dashed line to one tenth of 0.2 0.4 0.6
the present time). With a larger underdensity at later times, we have ∆z1 > ∆z4 , and
-90 Redshift
∆z2 + ∆z3 < 0, giving an overall difference ∆z1 > ∆z2 + ∆z3 + ∆z4 or, equivalently, a
Looking the void in the eyes - the kSZ effect in LTB
subdominant dipole with a blueshift towards the centre of the void. The overall effect
is a blueshift away from the centre.
models
e 3. The angular and redshift distribution of current observations together with
1 1,2
quently, in the ideal case Juan Garc´void, and a well embedded cluster, the
of a sphericalıa-Bellido , Troels Haugbølle
server will see an almost perfect dipole in the CMB, aligned along the radial parsec sized void model. Red triangles and
dicted dipoleInstituto de 28049 Madrid, UAM-CSIC, a gigaAut´noma de Madrid,
1
distribution for Universidad o
F´ısica Te´rica
o
008
Cantoblanco, Spain,
and with the blueshift pointing away from the centre of the void, where the
suares26 January 12 Department of Physics and Astronomy,negative peculiar C,
(see Fig. 1).represent of a spherical void and CMB sky of of Aarhus, DK-8000 Aarhus velocities respectively, with the
The detailed effect positive on the University an
2
Thursday,
53. e 2. Examples of the size of the dipole for different parameters of the constrained
model [19]. strong constraint left figure is the first order approximation
kSZ The dashed line in the
n [30].
• kSZ (and SZ) effect can look inside our past lightcone
!in=0.23, r0=1.8, H0=0.65, "r/r0=0.35
e void in90 eyes - the kSZ effect in LTB models
the 6
8
60
6
30 4
vP [1000 km/s]
2
0 -45 -90 -135
0
-2
-30
Figure 1. An off-centre cluster of galaxies in a void will “observe” CMB photons
-4
coming from the last scattering surface from all directions. Due to the higher expansion
rate inside the void, photons arriving through the centre (from the right in the figure)
will have a larger redshift (∆zin ), than photons arriving directly from the LSS (left,
-60
-6
with ∆zout ). There is a subdominant effect due to the time-dependent density profile
0.0
(the solid line corresponds to the current time, while the dot-dashed line to one tenth of 0.2 0.4 0.6
the present time). With a larger underdensity at later times, we have ∆z1 > ∆z4 , and
-90 Redshift
∆z2 + ∆z3 < 0, giving an overall difference ∆z1 > ∆z2 + ∆z3 + ∆z4 or, equivalently, a
Looking the void in the eyes - the kSZ effect in LTB
subdominant dipole with a blueshift towards the centre of the void. The overall effect
is a blueshift away from the centre.
models
e 3. The angular and redshift distribution of current observations together with
1 1,2
quently, in the ideal case Juan Garc´void, and a well embedded cluster, the
of a sphericalıa-Bellido , Troels Haugbølle
server will see an almost perfect dipole in the CMB, aligned along the radial parsec sized void model. Red triangles and
dicted dipoleInstituto de 28049 Madrid, UAM-CSIC, a gigaAut´noma de Madrid,
1
distribution for Universidad o
F´ısica Te´rica
o
008
Cantoblanco, Spain,
and with the blueshift pointing away from the centre of the void, where the
suares26 January 12 Department of Physics and Astronomy,negative peculiar C,
(see Fig. 1).represent of a spherical void and CMB sky of of Aarhus, DK-8000 Aarhus velocities respectively, with the
The detailed effect positive on the University an
2
Thursday,
54. e 2. Examples of the size of the dipole for different parameters of the constrained
model [19]. strong constraint left figure is the first order approximation
kSZ The dashed line in the
n [30].
• kSZ (and SZ) effect can look inside our past lightcone
!in=0.23, r0=1.8, H0=0.65, "r/r0=0.35
e void in90 eyes - the kSZ effect in LTB models
the 6
8
60
6
30 4
vP [1000 km/s]
2
0 -45 -90 -135
0
-2
-30
Figure 1. An off-centre cluster of galaxies in a void will “observe” CMB photons
-4
coming from the last scattering surface from all directions. Due to the higher expansion
rate inside the void, photons arriving through the centre (from the right in the figure)
will have a larger redshift (∆zin ), than photons arriving directly from the LSS (left,
-60
-6
with ∆zout ). There is a subdominant effect due to the time-dependent density profile
0.0
(the solid line corresponds to the current time, while the dot-dashed line to one tenth of 0.2 0.4 0.6
the present time). With a larger underdensity at later times, we have ∆z1 > ∆z4 , and
-90 Redshift
∆z2 + ∆z3 < 0, giving an overall difference ∆z1 > ∆z2 + ∆z3 + ∆z4 or, equivalently, a
Looking the void in the eyes - the kSZ effect in LTB
subdominant dipole with a blueshift towards the centre of the void. The overall effect
is a blueshift away from the centre.
models
e 3. The angular and redshift distribution of current observations together with
1 1,2
quently, in the ideal case Juan Garc´void, and a well embedded cluster, the
of a sphericalıa-Bellido , Troels Haugbølle
server will see an almost perfect dipole in the CMB, aligned along the radial parsec sized void model. Red triangles and
dicted dipoleInstituto de 28049 Madrid, UAM-CSIC, a gigaAut´noma de Madrid,
1
distribution for Universidad o
F´ısica Te´rica
o
008
Cantoblanco, Spain,
and with the blueshift pointing away from the centre of the void, where the
suares26 January 12 Department of Physics and Astronomy,negative peculiar C,
(see Fig. 1).represent of a spherical void and CMB sky of of Aarhus, DK-8000 Aarhus velocities respectively, with the
The detailed effect positive on the University an
2
Thursday,
55. e 2. Examples of the size of the dipole for different parameters of the constrained
model [19]. strong constraint left figure is the first order approximation
kSZ The dashed line in the
n [30].
• kSZ (and SZ) effect can look inside our past lightcone
!in=0.23, r0=1.8, H0=0.65, "r/r0=0.35
e void in90 eyes - the kSZ effect in LTB models
the 6
8
60
6
30 4
vP [1000 km/s]
2
0 -45 -90 -135
0
-2
-30
Figure 1. An off-centre cluster of galaxies in a void will “observe” CMB photons
-4
coming from the last scattering surface from all directions. Due to the higher expansion
rate inside the void, photons arriving through the centre (from the right in the figure)
will have a larger redshift (∆zin ), than photons arriving directly from the LSS (left,
-60
-6
with ∆zout ). There is a subdominant effect due to the time-dependent density profile
0.0
(the solid line corresponds to the current time, while the dot-dashed line to one tenth of 0.2 0.4 0.6
the present time). With a larger underdensity at later times, we have ∆z1 > ∆z4 , and
-90 Redshift
∆z2 + ∆z3 < 0, giving an overall difference ∆z1 > ∆z2 + ∆z3 + ∆z4 or, equivalently, a
Looking the void in the eyes - the kSZ effect in LTB
subdominant dipole with a blueshift towards the centre of the void. The overall effect
is a blueshift away from the centre.
models
e 3. The angular and redshift distribution of current observations together with
1 1,2
quently, in the ideal case Juan Garc´void, and a well embedded cluster, the
of a sphericalıa-Bellido , Troels Haugbølle
server will see an almost perfect dipole in the CMB, aligned along the radial parsec sized void model. Red triangles and
dicted dipoleInstituto de 28049 Madrid, UAM-CSIC, a gigaAut´noma de Madrid,
1
distribution for Universidad o
F´ısica Te´rica
o
008
Cantoblanco, Spain,
and with the blueshift pointing away from the centre of the void, where the
suares26 January 12 Department of Physics and Astronomy,negative peculiar C,
(see Fig. 1).represent of a spherical void and CMB sky of of Aarhus, DK-8000 Aarhus velocities respectively, with the
The detailed effect positive on the University an
2
Thursday,
56. measure CMB dipole
observed here
assume decoupling
temperature here
Thursday, 26 January 12
57. so...
• voids fit key background observations [just!]: SN+H0+CMB
• but simplest ‘adiabatic’ voids ruled out - probably not solution to DE!
• they assume everything homogeneous except matter density
• does that make sense?
• if we don’t have a theory to make a void, we can only make a map of it
• everything could be inhomogeneous ... what measures what?
Thursday, 26 January 12
58. kSZ measures early (in)homogeneity
measure CMB dipole
observed here
assume decoupling
temperature here
Thursday, 26 January 12
59. kSZ measures early (in)homogeneity
measure CMB dipole
observed here
assume decoupling
temperature here
Thursday, 26 January 12
60. kSZ measures early (in)homogeneity
measure CMB dipole
observed here
Bull, Clifton, assume decoupling
Ferriera 1108.2222
temperature here
Thursday, 26 January 12
61. BAO measures baryon fraction (r)
infer expansion
rate here
CMB gives
sound horizon
rate here
assume sound
horizon here
Thursday, 26 January 12
62. large-scale CMB, BAO, structure formation...
• ... all require perturbation theory
• unsolved!
• k-modes not independent - important for BAO.
Thursday, 26 January 12
63. large-scale CMB, BAO, structure formation...
• ... all require perturbation theory
• unsolved!
• k-modes not independent - important for BAO.
Thursday, 26 January 12
64. large-scale CMB, BAO, structure formation...
• ... all require perturbation theory
• unsolved!
• k-modes not independent - important for BAO.
Thursday, 26 January 12
65. could specify model as a Cauchy problem
re
he
ta
in
da
te
ify
gr
a
ec
te
sp
in
to
pa
s t
hard to ‘rule out’!
Thursday, 26 January 12
66. testing the Copernican/cosmological principles
• we only view the universe
from one event
• fixed in space & time
• what observations take us
form CP -> homogeneity?
• how to we test CP
generically?
• independently of theory of
gravity or dark energy
Thursday, 26 January 12
67. when does CP imply homogeneity ?
• if everyone sees an isotropic CMB => homo [Ehlers, Geren, Sachs, 1968]
• if everyone sees isotropic distances => homo [Hasse, Perlick, 199..]
• etc
• can we see the universe from anywhere else?
• do we need to?
Thursday, 26 January 12
68. kSZ lets us see CMB as others see it
not enough observers - need to detect double scatterings!
Thursday, 26 January 12
69. check consistency of
the standard model
infer expansion
rate here from BAO
} estimate age along
here
Heavens, Jimenez, Maartens 1107.5910
Thursday, 26 January 12
70. ‘on lightcone’ test
• in FLRW we can combine Hubble rate and distance data to find curvature
2
[H(z)D (z)] 1
k =
[H0 D(z)]2
⇥
dL = (1 + z)D = (1 + z) dA
2
• independent of all other cosmological parameters, including dark energy
model, and theory of gravity
• tests the Copernican principle and the basis of FLRW
⇥
C (z) = 1 + H 2
DD D 2
+ HH DD = 0
Clarkson, Basset & Lu, PRL 100 191303
Thursday, 26 January 12
71. Using age data to reconstruct H(z)
need to reconstruct D(z) and H(z)
independently of model - difficult
Shafieloo & Clarkson, PRD
Thursday, 26 January 12
72. consistency of standard model
• void models unlikely to be DE explanation
• highlights need to test homogeneity assumption
• ‘tests’ formulate CP as null hypothesis
• compare observables or observe inside lightcone
• ideally, in model-independent ways - independently of DE/GR
• how do we place confidence limits on FLRW?
Thursday, 26 January 12