Relativistic Cosmology.

By: Ellis, George F. RContributor(s): Maartens, Roy | MacCallum, Malcolm A. HMaterial type: TextTextPublisher: Cambridge : Cambridge University Press, 2012Copyright date: ©2012Description: 1 online resource (638 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9781139217064Subject(s): Cosmology | Relativistic astrophysics | Relativistic quantum theoryGenre/Form: Electronic books.Additional physical formats: Print version:: Relativistic CosmologyDDC classification: 523.1 LOC classification: QB981 .E4654 2012Online resources: Click to View
Contents:
Cover -- Relativistic Cosmology -- Title -- Copyright -- Contents -- Preface -- PART 1: FOUNDATIONS -- 1: The nature of cosmology -- 1.1 The aims of cosmology -- 1.2 Observational evidence and its limitations -- 1.3 A summary of current observations -- 1.4 Cosmological concepts -- 1.5 Cosmological models -- 1.6 Overview -- 2: Geometry -- 2.1 Manifolds -- 2.2 Tangent vectors and 1-forms -- 2.3 Tensors -- 2.4 Lie derivatives -- 2.5 Connections and covariant derivatives -- 2.6 The curvature tensor -- 2.7 Riemannian geometry -- 2.8 General bases and tetrads -- 2.9 Hypersurfaces -- 3: Classical physics and gravity -- 3.1 Equivalence principles, gravity and local physics -- 3.2 Conservation equations -- 3.3 The field equations in relativity and their structure -- 3.4 Relation to Newtonian theory -- PART 2: RELATIVISTIC COSMOLOGICAL MODELS -- 4: Kinematics of cosmological models -- 4.1 Comoving coordinates -- 4.2 The fundamental 4-velocity -- 4.3 Time derivatives and the acceleration vector -- 4.4 Projection to give three-dimensional relations -- 4.5 Relative position and velocity -- 4.6 The kinematic quantities -- 4.7 Curvature and the Ricci identities for the 4-velocity -- 4.8 Identities for the projected covariant derivatives -- 5: Matter in the universe -- 5.1 Conservation laws -- 5.2 Fluids -- 5.3 Multiple fluids -- 5.4 Kinetic theory -- 5.5 Electromagnetic fields -- 5.6 Scalar fields -- 5.7 Quantum field theory -- 6: Dynamics of cosmological models -- 6.1 The Raychaudhuri-Ehlers equation -- 6.2 Vorticity conservation -- 6.3 The other Einstein field equations -- 6.4 The Weyl tensor and the Bianchi identities -- 6.5 The orthonormal 1+3 tetrad equations -- 6.6 Structure of the 1+3 system of equations -- 6.7 Global structure and singularities -- 6.8 Newtonian models and Newtonian limits -- 7: Observations in cosmological models.
7.1 Geometrical optics and null geodesics -- 7.2 Redshifts -- 7.3 Geometry of null geodesics and images -- 7.4 Radiation energy and flux -- 7.5 Specific intensity and apparent brightness -- 7.6 Number counts -- 7.7 Selection and detection issues -- 7.8 Background radiation -- 7.9 Causal and visual horizons -- 8: Light-cone approach to relativistic cosmology -- 8.1 Model-based approach -- 8.2 Direct observational cosmology -- 8.3 Ideal cosmography -- 8.4 Field equations: determining the geometry -- 8.5 Isotropic and partially isotropic observations -- 8.6 Implications and opportunities -- PART 3: THE STANDARD MODEL AND EXTENSIONS -- 9: Homogeneous FLRW universes -- 9.1 FLRW geometries -- 9.2 FLRW dynamics -- 9.3 FLRW dynamics with barotropic fluids -- 9.4 Phase planes -- 9.5 Kinetic solutions -- 9.6 Thermal history and contents of the universe -- 9.7 Inflation -- 9.8 Origin of FLRW geometry -- 9.9 Newtonian case -- 10: Perturbations of FLRW universes -- 10.1 The gauge problem in cosmology -- 10.2 Metric-based perturbation theory -- 10.3 Covariant nonlinear perturbations -- 10.4 Covariant linear perturbations -- 11: The cosmic background radiation -- 11.1 The CMB and spatial homogeneity: nonlinear analysis -- 11.2 Linearized analysis of distribution multipoles -- 11.3 Temperature anisotropies in the CMB -- 11.4 Thomson scattering -- 11.5 Scalar perturbations -- 11.6 CMB polarization -- 11.7 Vector and tensor perturbations -- 11.8 Other background radiation -- 12: Structure formation and gravitational lensing -- 12.1 Correlation functions and power spectra -- 12.2 Primordial perturbations from inflation -- 12.3 Growth of density perturbations -- 12.4 Gravitational lensing -- 12.5 Cosmological applications of lensing -- 13: Confronting the Standard Model with observations -- 13.1 Observational basis for FLRW models.
13.2 FLRW observations: probing the background evolution -- 13.3 Almost FLRW observations: probing structure formation -- 13.4 Constraints and consistency checks -- 13.5 Concordance model and further issues -- 14: Acceleration from dark energy or modified gravity -- 14.1 Overview of the problem -- 14.2 Dark energy in an FLRW background -- 14.3 Modified gravity in a RW background -- 14.4 Constraining effective theories -- 14.5 Conclusion -- 15: 'Acceleration' from large-scale inhomogeneity? -- 15.1 Lemaître-Tolman-Bondi universes -- 15.2 Observables and source evolution -- 15.3 Can we fit area distance and number count observations? -- 15.4 Testing background LTB with SNIa and CMB distances -- 15.5 Perturbations of LTB -- 15.6 Observational tests of spatial homogeneity -- 15.7 Conclusion: status of the Copernican Principle -- 16: 'Acceleration' from small-scale inhomogeneity? -- 16.1 Different scale descriptions -- 16.2 Cosmological backreaction -- 16.3 Specific models: almost FLRW -- 16.4 Inhomogeneous models -- 16.5 Importance of backreaction effects? -- 16.6 Effects on observations -- 16.7 Combination of effects: altering cosmic concordance? -- 16.8 Entropy and coarse-graining -- PART 4: ANISOTROPIC AND INHOMOGENEOUS MODELS -- 17: The space of cosmological models -- 17.1 Cosmological models with symmetries -- 17.2 The equivalence problem in cosmology -- 17.3 The space of models and the role of symmetric models -- 18: Spatially homogeneous anisotropic models -- 18.1 Kantowski-Sachs universes: geometry and dynamics -- 18.2 Bianchi I universes: geometry and dynamics -- 18.3 Bianchi geometries and their field equations -- 18.4 Bianchi universe dynamics -- 18.5 Evolution of particular Bianchi models -- 18.6 Cosmological consequences -- 18.7 The Bianchi degrees of freedom -- 19: Inhomogeneous models -- 19.1 LTB revisited -- 19.2 Swiss cheese revisited.
19.3 Self-similar models -- 19.4 Models with a G3 acting on S2 -- 19.5 G2 cosmologies -- 19.6 The Szekeres-Szafron family -- 19.7 The Stephani-Barnes family -- 19.8 Silent universes -- 19.9 General dynamics of inhomogeneous models -- 19.10 Cosmological applications -- PART 5: BROADER PERSPECTIVES -- 20: Quantum gravity and the start of the universe -- 20.1 Is there a quantum gravity epoch? -- 20.2 Quantum gravity effects -- 20.3 String theory and cosmology -- 20.4 Loop quantum gravity and cosmology -- 20.5 Physics horizon -- 20.6 Explaining the universe - the question of origins -- 21: Cosmology in a larger setting -- 21.1 Local physics and cosmology -- 21.2 Varying 'constants' -- 21.3 Anthropic question: fine-tuning for life -- 21.4 Special or general? Probable or improbable? -- 21.5 Possible existence of multiverses -- 21.6 Why is the universe as it is? -- 22: Conclusion: our picture of the universe -- 22.1 A coherent view? -- 22.2 Testing alternatives: probing the possibilities -- 22.3 Limits of cosmology -- Appendix: Some useful formulae -- A.1 Constants and units -- A.2 1+3 covariant equations -- A.3 Frequently used acronyms -- References -- Index.
Summary: Surveying key developments and open issues in cosmology for graduate students and researchers.
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Cover -- Relativistic Cosmology -- Title -- Copyright -- Contents -- Preface -- PART 1: FOUNDATIONS -- 1: The nature of cosmology -- 1.1 The aims of cosmology -- 1.2 Observational evidence and its limitations -- 1.3 A summary of current observations -- 1.4 Cosmological concepts -- 1.5 Cosmological models -- 1.6 Overview -- 2: Geometry -- 2.1 Manifolds -- 2.2 Tangent vectors and 1-forms -- 2.3 Tensors -- 2.4 Lie derivatives -- 2.5 Connections and covariant derivatives -- 2.6 The curvature tensor -- 2.7 Riemannian geometry -- 2.8 General bases and tetrads -- 2.9 Hypersurfaces -- 3: Classical physics and gravity -- 3.1 Equivalence principles, gravity and local physics -- 3.2 Conservation equations -- 3.3 The field equations in relativity and their structure -- 3.4 Relation to Newtonian theory -- PART 2: RELATIVISTIC COSMOLOGICAL MODELS -- 4: Kinematics of cosmological models -- 4.1 Comoving coordinates -- 4.2 The fundamental 4-velocity -- 4.3 Time derivatives and the acceleration vector -- 4.4 Projection to give three-dimensional relations -- 4.5 Relative position and velocity -- 4.6 The kinematic quantities -- 4.7 Curvature and the Ricci identities for the 4-velocity -- 4.8 Identities for the projected covariant derivatives -- 5: Matter in the universe -- 5.1 Conservation laws -- 5.2 Fluids -- 5.3 Multiple fluids -- 5.4 Kinetic theory -- 5.5 Electromagnetic fields -- 5.6 Scalar fields -- 5.7 Quantum field theory -- 6: Dynamics of cosmological models -- 6.1 The Raychaudhuri-Ehlers equation -- 6.2 Vorticity conservation -- 6.3 The other Einstein field equations -- 6.4 The Weyl tensor and the Bianchi identities -- 6.5 The orthonormal 1+3 tetrad equations -- 6.6 Structure of the 1+3 system of equations -- 6.7 Global structure and singularities -- 6.8 Newtonian models and Newtonian limits -- 7: Observations in cosmological models.

7.1 Geometrical optics and null geodesics -- 7.2 Redshifts -- 7.3 Geometry of null geodesics and images -- 7.4 Radiation energy and flux -- 7.5 Specific intensity and apparent brightness -- 7.6 Number counts -- 7.7 Selection and detection issues -- 7.8 Background radiation -- 7.9 Causal and visual horizons -- 8: Light-cone approach to relativistic cosmology -- 8.1 Model-based approach -- 8.2 Direct observational cosmology -- 8.3 Ideal cosmography -- 8.4 Field equations: determining the geometry -- 8.5 Isotropic and partially isotropic observations -- 8.6 Implications and opportunities -- PART 3: THE STANDARD MODEL AND EXTENSIONS -- 9: Homogeneous FLRW universes -- 9.1 FLRW geometries -- 9.2 FLRW dynamics -- 9.3 FLRW dynamics with barotropic fluids -- 9.4 Phase planes -- 9.5 Kinetic solutions -- 9.6 Thermal history and contents of the universe -- 9.7 Inflation -- 9.8 Origin of FLRW geometry -- 9.9 Newtonian case -- 10: Perturbations of FLRW universes -- 10.1 The gauge problem in cosmology -- 10.2 Metric-based perturbation theory -- 10.3 Covariant nonlinear perturbations -- 10.4 Covariant linear perturbations -- 11: The cosmic background radiation -- 11.1 The CMB and spatial homogeneity: nonlinear analysis -- 11.2 Linearized analysis of distribution multipoles -- 11.3 Temperature anisotropies in the CMB -- 11.4 Thomson scattering -- 11.5 Scalar perturbations -- 11.6 CMB polarization -- 11.7 Vector and tensor perturbations -- 11.8 Other background radiation -- 12: Structure formation and gravitational lensing -- 12.1 Correlation functions and power spectra -- 12.2 Primordial perturbations from inflation -- 12.3 Growth of density perturbations -- 12.4 Gravitational lensing -- 12.5 Cosmological applications of lensing -- 13: Confronting the Standard Model with observations -- 13.1 Observational basis for FLRW models.

13.2 FLRW observations: probing the background evolution -- 13.3 Almost FLRW observations: probing structure formation -- 13.4 Constraints and consistency checks -- 13.5 Concordance model and further issues -- 14: Acceleration from dark energy or modified gravity -- 14.1 Overview of the problem -- 14.2 Dark energy in an FLRW background -- 14.3 Modified gravity in a RW background -- 14.4 Constraining effective theories -- 14.5 Conclusion -- 15: 'Acceleration' from large-scale inhomogeneity? -- 15.1 Lemaître-Tolman-Bondi universes -- 15.2 Observables and source evolution -- 15.3 Can we fit area distance and number count observations? -- 15.4 Testing background LTB with SNIa and CMB distances -- 15.5 Perturbations of LTB -- 15.6 Observational tests of spatial homogeneity -- 15.7 Conclusion: status of the Copernican Principle -- 16: 'Acceleration' from small-scale inhomogeneity? -- 16.1 Different scale descriptions -- 16.2 Cosmological backreaction -- 16.3 Specific models: almost FLRW -- 16.4 Inhomogeneous models -- 16.5 Importance of backreaction effects? -- 16.6 Effects on observations -- 16.7 Combination of effects: altering cosmic concordance? -- 16.8 Entropy and coarse-graining -- PART 4: ANISOTROPIC AND INHOMOGENEOUS MODELS -- 17: The space of cosmological models -- 17.1 Cosmological models with symmetries -- 17.2 The equivalence problem in cosmology -- 17.3 The space of models and the role of symmetric models -- 18: Spatially homogeneous anisotropic models -- 18.1 Kantowski-Sachs universes: geometry and dynamics -- 18.2 Bianchi I universes: geometry and dynamics -- 18.3 Bianchi geometries and their field equations -- 18.4 Bianchi universe dynamics -- 18.5 Evolution of particular Bianchi models -- 18.6 Cosmological consequences -- 18.7 The Bianchi degrees of freedom -- 19: Inhomogeneous models -- 19.1 LTB revisited -- 19.2 Swiss cheese revisited.

19.3 Self-similar models -- 19.4 Models with a G3 acting on S2 -- 19.5 G2 cosmologies -- 19.6 The Szekeres-Szafron family -- 19.7 The Stephani-Barnes family -- 19.8 Silent universes -- 19.9 General dynamics of inhomogeneous models -- 19.10 Cosmological applications -- PART 5: BROADER PERSPECTIVES -- 20: Quantum gravity and the start of the universe -- 20.1 Is there a quantum gravity epoch? -- 20.2 Quantum gravity effects -- 20.3 String theory and cosmology -- 20.4 Loop quantum gravity and cosmology -- 20.5 Physics horizon -- 20.6 Explaining the universe - the question of origins -- 21: Cosmology in a larger setting -- 21.1 Local physics and cosmology -- 21.2 Varying 'constants' -- 21.3 Anthropic question: fine-tuning for life -- 21.4 Special or general? Probable or improbable? -- 21.5 Possible existence of multiverses -- 21.6 Why is the universe as it is? -- 22: Conclusion: our picture of the universe -- 22.1 A coherent view? -- 22.2 Testing alternatives: probing the possibilities -- 22.3 Limits of cosmology -- Appendix: Some useful formulae -- A.1 Constants and units -- A.2 1+3 covariant equations -- A.3 Frequently used acronyms -- References -- Index.

Surveying key developments and open issues in cosmology for graduate students and researchers.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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