Relativity and Cosmology

From First Principles to Interpretations

1st Edition - January 22, 2024
Author: Balša Terzić
Language: English
Paperback ISBN:
9 7 8 - 0 - 4 4 3 - 2 3 5 4 2 - 9
eBook ISBN:
9 7 8 - 0 - 4 4 3 - 2 3 5 4 3 - 6

Relativity and Cosmology: From First Principles to Interpretations provides a high-quality and highly relevant astrophysics grounding for senior undergraduate students. This comp… Read more

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Relativity and Cosmology: From First Principles to Interpretations provides a high-quality and highly relevant astrophysics grounding for senior undergraduate students. This comprehensive textbook emphasizes an illustrative, pedagogical approach and aims to strike a balance between the breadth and depth of the material presented, frequently tying new material – relativistic mechanics and gravity – to the classical mechanics and gravity with which readers are more familiar. It includes robust content and corresponding exercises, figures, and appendices on many exciting developments, including relativistic mechanics; Newtonian classical mechanics; relativistic spacetime; special relativity; general relativity; tensor calculus; cosmology; Einstein’s field equations; dark matter; dark energy; and black holes.

This accessible edition delivers helpful and engaging additions to the role and importance of physics in cosmology and relativity. It is ideal for courses in physics, astrophysics, astronomy, and related subjects.

Cover image
Title page
Table of Contents
Copyright
Dedication
Praise for Relativity and Cosmology
Preface
Acknowledgments
Organization of the book
Chapter 1: Introduction
1.1. Motivation: Newton vs. Einstein
1.2. General relativity: a new theory of gravity
1.3. Book outline
Chapter 2: Special relativity
2.1. Newtonian (non-relativistic) physics
2.2. Foundational premises of special relativity
2.3. Lorentz transformations
2.4. Length contraction
2.5. Time dilation
2.6. Invariance of the volume element
2.7. Timelike, spacelike, and null intervals
2.8. Recovering Newtonian mechanics: special limit v≪c
2.9. Covariant and contravariant four-vectors
2.10. Energy–momentum four-vector
2.11. Spacetime diagrams
2.12. Geodesics: equations of motion from an action principle
2.13. What an observer observes
References
Chapter 3: The Equivalence Principle
3.1. Newtonian gravity is inconsistent with special relativity
3.2. The equivalence of gravitational and inertial mass
3.3. A scientific fable
3.4. Gravity as geometry
3.5. Geometric derivation of Newtonian gravity
Chapter 4: General relativity
4.1. Notation and conventions
4.2. General coordinate transformation
4.3. Spacetime coordinates and their metric tensors
4.4. Metric tensors
4.5. Freely falling frames
4.6. Area, volume, and four-volume
4.7. Vectors in curved spacetime
4.8. Covariant derivative
4.9. Geodesic equation
References
Chapter 5: Einstein's field equations
5.1. Bulk macroscopic description of matter: the Eulerian form
5.2. The energy–momentum tensor
5.3. The Riemann tensor, the Ricci tensor, the Ricci scalar, and the Einstein tensor
5.4. Evolution of energy density
5.5. Einstein's field equations
References
Chapter 6: The Schwarzschild metric and black holes
6.1. The Schwarzschild problem
6.2. Solving the Schwarzschild problem
6.3. Schwarzschild radius, event horizon, and black holes
6.4. Orbits in Schwarzschild's geometry
References
Chapter 7: The cosmological metric and Friedmann's equations
7.1. Hubble's law and the evolving Universe
7.2. Friedmann's equations
7.3. A Newtonian analogy to Friedmann's equations
References
Chapter 8: Solutions of Friedmann's equations
8.1. Cosmological models
8.2. Flat Universe (k=0, q0=1/2)
8.3. Closed Universe (k=+1, q0>1/2)
8.4. Open Universe (k=−1, q0<1/2)
8.5. Big Bang: a radiation/matter-dominated singularity
Chapter 9: Cosmological constant and the dark Universe
9.1. Age of a matter-dominated Friedmann Universe
9.2. Einstein's field equations revisited: cosmological constant
9.3. Age of the Universe revisited
9.4. Particle horizon revisited: the horizon problem
9.5. Possible solutions to the horizon problem
References
Chapter 10: Cosmic distances
10.1. Redshift
10.2. Proper distance
10.3. Comoving coordinates and comoving distance
10.4. Angular diameter distance
10.5. Luminosity distance
10.6. Particle horizon
Chapter 11: Summary of the foundations of cosmology
11.1. General relativity: kinematics in curved spacetime
11.2. Cosmology: solutions of Friedmann's equations
11.3. Expanding Universe
Chapter 12: Cosmic content
12.1. Particle distribution function
12.2. Particle distribution function of species
12.3. Entropy density
12.4. Cosmic microwave background photons
12.5. Cosmic neutrino background
12.6. Baryonic matter
12.7. Dark matter
12.8. Dark energy
References
Chapter 13: Brief history of the early Universe
13.1. Keeping track of the Universe's history
13.2. Early Universe at a glance: major benchmarks
13.3. Very early Universe: the first three minutes
13.4. Early Universe: the first 400,000 years
Chapter 14: Cosmic microwave background radiation
14.1. Importance of the CMB radiation
14.2. Systematic bias: the dipole anisotropy
14.3. Angular power spectrum
14.4. Scales in the angular power spectrum
14.5. Baryon acoustic oscillations
14.6. Physical effects affecting the CMB radiation
References
Epilogue
Further reading
References
Appendix A: An alternative Lagrangian
Appendix B: Geodesic equation in spherical coordinates
Appendix C: Example of metric conversion
Appendix D: Applying the geodesic equation
Appendix E: Matter–dark energy equality
Appendix F: Radiation–dark energy equality
Appendix G: Radiation–matter equality
Appendix H: Chemical potential
Appendix I: How to compute the relative abundances of the light elements
Dependence on various inputs
Basic trends
Realistic uncertainties
Appendix J: Equation of state for the perfect fluid
Appendix K: Origins of the large-scale structure in the Universe
Constants, units, and conversions
References
References
Index

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Balša Terzić