Introduction to General Relativity and Cosmology

Preface
Acknowledgments
About the Author
Ian R. Kenyon
Author Tribute
Physical Constants and Parameters
Chapter 1 Introduction
1.1 Prologue
1.2 Einstein’s Insight
1.3 Structures Seen Today
1.4 Hubble’s Law
1.5 Olbers’ Paradox
1.6 The Big Bang and the Cosmic Microwave Background
1.7 Inflation
1.8 Dark Matter
1.9 Structure Formation
1.10 Dark Energy
1.11 The Model of the Universe
1.12 The Telescopes
1.13 Luminosity
1.14 Summary of Results in Special Relativity
1.15 Exercises
Further Reading
References
Chapter 2 The Equivalence Principle
2.1 The Equivalence Principle
2.2 Experimental Tests of the Equivalence Principle
2.3 Lunar Laser Ranging
2.4 The Gravitational Spectral Shift and the Deflection of Light
2.5 Exercises
Further Reading
References
Chapter 3 Space and Spacetime Curvature
3.1 Two-dimensional Surfaces
3.2 Measurement of Curvature
3.3 Local Vectors and Parallel Transport
3.4 Curvature and the Metric Equation
3.5 The Metric Equation of Special Relativity
3.6 Geodesics, Tidal Acceleration, and Curvature
3.7 The Schwarzschild Metric
3.8 Exercises
Further Reading
References
Chapter 4 Elementary Tensor Analysis
4.1 General Transformations
4.2 Vector and Covector Components
4.3 Other Tensors
4.4 Exercises
Further Reading
Chapter 5 Einstein’s Theory I
5.1 The Covariant Derivative
5.2 The Calculation of the Metric Connection
5.3 More on the Covariant Derivative
5.4 The Principle of Generalized Covariance
5.5 The Geodesic Equation
5.6 Geodesics as Stationary Paths
5.7 Familiar Quantities
5.8 Exercises
Further Reading
Chapter 6 Einstein’s Theory II
6.1 The Riemann Curvature Tensor
6.2 The Stress–Energy Tensor
6.3 Einstein’s equation
6.4 The Newtonian Limit
6.5 Exercises
Chapter 7 Tests of General Relativity
7.1 The Perihelion Advance of Mercury
7.2 The Deflection of Light by the Sun
7.3 Radar Echo Delays
7.4 Geodetic and Frame Dragging Effects
7.5 Gravitational Lensing
7.6 Exercises
Further Reading
References
Chapter 8 Black Holes
8.1 The Spacetime Structure
8.2 Orbits Around Black Holes
8.3 Rotating Black Holes
8.4 The Planck Scale
8.5 Hawking Radiation
8.6 Black Hole Thermodynamics
8.7 The Information Paradox
8.8 Stellar Black Holes
8.9 Cygnus X-1
8.10 Supermassive Black Holes
8.11 Active Galactic Nuclei
8.12 Exercises
Further Reading
References
Chapter 9 The Discovery and Study of Gravitational Waves
9.1 Properties of Gravitational Radiation
9.2 The Effects of Gravitational Waves
9.3 PSR 1913+16
9.4 The LIGO and Virgo Interferometers
9.5 The Interferometers
9.6 The Standard Quantum Limit
9.6.1 Cavity Enhancement
9.7 Squeezing
9.8 GW170817 and the Velocity of Gravitational Waves
9.9 Exercises
Further Reading
References
Chapter 10 Cosmic Dynamics
10.1 Introduction
10.2 Flat and Spatially-curved Universes
10.3 The Friedmann–Robertson–Walker Metric
10.3.1 The Comoving Frame
10.4 The Friedmann–Le Maître equations
10.5 Models of the Universe
10.6 Radiation, Matter and Λ Dominated Eras
10.7 The ΛCDM Model
10.8 Exercises
Further Reading
References
Chapter 11 Distances, Horizons and Measurements
11.1 Introduction
11.2 Proper Distance and Horizons
11.3 Measuring Distance
11.3.1 Cosmology Calculators
11.4 Exercises
Further Reading
Chapter 12 Cosmic Microwave Background
12.1 Introduction
12.2 The Origin of the Cosmic Microwave Background
12.3 Thermal Fluctuations
12.4 Interpreting the Power Spectrum
12.5 The Sachs–Wolfe Plateau
12.6 The Three-dimensional Power Spectrum
12.7 Optical Depth
12.8 Polarization
12.9 The Horizon Distance
12.10 Neutrino Decoupling
12.11 Exercises
Further Reading
References
Chapter 13 Inflation in the Early Universe
13.1 The Horizon and Flatness Problems
13.2 Inflation
13.3 The Vacuum Transition
13.4 Plasma Wave Coherence
13.5 Slow Roll Inflation
13.6 Exercises
Further Reading
References
Chapter 14 Big Bang Nucleosynthesis
14.1 Timeline
14.2 Big Bang Nucleosynthesis
14.3 The Neutron Decay
14.4 Deuterium Formation
14.5 4He Formation
14.6 Primordial Abundances: Prediction and Measurement
14.7 Exercises
Further Reading
References
Chapter 15 Structure Origins
15.1 Introduction
15.2 Gravitational Instability
15.3 Instability in an Expanding Universe
15.4 Collapse and Virialization
15.5 Baryonic Gas Cloud
15.6 Growth of Structures
15.7 Baryon Acoustic Oscillations
15.8 Exercises
Further Reading
References
Chapter 16 Baryonic Structures
16.1 Introduction
16.2 The Cooling of Baryonic Matter
16.3 First Light and Reionization
16.4 The Lyα Forest
16.5 Formation of Stars
16.5.1 The Initial Mass Function
16.6 Galaxies
16.6.1 Low Redshift Galaxies’ Stellar Mass Distributions
16.7 Clusters and Superclusters of Galaxies
16.8 Intergalactic Baryonic Matter
16.9 Exercises
Further Reading
References
Chapter 17 The Dark Sector
17.1 Introduction
17.2 Dark Matter
17.3 Gravitational Lensing
17.4 MACHOs
17.5 Cosmic Shearing
17.6 The Bullet Cluster
17.7 Dark Energy
17.8 SNe Ia and the Distance Scale
17.9 What Is Dark Energy?
17.10 Exercises
Further Reading
References
Appendix A
Appendix B
Appendix C
Appendix D
Appendix E
Appendix F
References
Appendix G
Appendix H