Modern Cosmology
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Table of contents
- Contentsv
- Chapter 1. The Standard Model and Beyond1
- 1.1 The Expanding Universe1
- 1.2 The Hubble Diagram7
- 1.3 Big Bang Nucleosynthesis9
- 1.4 The Cosmic Microwave Background13
- 1.5 Beyond the Standard Model14
- 1.6 Summary19
- Exercises21
- Chapter 2. The Smooth, Expanding Universe23
- 2.1 General Relativity23
- 2.2 Distances33
- 2.3 Evolution of Energy37
- 2.4 Cosmic Inventory40
- 2.5 Summary51
- Exercises53
- Chapter 3. Beyond Equilibrium58
- 3.1 Boltzmann Equation for Annihilation59
- 3.2 Big Bang Nucleosynthesis62
- 3.3 Recombination70
- 3.4 Dark Matter73
- 3.5 Summary78
- Exercises80
- Chapter 4. The Boltzmann Equations84
- 4.1 The Boltzmann Equation for the Harmonic Oscillator85
- 4.2 The Collisionless Boltzmann Equation for Photons87
- 4.3 Collision Terms: Compton Scattering95
- 4.4 The Boltzmann Equation for Photons100
- 4.5 The Boltzmann Equation for Cold Dark Matter102
- 4.6 The Boltzmann Equation for Baryons106
- 4.7 Summary110
- Exercises113
- Chapter 5. Einstein Equations117
- 5.1 The Perturbed Ricci Tensor and Scalar117
- 5.2 Two Components of the Einstein Equations121
- 5.3 Tensor Perturbations124
- 5.4 The Decomposition Theorem131
- 5.5 From Gauge to Gauge132
- 5.6 Summary135
- Exercises136
- Chapter 6. Initial Conditions139
- 6.1 The Einstein-Boltzmann Equations at Early Times139
- 6.2 The Horizon142
- 6.3 Inflation144
- 6.4 Gravity Wave Production155
- 6.5 Scalar Perturbations162
- 6.6 Summary and Spectral Indices170
- Exercises175
- Chapter 7. Inhomogeneities180
- 7.1 Prelude180
- 7.2 Large Scales189
- 7.3 Small Scales194
- 7.4 Numerical Results and Fits203
- 7.5 Growth Function205
- 7.6 Beyond Cold Dark Matter207
- Exercises212
- Chapter 8. Anisotropies216
- 8.1 Overview217
- 8.2 Large-Scale Anisotropies222
- 8.3 Acoustic Oscillations224
- 8.4 Diffusion Damping230
- 8.5 Inhomogeneities to Anisotropies234
- 8.6 The Anisotropy Spectrum Today243
- 8.7 Cosmological Parameters248
- Exercises257
- Chapter 9. Probes of Inhomogeneities261
- 9.1 Angular Correlations262
- 9.2 Peculiar Velocities270
- 9.3 Direct Measurements of Peculiar Velocities271
- 9.4 Redshift Space Distortions275
- 9.5 Galaxy Clusters282
- Exercises289
- Chapter 10. Weak Lensing and Polarization292
- 10.1 Gravitational Distortion of Images293
- 10.2 Geodesics and Shear296
- 10.3 Ellipticity as an Estimator of Shear300
- 10.4 Weak Lensing Power Spectrum302
- 10.5 Polarization: The Quadrupole and the Q/U Decomposition310
- 10.6 Polarization from a Single Plane Wave313
- 10.7 Boltzmann Solution320
- 10.8 Polarization Power Spectra323
- 10.9 Detecting Gravity Waves326
- Exercises331
- Chapter 11. Analysis336
- 11.1 The Likelihood Function337
- 11.2 Signal Covariance Matrix344
- 11.3 Estimating the Likelihood Function356
- 11.4 The Fisher Matrix: Limits and Applications368
- 11.5 Mapmaking and Inversion375
- 11.6 Systematics378
- Exercises389
- Appendix A. Solutions to Selected Problems392
- Appendix B. Numbers415
- B.1 Physical Constants415
- B.2 Cosmological Constants416
- Appendix C. Special Functions418
- C.1 Legendre Polynomials418
- C.2 Spherical Harmonics418
- C.3 Spherical Bessel Functions419
- C.4 Fourier Transforms420
- C.5 Miscellaneous420
- Appendix D. Symbols422
- Bibliography426
- Index435
- Color Plate SectionColor Plat
Modern Cosmology begins with an introduction to the smooth, homogeneous universe described by a Friedman-Robertson-Walker metric, including careful treatments of dark energy, big bang nucleosynthesis, recombination, and dark matter. From this starting point, the reader is introduced to perturbations about an FRW universe: their evolution with the Einstein-Boltzmann equations, their generation by primordial inflation, and their observational consequences. These consequences include the anisotropy spectrum of the cosmic microwave background (CMB) featuring acoustic peaks and polarization, the matter power spectrum with baryonic wiggles, and their detection via photometric galaxy surveys, redshift distortions, cluster abundances, and weak lensing. The book concludes with a long chapter on data analysis.
Modern Cosmology is the first book to explain in detail the structure of the acoustic peaks in the CMB, the E/B decomposition in polarization which may allow for detection of primordial gravity waves, and the modern analysis techniques used on increasingly large cosmological data sets. Readers will gain the tools needed to work in cosmology and learn how modern observations are rapidly revolutionizing our picture of the universe.
* Provides foundations, calculations, and interpretations which illuminate current thinking in cosmology
* Covers the major advances in cosmology over the past decade
* Includes over 100 unique, pedagogical figures
Modern Cosmology is the first book to explain in detail the structure of the acoustic peaks in the CMB, the E/B decomposition in polarization which may allow for detection of primordial gravity waves, and the modern analysis techniques used on increasingly large cosmological data sets. Readers will gain the tools needed to work in cosmology and learn how modern observations are rapidly revolutionizing our picture of the universe.
* Provides foundations, calculations, and interpretations which illuminate current thinking in cosmology
* Covers the major advances in cosmology over the past decade
* Includes over 100 unique, pedagogical figures