Modern cosmology / Scott Dodelson.

Format:

Book

Author/Creator:

Dodelson, Scott.

Contributor:

Alumni and Friends Memorial Book Fund.

Language:

English

Subjects (All):

Cosmology.

Physical Description:

xiii, 440 pages : illustrations ; 24 cm

Place of Publication:

San Diego, Calif. : Academic Press, [2003]

Summary:

Cosmology, the attempt to understand the nature and history of the universe and all it contains, is the largest and broadest conceivable subject in science. Over the last decade, cosmology has emerged as a mature science. Theories of the universe are now well developed, and there is more data than ever before. Therefore, many of the old cosmology books are obsolete.

Twenty years ago, theorists and observers agreed that the early universe was basically smooth, but they could not agree on how the clumps (inhomogeneities), such as galaxies, emerge from this smoothness (anisotropies). Today scientists agree that the deviations from smoothness -- anisotropies and inhomogeneities -- can be both measured observationally and understood theoretically. It is these deviations to which Modern Cosmology, and indeed much of cosmological research, is devoted.

Contents:

1 The Standard Model and Beyond 1

1.1 The Expanding Universe 1

1.2 The Hubble Diagram 7

1.3 Big Bang Nucleosynthesis 9

1.4 The Cosmic Microwave Background 13

1.5 Beyond the Standard Model 14

2 The Smooth, Expanding Universe 23

2.1 General Relativity 23

2.1.1 The Metric 24

2.1.2 The Geodesic Equation 28

2.1.3 Einstein Equations 32

2.2 Distances 33

2.3 Evolution of Energy 37

2.4 Cosmic Inventory 40

2.4.1 Photons 40

2.4.2 Baryons 41

2.4.3 Matter 42

2.4.4 Neutrinos 44

2.4.5 Dark Energy 47

2.4.6 Epoch of Matter-Radiation Equality 50

3 Beyond Equilibrium 58

3.1 Boltzmann Equation for Annihilation 59

3.2 Big Bang Nucleosynthesis 62

3.2.1 Neutron Abundance 65

3.2.2 Light Element Abundances 68

3.3 Recombination 70

3.4 Dark Matter 73

4 The Boltzmann Equations 84

4.1 The Boltzmann Equation for the Harmonic Oscillator 85

4.2 The Collisionless Boltzmann Equation for Photons 87

4.2.1 Zero-Order Equation 93

4.2.2 First-Order Equation 94

4.3 Collision Terms: Compton Scattering 95

4.4 The Boltzmann Equation for Photons 100

4.5 The Boltzmann Equation for Cold Dark Matter 102

4.6 The Boltzmann Equation for Baryons 106

5 Einstein Equations 117

5.1 The Perturbed Ricci Tensor and Scalar 117

5.1.1 Christoffel Symbols 118

5.1.2 Ricci Tensor 119

5.2 Two Components of the Einstein Equations 121

5.3 Tensor Perturbations 124

5.3.1 Christoffel Symbols for Tensor Perturbations 125

5.3.2 Ricci Tensor for Tensor Perturbations 127

5.3.3 Einstein Equations for Tensor Perturbations 129

5.4 The Decomposition Theorem 131

5.5 From Gauge to Gauge 132

6 Initial Conditions 139

6.1 The Einstein-Boltzmann Equations at Early Times 139

6.2 The Horizon 142

6.3 Inflation 144

6.3.1 A Solution to the Horizon Problem 146

6.3.2 Negative Pressure 151

6.3.3 Implementation with a Scalar Field 151

6.4 Gravity Wave Production 155

6.4.1 Quantizing the Harmonic Oscillator 156

6.4.2 Tensor Perturbations 157

6.5 Scalar Perturbations 162

6.5.1 Scalar Field Perturbations around a Smooth Background 162

6.5.2 Super-Horizon Perturbations 164

6.5.3 Spatially Flat Slicing 169

6.6 Summary and Spectral Indices 170

7 Inhomogeneities 180

7.1.1 Three Stages of Evolution 182

7.2 Large Scales 189

7.2.1 Super-horizon Solution 189

7.2.2 Through Horizon Crossing 192

7.3 Small Scales 194

7.3.1 Horizon Crossing 195

7.3.2 Sub-horizon Evolution 199

7.4 Numerical Results and Fits 203

7.5 Growth Function 205

7.6 Beyond Cold Dark Matter 207

7.6.1 Baryons 208

7.6.2 Massive Neutrinos 209

7.6.3 Dark Energy 210

8 Anisotropies 216

8.2 Large-Scale Anisotropies 223

8.3 Acoustic Oscillations 224

8.3.1 Tightly Coupled Limit of the Boltzmann Equations 224

8.3.2 Tightly Coupled Solutions 227

8.4 Diffusion Damping 230

8.5 Inhomogeneities to Anisotropies 234

8.5.1 Free Streaming 234

8.5.2 The C[subscript l]'s 239

8.6 The Anisotropy Spectrum Today 242

8.6.1 Sachs-Wolfe Effect 242

8.6.2 Small Scales 245

8.7 Cosmological Parameters 248

8.7.1 Curvature 249

8.7.2 Degenerate Parameters 251

8.7.3 Distinct Imprints 253

9 Probes of Inhomogeneities 261

9.1 Angular Correlations 262

9.2 Peculiar Velocities 270

9.3 Direct Measurements of Peculiar Velocities 271

9.4 Redshift Space Distortions 275

9.5 Galaxy Clusters 282

10 Weak Lensing and Polarization 292

10.1 Gravitational Distortion of Images 293

10.2 Geodesics and Shear 296

10.3 Ellipticity as an Estimator of Shear 300

10.4 Weak Lensing Power Spectrum 302

10.5 Polarization: The Quadrupole and the Q/U Decomposition 310

10.6 Polarization from a Single Plane Wave 313

10.7 Boltzmann Solution 320

10.8 Polarization Power Spectra 323

10.9 Detecting Gravity Waves 326

11 Analysis 336

11.1 The Likelihood Function 337

11.1.2 CMB Likelihood 340

11.1.3 Galaxy Surveys 343

11.2 Signal Covariance Matrix 344

11.2.1 CMB Window Functions 345

11.2.2 Examples of CMB Window Functions 347

11.2.3 Window Functions for Galaxy Surveys 350

11.3 Estimating the Likelihood Function 356

11.3.1 Karhunen-Loeve Techniques 356

11.3.2 Optimal Quadratic Estimator 362

11.4 The Fisher Matrix: Limits and Applications 368

11.4.1 CMB 368

11.4.2 Galaxy Surveys 370

11.4.3 Forecasting 371

11.5 Mapmaking and Inversion 375

11.6 Systematics 378

11.6.1 Foregrounds 378

11.6.2 Mode Subtraction 384

B Numbers 415

B.1 Physical Constants 415

B.2 Cosmological Constants 416

C Special Functions 418

C.1 Legendre Polynomials 418

C.2 Spherical Harmonics 418

C.3 Spherical Bessel Functions 419

C.4 Fourier Transforms 420.

Notes:

Includes bibliographical references (pages 426-434) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Alumni and Friends Memorial Book Fund.

ISBN:

0122191412

OCLC:

50271486