کیهان‌شناسی مدرن (ویرایش دوم)

__Modern Cosmology, Second Edition,__ provides a detailed introduction to the field of cosmology. Beginning with the smooth, homogeneous universe described by a Friedmann-Lemaître-Robertson-Walker metric, this trusted resource includes careful treatments of dark energy, big bang nucleosynthesis, recombination, and dark matter. The reader is then introduced to perturbations about an FLRW universe: their evolution with the Einstein-Boltzmann equations, their primordial generation by inflation, and their observational consequences: the acoustic peaks in the CMB; the __E/B__ decomposition in polarization; gravitational lensing of the CMB and large-scale structure; and the BAO standard ruler and redshift-space distortions in galaxy clustering. The Second Edition now also covers nonlinear structure formation including perturbation theory and simulations. The book concludes with a substantially updated chapter on data analysis. __Modern Cosmology, Second Edition,__ shows how modern observations are rapidly revolutionizing our picture of the universe, and supplies readers with all the tools needed to work in cosmology. Modern Cosmology, Second Edition (2021) i-iii. doi:10.1016/B978-0-12-815948-4.00002-4 Contents 6 About the authors 14 Preface 15 1 The concordance model of cosmology 17 1.1 A nutshell history of the universe 17 1.2 The Hubble diagram 22 1.3 Big Bang nucleosynthesis 24 1.4 The cosmic microwave background 25 1.5 Structure in the universe 26 1.6 ΛCDM: the concordance model of cosmology 31 1.7 Summary and outlook 32 Exercises 33 2 The expanding universe 36 2.1 Expanding space 36 2.1.1 The metric 37 2.1.2 The geodesic equation 41 2.2 Distances 45 2.3 Evolution of energy 49 2.4 Cosmic inventory 55 2.4.1 Photons 55 2.4.2 Baryons 56 2.4.3 Dark matter 57 2.4.4 Neutrinos 58 2.4.5 Epoch of matter-radiation equality 62 2.4.6 Dark energy 62 2.5 Summary 67 Exercises 68 3 The fundamental equations of cosmology 71 3.1 Einstein equations 71 3.2 Boltzmann equation 76 3.2.1 Boltzmann equation for particles in a harmonic potential 77 3.2.2 Boltzmann equation in an expanding universe 79 3.2.3 Collision terms 82 3.3 Beyond the homogeneous universe 84 3.3.1 Perturbed spacetime 85 3.3.2 The geodesic equation 87 3.3.3 The collisionless Boltzmann equation for radiation 91 3.3.4 The collisionless Boltzmann equation for massive particles 92 3.4 Summary 93 Exercises 95 4 The origin of species 98 4.1 The homogeneous Boltzmann equation revisited 98 4.2 Big Bang nucleosynthesis 101 4.2.1 Neutron abundance 104 4.2.2 Light element abundances 107 4.3 Recombination 108 4.4 Dark matter 112 4.5 Summary 119 Exercises 120 5 The inhomogeneous universe: matter & radiation 123 5.1 The collisionless Boltzmann equation for photons 124 5.2 Collision terms: Compton scattering 126 5.3 The Boltzmann equation for photons 131 5.4 The Boltzmann equation for cold dark matter 134 5.5 The Boltzmann equation for baryons 138 5.6 The Boltzmann equation for neutrinos 141 5.7 Summary 142 Exercises 145 6 The inhomogeneous universe: gravity 146 6.1 Scalar-vector-tensor decomposition 146 6.2 From gauge to gauge 148 6.3 The Einstein equations for scalar perturbations 152 6.3.1 Ricci tensor 152 6.3.2 Two components of the Einstein equations 154 6.4 Tensor perturbations 158 6.4.1 Christoffel symbol for tensor perturbations 159 6.4.2 Ricci tensor for tensor perturbations 160 6.4.3 Einstein equations for tensor perturbations 161 6.4.4 Verifying the decomposition theorem 164 6.5 Summary 165 Exercises 166 7 Initial conditions 168 7.1 The horizon problem and a solution 168 7.2 Inflation 174 7.3 Gravitational wave production 178 7.3.1 Quantizing the harmonic oscillator 179 7.3.2 Tensor perturbations 181 7.4 Scalar perturbations 184 7.4.1 Scalar field perturbations around an unperturbed background 186 7.4.2 Super-horizon perturbations 188 7.4.3 Spatially flat slicing 192 7.5 The Einstein-Boltzmann equations at early times 194 7.6 Summary 197 Exercises 200 8 Growth of structure: linear theory 206 8.1 Prelude 206 8.1.1 Three stages of evolution 207 8.1.2 Closing the Boltzmann hierarchy 211 8.2 Large scales 214 8.2.1 Super-horizon solution 214 8.2.2 Through horizon crossing 218 8.3 Small scales 220 8.3.1 Horizon crossing 220 8.3.2 Sub-horizon evolution 225 8.4 The transfer function 228 8.5 The growth factor 231 8.6 Beyond cold dark matter and radiation 233 8.6.1 Baryons 233 8.6.2 Massive neutrinos 235 8.6.3 Dark energy 236 8.7 Summary 236 Exercises 237 9 The cosmic microwave background 241 9.1 Overview 241 9.2 Large-scale anisotropies 247 9.3 Acoustic oscillations 248 9.3.1 Tightly-coupled limit of the Boltzmann equations 248 9.3.2 Tightly-coupled solutions 252 9.4 Diffusion damping 254 9.5 Inhomogeneities to anisotropies 257 9.5.1 Free streaming 257 9.5.2 The angular power spectrum 261 9.6 The CMB power spectrum 265 9.6.1 Large angular scales 265 9.6.2 Acoustic peaks 267 9.7 Cosmological parameters 269 9.7.1 Curvature and Λ 270 9.7.2 Amplitude, spectral index, and optical depth 272 9.7.3 Baryon and CDM densities 273 9.8 Summary 275 Exercises 276 10 The polarized CMB 280 10.1 Polarization 280 10.2 Generating polarization from Compton scattering 284 10.3 Polarization from a single plane wave 287 10.4 Boltzmann solution 292 10.5 Polarization power spectra 294 10.6 Detecting gravitational waves 297 10.7 Summary 300 Exercises 301 11 Probes of structure: tracers 303 11.1 Galaxy clustering 304 11.1.1 Galaxy statistics 307 11.1.2 Redshift-space distortions 309 11.1.3 BAO and Alcock-Paczyński 313 11.2 Angular correlations 319 11.3 The Sunyaev-Zel'dovich effect 323 11.4 Summary 328 Exercises 329 12 Growth of structure: beyond linear theory 332 12.1 Prelude 333 12.2 Perturbation theory 337 12.3 Simulations 350 12.4 Dark matter halos 354 12.4.1 Halo masses and profiles 356 12.4.2 The halo mass function 357 12.5 Galaxy clusters 362 12.6 Galaxy clustering and bias 366 12.7 The halo model 371 12.8 Summary 373 Exercises 376 13 Probes of structure: lensing 380 13.1 Overview 380 13.2 Photon geodesics 383 13.3 CMB lensing 388 13.4 Galaxy shapes 391 13.5 Weak-lensing statistics 395 13.5.1 Shear power spectrum 395 13.5.2 Shear correlation function 398 13.5.3 Shear cross-correlations 400 13.6 Summary 403 Exercises 404 14 Analysis and inference 407 14.1 The likelihood function 408 14.2 Overview: from raw data to parameter constraints 413 14.3 Mapmaking 415 14.4 Two-point functions 418 14.4.1 CMB power spectrum 419 14.4.2 Galaxy power spectrum 423 14.5 The Fisher matrix 427 14.6 Sampling the likelihood function 430 14.7 Summary 433 Exercises 434 A Solutions to selected exercises 438 Chapter 1 438 Exercise 1.1 438 Exercise 1.2 438 Exercise 1.4 439 Chapter 2 439 Exercise 2.1 439 Exercise 2.4 440 Exercise 2.5 440 Exercise 2.7 441 Exercise 2.8 442 Exercise 2.11 442 Chapter 3 443 Exercise 3.2 443 Exercise 3.6 445 Exercise 3.7 446 Exercise 3.8 446 Exercise 3.12 447 Chapter 4 447 Exercise 4.1 447 Exercise 4.6 449 Exercise 4.9 449 Chapter 5 449 Exercise 5.3 449 Exercise 5.4 450 Chapter 6 451 Exercise 6.1 451 Exercise 6.3 451 Exercise 6.8 451 Chapter 7 452 Exercise 7.2 452 Exercise 7.12 453 Exercise 7.13 453 Chapter 8 454 Exercise 8.4 454 Exercise 8.8 454 Exercise 8.13 455 Chapter 9 457 Exercise 9.2 457 Exercise 9.9 457 Exercise 9.16 457 Exercise 9.17 458 Chapter 10 459 Exercise 10.1 459 Exercise 10.6 460 Chapter 11 460 Exercise 11.1 460 Exercise 11.4 461 Exercise 11.8 461 Chapter 12 461 Exercise 12.4 461 Exercise 12.10 462 Exercise 12.13 464 Chapter 13 466 Exercise 13.1 466 Exercise 13.4 467 Chapter 14 467 Exercise 14.4 467 Exercise 14.10 468 B Numbers 470 B.1 Physical constants 470 B.2 Astrophysical constants 470 B.3 Fiducial cosmology 471 C Special functions 472 C.1 Legendre polynomials 472 C.2 Spherical harmonics 472 C.3 Spherical Bessel functions 474 C.4 Fourier transforms 475 C.5 Miscellaneous 475 D Symbols 477 D.1 Mathematical and geometrical definitions 477 D.2 Frequently used relations 477 D.3 Symbol definitions 478 Bibliography 481 Index 486 Modern Cosmology, Second Edition, provides a detailed introduction to the field of cosmology. Beginning with the smooth, homogeneous universe described by a Friedmann-Lemaître-Robertson-Walker metric, this trusted resource includes careful treatments of dark energy, big bang nucleosynthesis, recombination, and dark matter. The reader is then introduced to perturbations about an FLRW universe: their evolution with the Einstein-Boltzmann equations, their primordial generation by inflation, and their observational consequences: the acoustic peaks in the CMB; the E/B decomposition in polarization; gravitational lensing of the CMB and large-scale structure; and the BAO standard ruler and redshift-space distortions in galaxy clustering. The Second Edition now also covers nonlinear structure formation including perturbation theory and simulations. The book concludes with a substantially updated chapter on data analysis.Modern Cosmology, Second Edition, shows how modern observations are rapidly revolutionizing our picture of the universe, and supplies readers with all the tools needed to work in cosmology.- Offers a unique and practical approach for learning how to perform cosmological calculations. - New material on theory, simulations, and analysis of nonlinear structure.- Substantial updates on new developments in cosmology since the previous edition Modern Cosmology, Second Edition Provides A Detailed Introduction To The Field Of Cosmology. Beginning With The Smooth, Homogeneous Universe Described By A Friedmann-lemaître-robertson-walker Metric, This Trusted Resource Includes Careful Treatments Of Dark Energy, Big Bang Nucleosynthesis, Recombination, And Dark Matter. The Reader Is Then Introduced To Perturbations About An Flrw Universe: Their Evolution With The Einstein-boltzmann Equations, Their Primordial Generation By Inflation, And Their Observational Consequences: The Acoustic Peaks In The Cmb; The E/b Decomposition In Polarization; Gravitational Lensing Of The Cmb And Large-scale Structure; And The Bao Standard Ruler And Redshift-space Distortions In Galaxy Clustering. The Second Edition Now Also Covers Nonlinear Structure Formation Including Perturbation Theory And Simulations. The Book Concludes With A Substantially Updated Chapter On Data Analysis. Modern Cosmology, Second Edition Shows How Modern Observations Are Rapidly Revolutionizing Our Picture Of The Universe, And Supplies Readers With All The Tools Needed To Work In Cosmology. Offers A Unique And Practical Approach For Learning How To Perform Cosmological Calculations. New Material On Theory, Simulations, And Analysis Of Nonlinear Structure. Substantial Updates On New Developments In Cosmology Since The Previous Edition. Modern Cosmology, Second Edition, provides a detailed introduction to the field of cosmology. Beginning with the smooth, homogeneous universe described by a Friedmann-Lemaître-Robertson-Walker metric, this trusted resource includes careful treatments of dark energy, big bang nucleosynthesis, recombination, and dark matter. The reader is then introduced to perturbations about an FLRW universe: their evolution with the Einstein-Boltzmann equations, their primordial generation by inflation, and their observational consequences: the acoustic peaks in the CMB; the E/B decomposition in polarization; gravitational lensing of the CMB and large-scale structure; and the BAO standard ruler and redshift-space distortions in galaxy clustering. The Second Edition now also covers nonlinear structure formation including perturbation theory and simulations. The book concludes with a substantially updated chapter on data analysis. Modern Cosmology, Second Edition, shows how modern observations are rapidly revolutionizing our picture of the universe, and supplies readers with all the tools needed to work in cosmology.-- Source other than the Library of Congress