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E-grāmata: Cosmology

(Universitą di Roma Tor Vergata, Roma, Italy)
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Modern cosmology has changed significantly over the years, from the discovery to the precision measurement era. The data now available provide a wealth of information, mostly consistent with a model where dark matter and dark energy are in a rough proportion of 3:7. The time is right for a fresh new textbook which captures the state-of-the art in cosmology.

Written by one of the world's leading cosmologists, this brand new, thoroughly class-tested textbook provides graduate and undergraduate students with coverage of the very latest developments and experimental results in the field. Prof. Nicola Vittorio shows what is meant by precision cosmology, from both theoretical and observational perspectives.

This book is divided into three main parts:











Part I provides a pedagogical, but rigorous, general relativity-based discussion of cosmological models, showing the evidence for dark energy, the constraints from primordial nucleosynthesis and the need for inflation











Part II introduces density fluctuations and their statistical description, discussing different theoretical scenarios, such as CDM, as well as observations















Part III introduces the general relativity approach to structure formation and discusses the physics behind the CMB temperature and polarization pattern of the microwave sky

Carefully adapted from the course taught by Prof. Vittorio at the University of Rome Tor Vergata, this book will be an ideal companion for advanced students undertaking a course in cosmology.

Features:





Incorporates the latest experimental results, at a time of rapid change in this field, with balanced coverage of both theoretical and experimental perspectives Each chapter is accompanied by problems, with detailed solutions The basics of tensor calculus and GR are given in the appendices

Recenzijas

"The material is well presented, the equations are rigorously derived and complemented by the physical insight of an expert in the field, and all chapters are accompanied by useful exercises and their solutionsthis book is a valuable and well-written introduction to the very active field of observational cosmology. It will serve as a welcome complement to the current literature in the field and will be very useful, especially for PhD students entering the field of cosmology." Ruth Durrer, Department de Physique Theorique, Universite de Geneve

"This textbook provides a full exploration of the developments in cosmological studies over the past hundred years; from the invention of General Relativity (GR) and the somewhat academic earlier exercises of its applications to the Universe, to the present practices of "precision cosmology", as a result of an impressive sequence of extensive observations and discoveries. The text is very clear, well-written throughout, and its various topics are all treated with mathematical rigour. The book has 14 chapters, which are conveniently organized into three main sections, and each chapter ends with a number of exercises and fully-developed solutions, which provide further tools for a deeper understanding of the subject matters discussed. More than 350 well-selected figures (in black and white) clarify the texts physical assumptions, findings, and formal mathematical treatment. In addition, five appendices illustrate the basic mathematical tools required for a fuller appreciation of the GR theory, which is the foundation at the heart of our present understanding of cosmology. And finally, the bibliography of more than 200 entries will enable the keen student to locate the original works quoted in the text. The contents of the first, and at least parts of the second, section can also be used as a tutorial for students approaching the studies of cosmology, while the remaining parts of the textbook

List of Figures
xix
List of Tables
xxiii
Preface xxv
Section I Background universe
Chapter 1 Cosmological models
3(26)
1.1 Introduction
3(1)
1.2 Synchronous Reference Frame
3(2)
1.3 Friedmann-Robertson-Walker Metric
5(5)
1.3.1 Field equations
6(1)
1.3.2 Spatial sector of FRW space-time
7(3)
1.3.3 FRW metric in trigonometric form
10(1)
1.4 Friedmann Equations
10(1)
1.5 Cosmological Constant
11(1)
1.6 Conservation Laws
12(1)
1.7 Cosmological Parameters
13(1)
1.8 Dust-Filled Universes
14(2)
1.8.1 Closed universe
14(1)
1.8.2 Flat or open universe
15(1)
1.9 Cosmological Models
16(8)
1.9.1 Milne model
16(2)
1.9.2 Einstein static model
18(1)
1.9.3 de Sitter model
18(1)
1.9.4 Closed Friedmann universe
19(2)
1.9.5 Einstein-de Sitter universe
21(1)
1.9.6 Open Friedmann universe
21(1)
1.9.7 Concordance model
22(2)
1.10 Exercises
24(1)
1.11 Solutions
25(4)
Chapter 2 Measurable properties of FRW models
29(28)
2.1 Introduction
29(1)
2.2 Observable Universe
29(2)
2.2.1 Cosmological redshift
30(1)
2.2.2 Hubble flow
30(1)
2.3 Comoving Distances and Coordinates
31(7)
2.3.1 Closed Friedmann model
33(1)
2.3.2 Einstein-de Sitter model
33(1)
2.3.3 Open Friedmann model
33(2)
2.3.4 Concordance model
35(1)
2.3.5 Particle horizon
35(3)
2.4 Angular Diameter Distance VA
38(3)
2.4.1 Closed Friedmann model
38(1)
2.4.2 Einstein-de Sitter model
39(1)
2.4.3 Open Friedmann model
39(2)
2.4.4 Concordance model
41(1)
2.5 Luminosity Distance DL
41(2)
2.6 Comoving Volume and Number Counts
43(1)
2.7 Distance Indicators
44(3)
2.7.1 Cepheids
45(1)
2.7.2 Supernovae Ia
46(1)
2.8 Ho and Age of Universe
47(4)
2.8.1 H0 determination
48(2)
2.8.2 Age of universe
50(1)
2.9 Supernovae Ia and Dark Energy
51(3)
2.10 Exercises
54(1)
2.11 Solutions
55(2)
Chapter 3 Hot Big Bang model
57(28)
3.1 Introduction
57(1)
3.2 Cosmic Microwave Background
57(2)
3.3 Hot Big Bang
59(5)
3.3.1 Baryon-to-photon ratio
61(1)
3.3.2 Friedmann equation
61(1)
3.3.3 Radiation-dominated universe
62(2)
3.4 Neutron-To-Baryon Ratio
64(3)
3.5 Neutrino Cosmic Background
67(2)
3.6 Refined Estimate Of XN
69(1)
3.7 Primordial Helium Production
70(3)
3.8 Primordial Deuterium and Light Elements
73(2)
3.9 Recombination
75(7)
3.9.1 Saha approximation
76(1)
3.9.2 Out-of-equilibrium recombination
77(3)
3.9.3 Last scattering surface
80(2)
3.10 Exercises
82(1)
3.11 Solutions
83(2)
Chapter 4 Inflation
85(24)
4.1 Introduction
85(1)
4.2 Puzzles of Standard Model
85(5)
4.2.1 Horizon problem
85(3)
4.2.2 Curvature problem
88(2)
4.3 Cosmic Inflation As Solution
90(2)
4.4 De Sitter Inflation
92(1)
4.5 Slow-Roll Scenario
93(2)
4.6 Slow-Roll Parameters
95(1)
4.7 Inflationary Models
96(8)
4.7.1 Exponential potential
97(3)
4.7.2 Power law potential
100(4)
4.8 Exercises
104(1)
4.9 Solutions
105(4)
Section II Structure formation: A Newtonian approach
Chapter 5 Gravitational instability scenario
109(24)
5.1 Introduction
109(1)
5.2 Creating Spherical "Seed"
109(2)
5.3 Formation of Cosmic Structure
111(3)
5.4 Linear Approximations
114(5)
5.4.1 Density fluctuations
116(1)
5.4.2 Peculiar velocities
117(1)
5.4.3 Potential fluctuations
118(1)
5.4.4 Some remarks
118(1)
5.5 Density Fluctuation Field
119(3)
5.5.1 Continuity equation
120(1)
5.5.2 Poisson equation
121(1)
5.5.3 Euler equation
121(1)
5.6 Gravitational Instability Equation
122(1)
5.7 Gravity-Dominated Regime
123(3)
5.7.1 Critical universe
123(1)
5.7.2 Open universe
123(2)
5.7.3 Flat ΩΔ models
125(1)
5.8 Peculiar Velocities
126(3)
5.8.1 Rotational velocities
127(1)
5.8.2 Potential velocities
127(2)
5.9 Pressure-Dominated Regime
129(1)
5.10 Exercises
130(1)
5.11 Solutions
131(2)
Chapter 6 Density fluctuations: Statistical tools and observables
133(28)
6.1 Introduction
133(1)
6.2 Random Gaussian Fields
133(3)
6.3 Spectral Decomposition
136(1)
6.4 Variance of Density Fluctuation Field On Given Scale
137(1)
6.5 Random Point Process
138(1)
6.6 Estimators of Galaxy-Galaxy Correlation Function
139(2)
6.7 Observations
141(4)
6.7.1 Galaxy-galaxy correlation function on 0.1 < r(h-1Mpc) < 30
143(1)
6.7.2 Cluster-cluster correlation function on 1 < r(h-1Mpc) < 100
144(1)
6.8 Statistics of Peaks
145(4)
6.9 Peculiar Velocities As Random Field
149(1)
6.10 Cmb Dipole and Large-Scale Flows
150(3)
6.10.1 CMB dipole
150(2)
6.10.2 Bulk flows
152(1)
6.11 Pairwise Velocity Dispersion and β Parameter
153(4)
6.11.1 Plane-parallel limit in linear theory
153(2)
6.11.2 Biased galaxy formation
155(1)
6.11.3 β factor
155(2)
6.12 Exercises
157(1)
6.13 Solutions
158(3)
Chapter 7 Luminous universe
161(18)
7.1 Introduction
161(1)
7.2 Initial Conditions
161(3)
7.3 Sound Speed
164(2)
7.4 Drag Epoch and Sound Horizon
166(2)
7.5 Diffusion-Dominated Regime
168(1)
7.6 Transfer Function
169(3)
7.7 Expected Cmb Anisotropy: Back-of-Envelope Calculation
172(1)
7.8 Isocurvature Perturbations
173(2)
7.9 Meszaros Effect
175(1)
7.10 Exercises
176(1)
7.11 Solutions
177(2)
Chapter 8 Dark universe
179(26)
8.1 Introduction
179(1)
8.2 Flat Massive Neutrino-Dominated Universe
180(2)
8.3 Neutrino Free Streaming
182(2)
8.4 Gravitational Instability In Massive Neutrino-Dominated Universe
184(3)
8.5 Two-Component Universe: Baryons and Massive Neutrinos
187(3)
8.6 Drawbacks of Hdm Scenario
190(2)
8.7 Weakly Interacting Massive Particles
192(1)
8.8 Gravitational Instability In CDM Component
192(2)
8.9 CDM Transfer Function
194(2)
8.10 RMS CDM Density Fluctuations
196(2)
8.11 Bulk Flows
198(2)
8.12 Concordance Model
200(5)
Section III Structure formation: A relativistic approach
Chapter 9 Lemaitre-Tolman-Bondi solution
205(24)
9.1 Introduction
205(1)
9.2 Geometry of Space-Time
205(1)
9.3 Conservation Equations
206(1)
9.4 Field Equations
207(2)
9.4.1 Time-space component
207(1)
9.4.2 Time-time component
208(1)
9.4.3 Mass function m(r, t)
208(1)
9.4.4 g11 element of metric tensor
209(1)
9.5 Function ε2
209(1)
9.6 Equation of Motion
210(2)
9.7 Time-Time Component of Metric Tensor
212(1)
9.8 Pressureless Configuration
213(1)
9.8.1 Proper time and coordinate time
213(1)
9.8.2 Observable mass
214(1)
9.8.3 ε function
214(1)
9.8.4 Space-time metric
214(1)
9.9 Dynamics of Pressureless Mass Distribution
214(2)
9.10 Parabolic Uniform Case
216(1)
9.11 Formation of Cosmic Structure
217(2)
9.12 Formation of Cosmic Void
219(2)
9.13 Accelerating Universe?
221(5)
9.14 Exercises
226(1)
9.15 SOlutions
227(2)
Chapter 10 Structure formation: Relativistic approach I
229(30)
10.1 Introduction
229(1)
10.2 Background Universe
229(1)
10.3 Perturbed Frw Space-Time
230(1)
10.4 Helmholtz Theorem
231(1)
10.5 SVT Decomposition
232(1)
10.6 Perturbed Energy-Momentum Tensor
233(1)
10.7 Choosing Gauges
234(3)
10.7.1 Perturbed metric tensor
235(1)
10.7.2 Perturbed energy-momentum tensor
236(1)
10.7.3 Different gauge choices
237(1)
10.8 Perturbed Field Equations In Synchronous Gauge
237(1)
10.9 Perturbed Conservation Laws In Synchronous Gauge
238(2)
10.10 Super-Horizon Perturbations In Synchronous Gauge
240(2)
10.10.1 Matter-dominated universes
240(1)
10.10.2 Radiation-dominated universes
240(1)
10.10.3 Gauge modes
241(1)
10.11 Sub-Horizon Perturbations In Synchronous Gauge
242(1)
10.12 Gauge-Invariant Formalism
243(1)
10.13 Perturbations In Longitudinal Gauge
244(2)
10.14 Gauge-Invariant Evolution of Scalar Degrees of Freedom
246(1)
10.15 Perturbed Conservation Laws In Longitudinal Gauge
247(1)
10.16 Super-Horizon Perturbations In Longitudinal Gauge
247(4)
10.17 Exercises
251(1)
10.18 Solutions
252(7)
Chapter 11 Structure formation: Relativistic approach II
259(20)
11.1 Introduction
259(1)
11.2 Synchronous Gauge: Liouville Equation
259(3)
11.2.1 Massive particles
259(2)
11.2.2 Massless particles
261(1)
11.3 Synchronous Gauge: Boltzmann Equation
262(3)
11.4 Synchronous Gauge: Coupling of Matter and Radiation
265(1)
11.5 Synchronous Gauge: Tight Coupling Limit
266(1)
11.6 Synchronous Gauge: Photon Diffusion
267(2)
11.7 Synchronous Gauge: Energy-Momentum Tensor for Collisionless Particles
269(2)
11.8 Longitudinal Gauge: Liouville Equation
271(4)
11.9 Exercises
275(1)
11.10 Solutions
276(3)
Chapter 12 CMB temperature anisotropy
279(30)
12.1 Introduction
279(1)
12.2 Flat CDM Universe In Synchronous Gauge
279(1)
12.3 Free Streaming Solution
280(3)
12.4 CMB Anisotropy Correlation Function
283(2)
12.5 CMB Dipole Anisotropy
285(1)
12.6 Sachs-Wolfe Effect
286(3)
12.6.1 Cl coefficients
287(2)
12.7 First Detection Of CMB Anisotropies: COBE DMR Experiment
289(1)
12.8 CMB Angular Power Spectrum
290(3)
12.9 Acoustic Peaks
293(6)
12.9.1 Numerical approach
294(4)
12.9.2 Analytical approach
298(1)
12.10 Dependence On Cosmological Parameters
299(7)
12.10.1 Lowering Δ0 (ΔA = 0)
299(1)
12.10.2 Lowering Δ0 (Δk = 0)
300(1)
12.10.3 Effect of baryons
301(2)
12.10.4 Effect of late reheating of intergalactic medium
303(3)
12.11 Exercises
306(1)
12.12 Solutions
307(2)
Chapter 13 CMB polarisation
309(32)
13.1 Introduction
309(1)
13.2 Stokes Parameters
309(2)
13.3 Source Term In Radiative Transfer Equation
311(4)
13.4 CMB Polarisation Induced By Scalar Modes
315(2)
13.5 CMB Polarisation Induced By Tensor Modes
317(2)
13.6 Generation Of Fluctuations During Inflation
319(5)
13.6.1 Tensor modes
321(1)
13.6.2 Scalar modes
322(1)
13.6.3 Scalar and tensor modes
323(1)
13.7 Statistics of CMB Polarisation Pattern
324(1)
13.8 CMB Polarisation As Cosmological Tool
325(5)
13.9 Exercises
330(1)
13.10 Solutions
331(10)
Section IV Future perspectives
Chapter 14 Precision cosmology
341(20)
14.1 Introduction
341(1)
14.2 Observations of CMB Temperature Anisotropy
341(7)
14.2.1 Polarization anisotropy
344(4)
14.3 Baryon Acoustic Oscillations
348(3)
14.3.1 Standard rulers
348(1)
14.3.2 Sound horizon
349(2)
14.3.3 Correlation baryon peak
351(1)
14.4 From 42 to ~420 High-Redshift SN IA
351(2)
14.5 Direct Vs. Indirect H0 Measurements
353(1)
14.6 Dark Energy
354(3)
14.7 Ci/B
357(2)
14.7.1 Effective neutrino number
357(1)
14.7.2 Neutrino mass
358(1)
14.8 Outlook
359(2)
Appendix A Tensors
361(8)
A.1 Vectors and Tensors
361(3)
A.1.1 Contravariant vectors
361(1)
A.1.2 Covariant vectors
362(1)
A.1.3 Tensors
363(1)
A.2 Operation With Tensors
364(1)
A.3 How to Recognise Tensors
365(2)
A.4 Exercises
367(1)
A.5 Solutions
368(1)
Appendix B Riemannian spaces
369(10)
B.1 Metric Form
369(3)
B.1.1 Metric tensor
369(1)
B.1.2 Lowering and raising indices
370(1)
B.1.3 Contra- and covariant components of vectors
370(2)
B.2 Covariant Derivatives
372(1)
B.3 Christoffel Symbols
373(2)
B.3.1 Locally flat reference frame
374(1)
B.3.2 Covariant derivative of metric tensor
374(1)
B.4 Geodesics
375(1)
B.5 Exercises
376(1)
B.6 Solutions
377(2)
Appendix C Curvature of space
379(10)
C.1 Parallel Transport
379(1)
C.2 Riemann Tensor
380(2)
C.3 Properties of Riemann Tensor
382(1)
C.4 Ricci Tensor
383(2)
C.5 Exercises
385(1)
C.6 Solutions
386(3)
Appendix D From special to general relativity
389(8)
D.1 Space-Time
389(1)
D.2 Proper Time and Clock Synchronization
390(1)
D.3 Proper Spatial Distances
391(1)
D.4 Geodesic Motion
392(1)
D.5 Equivalence Principle
393(1)
D.6 Geodesic Deviation
393(2)
D.7 Exercises
395(1)
D.8 Solutions
396(1)
Appendix E Field equations in vacuum
397(6)
E.1 Weak Field Limit
397(1)
E.2 Gravitational Redshift
398(1)
E.3 Field Equations In Vacuum
399(1)
E.4 Einstein Tensor
399(1)
E.5 Einstein-Hilbert Action
400(3)
Appendix F Field equations in non-empty space
403(20)
F.1 Energy-Momentum Tensor
403(1)
F.2 Covariant Divergence of Energy-Momentum Tensor
404(2)
F3 Field Equations In Presence of Matter
406(17)
Index 423(4)
Author Bio 427
Nicola Vittorio is full professor of Astronomy and Astrophysics at the Physics Department of the University of Rome Tor Vergata. He has been Dean (1999-2008) of the Faculty of Science and President (2006-2008) of the Association of the Deans of the Italian Faculties of Science. From 2010 to 2013 he was Vice-Rector for Higher Education of the University of Rome Tor Vergata. He is coordinating for the Ministry of Education, Universities and Research (MIUR) the project Lauree Scientifiche or Hard Science Diploma Project, promoted by the Association of the Deans of the Italian Faculties of Science together with the Association of Italian Industries. Since 2010, he has been the Deputy President of the Comitato del MIUR per lo Sviluppo della Cultura Scientifica e Tecnologica, chaired by Prof. Luigi Berlinguer.

In February 2012, he joined the Technical Secretariat for Scientific Policy of MIUR as an advisor to the Minister of Education, Universities and Research. Since 2012 he has been a Member of the Ministry of Education, Universities and Research MIUR Policies Board and Chairman of the Bologna Follow-Up Group BFUG Working Group on the Third Cycle of European Higher Education Area. Since 2013 he has been Vice-Rector for Doctoral Education and Internazionalization of the University of Rome Tor Vergata. His main research interest is in theoretical cosmology and data analysis of space missions. He has published more than 100 articles in refereed journals.

Nicola Vittorio is co-investigator of the ESA Planck mission for the observations of the Cosmic Microwave Background. He is a member of the Italian Astronomical Society, the Italian Physical Society, the Academy of Science of Turin, and the International Astronomical Union.
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