Cosmology

454 Pages·2018·67.445 MB·English

by  Nicola Vittorio

COSMOLOGY
Series in Astronomy and Astrophysics
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Series in Astronomy and Astrophysics
COSMOLOGY
Nicola Vittorio
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Version Date: 20171003
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To Liu` and Ludovico

Contents
List of Figures xix
List of Tables xxiii
Preface xxv
Section I Background universe
Chapter 1(cid:4) Cosmological models 3
1.1 INTRODUCTION 3
1.2 SYNCHRONOUSREFERENCEFRAME 3
1.3 FRIEDMANN-ROBERTSON-WALKERMETRIC 5
1.3.1 Field equations 6
1.3.2 Spatial sector of FRW space-time 7
1.3.3 FRW metric in trigonometric form 10
1.4 FRIEDMANNEQUATIONS 10
1.5 COSMOLOGICALCONSTANT 11
1.6 CONSERVATIONLAWS 12
1.7 COSMOLOGICALPARAMETERS 13
1.8 DUST-FILLEDUNIVERSES 14
1.8.1 Closed universe 14
1.8.2 Flat or open universe 15
1.9 COSMOLOGICALMODELS 16
1.9.1 Milne model 16
1.9.2 Einstein static model 18
1.9.3 de Sitter model 18
1.9.4 Closed Friedmann universe 19
1.9.5 Einstein-de Sitter universe 21
vii
viii (cid:4) Contents
1.9.6 Open Friedmann universe 21
1.9.7 Concordance model 22
1.10 EXERCISES 24
1.11 SOLUTIONS 25
Chapter 2(cid:4) Measurable properties of FRW models 29
2.1 INTRODUCTION 29
2.2 OBSERVABLEUNIVERSE 29
2.2.1 Cosmological redshift 30
2.2.2 Hubble flow 30
2.3 COMOVINGDISTANCESANDCOORDINATES 31
2.3.1 Closed Friedmann model 33
2.3.2 Einstein-de Sitter model 33
2.3.3 Open Friedmann model 33
2.3.4 Concordance model 35
2.3.5 Particle horizon 35
2.4 ANGULARDIAMETERDISTANCED 38
A
2.4.1 Closed Friedmann model 38
2.4.2 Einstein-de Sitter model 39
2.4.3 Open Friedmann model 39
2.4.4 Concordance model 41
2.5 LUMINOSITYDISTANCED 41
L
2.6 COMOVINGVOLUMEANDNUMBERCOUNTS 43
2.7 DISTANCEINDICATORS 44
2.7.1 Cepheids 45
2.7.2 Supernovae Ia 46
2.8 H ANDAGEOFUNIVERSE 47
0
2.8.1 H determination 48
0
2.8.2 Age of universe 50
2.9 SUPERNOVAEIAANDDARKENERGY 51
2.10 EXERCISES 54
2.11 SOLUTIONS 55
Chapter 3(cid:4) Hot Big Bang model 57
3.1 INTRODUCTION 57
3.2 COSMICMICROWAVEBACKGROUND 57
Contents (cid:4) ix
3.3 HOTBIGBANG 59
3.3.1 Baryon-to-photon ratio 61
3.3.2 Friedmann equation 61
3.3.3 Radiation-dominated universe 62
3.4 NEUTRON-TO-BARYONRATIO 64
3.5 NEUTRINOCOSMICBACKGROUND 67
3.6 REFINEDESTIMATEOFX 69
N
3.7 PRIMORDIALHELIUMPRODUCTION 70
3.8 PRIMORDIALDEUTERIUMANDLIGHTELEMENTS 73
3.9 RECOMBINATION 75
3.9.1 Saha approximation 76
3.9.2 Out-of-equilibrium recombination 77
3.9.3 Last scattering surface 80
3.10 EXERCISES 82
3.11 SOLUTIONS 83
Chapter 4(cid:4) Inflation 85
4.1 INTRODUCTION 85
4.2 PUZZLESOFSTANDARDMODEL 85
4.2.1 Horizon problem 85
4.2.2 Curvature problem 88
4.3 COSMICINFLATIONASSOLUTION 90
4.4 DESITTERINFLATION 92
4.5 SLOW-ROLLSCENARIO 93
4.6 SLOW-ROLLPARAMETERS 95
4.7 INFLATIONARYMODELS 96
4.7.1 Exponential potential 97
4.7.2 Power law potential 100
4.8 EXERCISES 104
4.9 SOLUTIONS 105
Section II Structure formation: A Newtonian
approach
Chapter 5(cid:4) Gravitational instability scenario 109
5.1 INTRODUCTION 109
5.2 CREATINGSPHERICAL“SEED” 109