Primordial cosmology:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford University Press
2009
|
| Edition: | 1. publ. in English |
| Series: | Oxford graduate texts
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index. - Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XIX, 836 S. Ill., graph. Darst. |
| ISBN: | 019920991X 9780199209910 |
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MARC
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| 100 | 1 | |a Peter, Patrick |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Cosmologie primordiale |
| 245 | 1 | 0 | |a Primordial cosmology |c by Patrick Peter, Jean-Philippe Uzan |
| 250 | |a 1. publ. in English | ||
| 264 | 1 | |a Oxford |b Oxford University Press |c 2009 | |
| 300 | |a XIX, 836 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Oxford graduate texts | |
| 500 | |a Includes bibliographical references and index. - Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Cosmology | |
| 650 | 0 | 7 | |a Kosmologie |0 (DE-588)4114294-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kosmologie |0 (DE-588)4114294-9 |D s |
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| 700 | 1 | |a Uzan, Jean-Philippe |e Verfasser |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017552611 | ||
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| _version_ | 1804139113057615872 |
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| adam_text | Contents
Foreword to the English edition v
Foreword to the French edition
vü
Acknowledgements
ix
Introduction
ι
Cosmology: an ancient yet contemporary subject
1
The specifics of cosmology
2
Primordial cosmology
2
Organization and objective of this book
3
Warnings
5
References
6
PART I OVERVIEW OF THE THEORETICAL BASIS
1
General relativity
Ц
11
Space-time and gravity
Ц
1.1.1
Absolute space and time of Newtonian physics
11
1.1.2
Space-time of special relativity
14
1.1.3
General relativity and curved space-time
19
1.2
Elements of differential geometry
21
1.2.1
Manifolds and tensors
21
1.2.2
Geodesic equations and
Christoffel
symbols
26
1.2.3
Covariant derivative, parallel transport and Lie derivative
28
1.2.4
Curvature
31
1.2.5
Covariant approach
34
1-3
Equations of motion
38
1.3.1
Einstein s equations
38
1.3.2
Conservation equations
41
1.3.3
ADM Hamiltonian formulation
44
1.4
Geodesies in a curved space-time
46
1.4.1
Conserved quantities along a geodesic
46
1.4.2
Geodesic deviation equation
47
15
Weak-field regime
49
1.5.1
Newtonian limit
49
1.5.2
Gravitational waves in an empty space-time
53
1.6
Tests of general relativity
55
1.6.1
Test of the equivalence principle
55
1.6.2
Tests in the Solar System
60
xü Contents
1.6.3
Gravitational radiation
62
1.6.4
Need for tests at astrophysical scales
65
References
66
2
Overview of particle physics and the Standard Model
68
2.1
Prom classical to quantum
68
2.1.1
Analytical classical mechanics
69
2.1.2
Quantum physics
79
2.1.3
Quantum and relativistic mechanics
86
2.2
Canonical decompositions
89
2.2.1
Technical clarification
89
2.2.2
Real free field
90
2.2.3
The complex scalar field
95
2.3
Classification and properties of the elementary particles
98
2.4
Internal symmetries
101
2.4.1
Group theory
101
2.4.2
Generators
103
2.5
Symmetry breaking
106
2.5.1
Gauge group
107
2.5.2
Higgs mechanism
108
2.5.3
Non-Abelian case
110
2.6
The standard model SU(3)c X SU(2)L X U(l)y
112
2.6.1
The strong interaction (QCD)
113
2.6.2
Electroweak interaction
114
2.6.3
A complete model
116
2.7
Discrete
invariances
121
2.7.1
Parity
121
2.7.2
Charge conjugation
123
2.7.3
Time reversal and CPT theorem
124
References
126
PART II THE MODERN STANDARD COSMOLOGICAL MODEL
3
The homogeneous Universe
129
3.1
The cosmological solution of
Friedmann-Lemaître
129
3.1.1
Constructing a Universe model
129
3.1.2
Cosmological and Copernican principles
130
3.1.3
Cosmological principle and metric
131
3.1.4
Kinematics
136
3.1.5
Space-time dynamics
138
3.2
Dynamics of
Friedmann-Lemaître
space-times
143
3.2.1
Some solutions
143
3.2.2
Dynamical evolution
144
3.2.3
Expansion and contraction
148
3.3
Time and distances
150
3.3.1
Age of the Universe and look-back time
150
Contents xiii
3.3.2 Comoving radial
distance
151
3.3.3
Angular
distances
152
3.3.4
Luminosity distance
154
3.3.5
Volume and number counts
157
3.4
Behaviour at small redshifts
158
3.4.1
Deceleration parameter
158
3.4.2
Expression of the time and distances
158
3.5
Horizons
160
3.5.1
Event horizon
160
3.5.2
Particle horizon
162
3.5.3
Global properties
163
3.6
Beyond the cosmological principle
167
3.6.1
Classifying space-times
168
3.6.2
Universe with non-homogeneous spatial sections
170
3.6.3
Universe with homogeneous spatial sections
171
References
175
The standard Big-Bang model
177
4.1
The Hubble diagram and the age of the Universe
177
4.1.1
The Hubble constant
178
4.1.2
The contribution of
supernovae
182
4.1.3
The age of the Universe
186
4.2
Thermodynamics in an expanding Universe
188
4.2.1
Equilibrium thermodynamics
188
4.2.2
Out-of-equilibrium thermodynamics
197
4.2.3
Two limiting cases
201
4.3
Primordial nucleosynthesis
204
4.3.1
Main stages of the mechanism
205
4.3.2
Initial state
206
4.3.3
Freeze-out of the weak interaction and neutron to proton
ratio
208
4.3.4
Abundances of the light elements
211
4.3.5
Observational status
215
4.4
The cosmic microwave background radiation
216
4.4.1
Recombination
217
4.4.2
Properties of the cosmic microwave background
221
4.4.3
Another proof of the expansion of the Universe
226
4.5
Status of the Big-Bang model
226
4.5.1
A good standard model...
226
4.5.2 ...
but an incomplete model
228
4.5.3
Conclusion
234
References
235
xiv Contents
5
The inhomogeneous Universe
238
5.1
Newtonian perturbations
238
5.1.1
Case of a static space
238
5.1.2
Case of an expanding space
240
5.1.3
Predictions and
observables
246
5.1.4
Towards the non-linear regime
249
5.2
Gauge invariant
cosmologica!
perturbation theory
251
5.2.1
Perturbed space-time
251
5.2.2
Description of matter
255
5.2.3
Choosing a gauge
257
5.2.4
Einstein equations: derivation
260
5.2.5
Einstein equations: SVT decomposition
262
5.2.6
Perturbed conservation equation for a fluid
264
5.2.7
Interpretation of the perturbation equations
265
5.3
Evolution
266
5.3.1
Vector and tensor modes
267
5.3.2
Evolution of the gravitational potential
269
5.3.3
Scalar modes in the adiabatic regime
272
5.3.4
Mixture of several fluids
278
5.4
Power spectrum of density fluctuations
282
5.4.1
Two equivalent approaches
283
5.4.2
Different regimes
285
5.4.3
Some refinements
292
5.5
The large-scale structure of the Universe
296
5.5.1
Observing the large-scale structure
296
5.5.2
Structures in the non-linear regime
299
References
304
6
The cosmic microwave background
307
6.1
Origin of the cosmic microwave background anisotropies
307
6.1.1
Sachs-Wolfe formula
307
6.1.2
Angular power spectrum
311
6.2
Properties of the angular power spectrum
316
6.2.1
Large angular scales
317
6.2.2
Intermediate scales
318
6.2.3
Small scales
323
6.2.4
Other effects
326
6.3
Kinetic description
329
6.3.1
Perturbed Boltzmann equation
330
6.3.2
Gauge invariant expressions
339
6.3.3
Thomson scattering and polarization
342
6.3.4
Numerical integration
355
6.4
Anisotropies of the cosmic microwave background
356
6.5
Effects of the parameters on the angular power spectrum
364
6.5.1
Cosmological parameters
364
6.5.2
Parameters describing the primordial physics
367
Contents xv
References
371
7
Gravitational lensing and dark matter
374
7.1
Gravitational lensing and its applications
374
7.1.1
Gravitational lensing in the thin-lens regime
375
7.1.2
Lensing by galaxies and galaxy clusters
387
7.1.3
Gravitational distortion by the large-scale structure
395
7.1.4
Cosmic convergence
399
7.1.5
Cosmic shear
402
7.1.6
Measurement of the cosmic shear
405
7.1.7
Lensing on the cosmic microwave background
408
7.2
Evidence for the existence of dark matter
411
7.2.1
Dark matter in galaxies
411
7.2.2
Dark matter in clusters and groups of galaxies
419
7.2.3
Cosmological evidence
422
7.2.4
Summary
423
7.2.5
Candidates and constraints
423
References
445
8
Inflation
450
8.1
Genesis of the paradigm
451
8.1.1
Original motivations
451
8.1.2
Resolution of the Big-Bang problems
452
8.1.3
First models of inflation
454
8.1.4
Inflation as
a de
Sitter phase
455
8.2
Dynamics of single-field inflation
457
8.2.1
Equations of evolution
457
8.2.2
Slow-roll parameters
459
8.2.3
End of inflation
463
8.2.4
Some examples
465
8.2.5
Classification of inflationary models
469
8.3
Quantum fluctuations during inflation
470
8.3.1
Massless test scalar field in
a de
Sitter space-time
470
8.3.2
Massive test field in
de
Sitter
476
8.3.3
Massive test field during slow-roll inflation
477
8.4
Quantum fluctuations of the inflaton
478
8.4.1
Overview of the questions to address and expected results
479
8.4.2
Perturbed quantities
479
8.4.3
Perturbation equations
481
8.4.4
Evolution of the long-wavelength modes
483
8.4.5
Junction conditions and their applications
485
8.4.6
Quantization of the density perturbations
488
8.4.7
Gravitational waves
492
8.5
Perturbations in the slow-roll regime
494
8.5.1
An exact solution: power-law inflation
495
8.5.2
General case
496
xvi Contents
8.5.3 Relation
to observations
501
8.5.4
Reconstruction of the potential
505
8.6
End of inflation and reheating
507
8.6.1
Perturbative reheating
507
8.6.2
Theory of preheating
510
8.7
Eternal inflation
516
8.7.1
Heuristic argument
516
8.7.2
Stochastic approach
518
8.8
Extensions
523
8.8.1
Multifield inflation
523
8.8.2
Non-Gaussianity
530
8.8.3
Trans-Planckian problem
532
8.9
Status of the paradigm
537
References
541
PART III BEYOND THE STANDARD MODELS
549
549
550
551
554
554
560
562
566
568
569
569
571
573
575
576
578
10
Extensions of the theoretical framework
579
10.1
Scalar-tensor theory of gravity
579
10.1.1
Formulation
580
10.1.2
Local constraints
584
10.1.3
Cosmologica!
aspects
584
10.1.4
Phenomenological aspects
588
10.1.5
f(R)
gravity and scalar-tensor theory
593
10.2
Quantum field theory in curved space-time
594
10.2.1
Quantum physics, classical gravity
594
10.2.2
Particle creation
597
10.2.3
A complete example
602
Grand unification and baryogenesis
9.1
Interactions
9.1.1
Superposition principle
9.1.2
TV-particle states
9.2
Grand unification
9.2.1
Problems of the standard model
9.2.2
Unification of the coupling constants
9.2.3
Unification models
9.2.4
Consequences of grand unification
9.2.5
Neutrino mass
9.3
Baryogenesis
9.3.1
Sakharov conditions for baryogenesis
9.3.2
Electroweak anomalies
9.3.3
Electroweak baryogenesis
9.3.4
Leptogenesis
9.3.5
Affleck-Dine mechanism
References
Contents xvii
10.3 Supersymmetry and supergravity 604
10.3.1 Technical
generalities
604
10.3.2 Wess-Zumino
model
610
10.3.3
Gauge field
614
10.3.4 Supersymmetry
breaking
615
10.3.5
The minimal supersymmetric standard model (MSSM)
618
10.3.6
Supergravity
621
References
625
11
Phase transitions and topological defects
628
11.1
Phase transitions
628
11.1.1
Thermal field theory
628
11.1.2
Dynamics of the symmetry breaking
630
11.1.3
Formation of topological defects
633
11.2
Domain walls
635
11.2.1
Correlation length
635
11.2.2
Static configurations
638
11.3
Vortices
640
11.3.1
Kibble mechanism for cosmic strings
641
11.3.2
Internal structure
643
11.4
Monopoles
647
11.5
Textures
648
11.6
Defects in general
648
11.6.1
Connectedness
649
11.6.2
Fundamental group
649
11.6.3
Homotopy group
650
11.6.4
Semi-topological defects
651
11.7
Walls in cosmology
653
11.7.1
Distribution and evolution
653
11.7.2
Observational constraints
655
11.8
Cosmological
monopoles
656
11.8.1
GUT
monopoles
are unavoidable
656
11.8.2
The
monopole
problem
656
11.8.3
Possible solutions to the
monopole
problem
660
11.9
Cosmic strings
661
11.9.1
General properties
661
11.9.2
Gravitational effects of strings
662
11.9.3
Effect of a network on the microwave background
666
11.9.4
Other consequences of cosmic strings
671
References
674
12
Cosmological extensions
678
12.1
Construction of inflationary models
678
12.1.1
A consistent model: supergravity
678
12.1.2
F-term inflation
681
12.1.3 unterm
inflation
683
xviii Contents
12.2 Cosmological
constant
and dark energy
684
12.2.1
The cosmological constant problem
685
12.2.2
The nature of dark energy
687
12.2.3
Quintessence
690
12.2.4
Other models
697
12.2.5
Other approaches
701
12.2.6
Parameterization of the equation of state
705
12.2.7
Implications for the formation of the large-scale structure
708
12.3
Varying constants
711
12.4
Topology of the Universe
716
12.4.1
Local and global structures
716
12.4.2
Mathematical introduction
718
12.4.3
Classification of the three-dimensional manifolds
718
12.4.4
Observational signatures
726
References
733
13
Advanced topics
737
13.1
Extra dimensions: Kaluza-Klein theory
737
13.1.1
General relativity in
D
dimensions
737
13.1.2
Projected equations in four dimensions
739
13.1.3
Dilaton and Einstein-Maxwell theory
741
13.1.4
Einstein frame
742
13.1.5
Compactification
743
13.2
A few words on string theory
744
13.2.1
Prom particles to strings
744
13.2.2
Superstrings
746
13.2.3
Open and closed strings
749
13.2.4
Dualities
752
13.2.5
Low-energy Lagrangians
753
13.2.6
Origin of three space-like dimensions
755
13.3
The Universe as
a brane
758
13.3.1
Motivations
758
13.3.2
Induced Einstein equations
761
13.3.3
The Randall-Sundrum model
764
13.3.4
Cosmological phenomenology
767
13.3.5
Possible extensions
768
13.3.6
The Universe as a defect
769
13.3.7
Models of induced gravity
771
13.4
Initial singularity and a bouncing Universe
772
13.4.1
Approaching the singularity
772
13.4.2
The pre-Big-Bang scenario
775
13.4.3
The cyclic scenarios
781
13.4.4
Regular bounce and power spectrum
785
References
793
Contents
xix
Appendix
A Numerical values
796
A.I Physical constants
796
A.2 Astrophysical quantities
796
A.3 Units
797
A.
3.1
Natural units
797
A.
3.2
Conversion factors
798
A.
4
Particle physics
798
A.5 Cosmological quantities
799
A.
6
Electromagnetic spectrum
799
References
803
Appendix
В
Special functions
804
B.I
Euler
functions
804
B.2 Spherical harmonics
805
B.2.1 Definition
805
B.2.
2
Expressions
805
B.2.3 Properties
805
B.2.
4
Fourier transform
806
B.2.
5
Useful integrals
807
B.3 Bessel functions
808
B.3.1 Definition
808
B.3.2 Asymptotic properties
808
B.3.3 Special cases
809
B.3.4 Spherical Bessel functions
809
B.3.
5
Some useful integrals
810
B.4 Legendre polynomials
811
B.4.1 Associated Legendre polynomials
811
B.4.2 Legendre polynomials
811
B.5 Fourier transform and the eigenmodes of the Laplacian
812
B.5.1 Fourier transform
812
B.5.2 Power spectrum
812
B.5.3 Cartesian coordinates
813
B.5.
4
Spherical coordinates
813
References
815
Appendix
С
Useful cosmological quantities
816
C.I Background space
816
С
1.1
Geometry
816
C.1.2 Matter
817
C.2 Perturbed quantities
819
C.2.1 Geometry
819
C.2.2 Matter
821
Index
823
|
| any_adam_object | 1 |
| author | Peter, Patrick Uzan, Jean-Philippe |
| author_facet | Peter, Patrick Uzan, Jean-Philippe |
| author_role | aut aut |
| author_sort | Peter, Patrick |
| author_variant | p p pp j p u jpu |
| building | Verbundindex |
| bvnumber | BV035496305 |
| callnumber-first | Q - Science |
| callnumber-label | QB981 |
| callnumber-raw | QB981 |
| callnumber-search | QB981 |
| callnumber-sort | QB 3981 |
| callnumber-subject | QB - Astronomy |
| classification_rvk | US 2000 |
| ctrlnum | (OCoLC)313665248 (DE-599)GBV594816416 |
| dewey-full | 523.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 523 - Specific celestial bodies and phenomena |
| dewey-raw | 523.1 |
| dewey-search | 523.1 |
| dewey-sort | 3523.1 |
| dewey-tens | 520 - Astronomy and allied sciences |
| discipline | Physik |
| edition | 1. publ. in English |
| format | Book |
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| id | DE-604.BV035496305 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:38:55Z |
| institution | BVB |
| isbn | 019920991X 9780199209910 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017552611 |
| oclc_num | 313665248 |
| open_access_boolean | |
| owner | DE-703 DE-20 DE-19 DE-BY-UBM |
| owner_facet | DE-703 DE-20 DE-19 DE-BY-UBM |
| physical | XIX, 836 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Oxford University Press |
| record_format | marc |
| series2 | Oxford graduate texts |
| spelling | Peter, Patrick Verfasser aut Cosmologie primordiale Primordial cosmology by Patrick Peter, Jean-Philippe Uzan 1. publ. in English Oxford Oxford University Press 2009 XIX, 836 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford graduate texts Includes bibliographical references and index. - Hier auch später erschienene, unveränderte Nachdrucke Cosmology Kosmologie (DE-588)4114294-9 gnd rswk-swf Kosmologie (DE-588)4114294-9 s DE-604 Uzan, Jean-Philippe Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017552611&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Peter, Patrick Uzan, Jean-Philippe Primordial cosmology Cosmology Kosmologie (DE-588)4114294-9 gnd |
| subject_GND | (DE-588)4114294-9 |
| title | Primordial cosmology |
| title_alt | Cosmologie primordiale |
| title_auth | Primordial cosmology |
| title_exact_search | Primordial cosmology |
| title_full | Primordial cosmology by Patrick Peter, Jean-Philippe Uzan |
| title_fullStr | Primordial cosmology by Patrick Peter, Jean-Philippe Uzan |
| title_full_unstemmed | Primordial cosmology by Patrick Peter, Jean-Philippe Uzan |
| title_short | Primordial cosmology |
| title_sort | primordial cosmology |
| topic | Cosmology Kosmologie (DE-588)4114294-9 gnd |
| topic_facet | Cosmology Kosmologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017552611&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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