Beyond Einstein gravity: a survey of gravitational theories for cosmology and astrophysics
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Springer
2011
|
| Schriftenreihe: | Fundamental theories of physics
170 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XIX, 428 S. graph. Darst. |
| ISBN: | 9789400701649 |
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| 245 | 1 | 0 | |a Beyond Einstein gravity |b a survey of gravitational theories for cosmology and astrophysics |c Salvatore Capozziello ; Valerio Faraoni |
| 264 | 1 | |a Dordrecht [u.a.] |b Springer |c 2011 | |
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Datensatz im Suchindex
| _version_ | 1805095571023724544 |
|---|---|
| adam_text |
Titel: Beyond Einstein Gravity
Autor: Faraoni, Valerio
Jahr: 2011
Contents
Extended gravity: a primer. 1
1.1 Why extending gravity?. 1
1.2 Cosmological and astrophysical motivation. 3
1.3 Mathematical motivation. 6
1.4 Quantum gravity motivation. 7
1.4.1 Emergent gravity and thermodynamicsof spacetime. 12
1.5 What a good theory of gravity should do: General
Relativity and its extensions. 13
1.6 Quantum field theory in curved space. 18
1.7 Mach's principle and other fundamental issues. 23
1.7.1 Higher order corrections to Einstein's theory. 25
1.7.2 Minimal and non-minimal coupling
and the Equivalence Principle. 27
1.7.3 Mach's principle and the Variation of G. 32
1.8 Extended gravity from higher dimensions and area metric approach. 35
1.9 Conclusions. 40
Mathematical tools. 41
2.1 Conformal transformations. 41
2.2 Variational principles in General Relativity. 47
2.2.1 Geodesics. 47
2.2.2 Field equations. 49
2.3 Adding torsion. 51
2.4 Noether symmetries. 54
2.5 Conclusions. 57
The landscape beyond Einstein gravity. 59
3.1 The variational principle and the field equations
of Brans-Dicke gravity. 59
3.2 The variational principle and the field equations of metric
f(R) gravity. 62
3.2.1 f(R) = R + aR2 theory. 62
3.2.2 Metric /(/?) gravity in general. 64
xiv Contents
3.3 A more general class of ETGs. 67
3.4 The Palatini formalism. 67
3.4.1 The Palatini approach and the conformal
structure of the theory. 68
3.4.2 Problems with the Palatini formalism . 73
3.5 Equivalence between /(R) and scalar-tensor gravity. 77
3.5.1 Equivalence between scalar-tensor and metric
f(R) gravity. 77
3.5.2 Equivalence between scalar-tensor and Palatini
f(R) gravity. 78
3.6 Conformal transformations applied to extended gravity. 79
3.6.1 Brans-Dicke gravity. 79
3.6.2 Scalar-tensor theories. 83
3.6.3 Mixed /(/?)/scalar-tensor gravity. 85
3.6.4 The issue of the conformal frame . 86
3.7 The initial value problem. 90
3.7.1 The Cauchy problem of scalar-tensor gravity. 92
3.7.2 The initial value problem of /(/?) gravity
in the ADM formulation. 97
3.7.3 The Gaussian normal coordinates approach. 98
3.8 Conclusions.106
4 Spherical symmetry.107
4.1 Spherically Symmetrie Solutions of GR and metric f(R) gravity.107
4.1.1 Spherical symmetry.108
4.1.2 The Ricci scalar in spherical symmetry.109
4.1.3 Spherical symmetry in metric /(/?) gravity.110
4.1.4 Solutions with constant Ricci scalar.112
4.1.5 Solutions with R = R(r) .115
4.1.6 Perturbations.117
4.1.7 Spherical symmetry in f(R) gravity
and the Noether approach.119
4.1.8 Noether Solutions of spherically Symmetrie
f(R) gravity.124
4.1.9 Non-asymptotically flat and non-static spherical
Solutions of metric /(R) gravity.128
4.2 Spherical symmetry in scalar-tensor gravity.134
4.2.1 Static Solutions of Brans-Dicke theory.134
4.2.2 Dynamical and asymptotically FLRW Solutions.136
4.2.3 Collapse to black holes in scalar-tensor theory.137
4.3 The Jebsen-Birkhoff theorem.139
4.3.1 The Jebsen-Birkhoff theorem ofGR.139
4.3.2 The non-vaeuum case.140
4.3.3 The vaeuum case.142
4.3.4 The Jebsen-Birkhoff theorem in scalar-tensor gravity.143
4.3.5 The trivial case p ? constant.144
Contents xv
4.3.6 Static non-constant Brans-Dicke-like field.145
4.3.7 The Jebsen-Birkhoff theorem in Einstein frame
scalar-tensor gravity.146
4.3.8 Hawking's theorem and Jebsen-Birkhoff
in Brans-Dicke gravity.148
4.3.9 The Jebsen-Birkhoff theorem in f(R) gravity.150
4.4 Black hole thermodynamics in extended gravity .151
4.4.1 Scalar-tensor gravity.153
4.4.2 Metric modified gravity.155
4.4.3 Palatini modified gravity.156
4.4.4 Dilaton gravity.157
4.5 From spherical to axial symmetry: an application to f(R) gravity. 158
4.6 Conclusions.163
5 Weak-field limit.165
5.1 The weak-field limit of extended gravity.165
5.2 The Newtonian and post-Newtonian approximations:
general remarks.167
5.2.1 The Newtonian and post-Newtonian limits
of metric f(R) gravity with spherical symmetry.171
5.2.2 Comparison with the Standard formalism
and the chameleon effect.180
5.3 The Post-Minkowskian approximation.185
5.3.1 The energy-momentum pseudotensor in f(R)
gravity and gravitational radiation.187
5.4 Gravitational waves.190
5.4.1 Gravitational waves in scalar-tensor gravity.192
5.4.2 Gravitational waves in higher order gravity.195
5.5 Conclusions.208
6 Qualitative analysis and exact Solutions in cosmology.209
6.1 The Ehlers-Geren-Sachs theorem.209
6.2 The phase space of FLRW cosmology in scalar-tensor
and f(R) gravity.210
6.2.1 The dynamical System.212
6.3 Analytical Solutions of Brans-Dicke and scalar-tensor cosmology . 220
6.3.1 Analytical Solutions of Brans-Dicke cosmology.221
6.3.2 Exact scalar-tensor cosmologies.232
6.4 Analytical Solutions of metric f(R) cosmology
by the Noether approach.233
6.4.1 Point-like f(R) cosmology.233
6.4.2 Noether symmetries in metric f(R) cosmology.235
6.4.3 Exact cosmologies.238
6.4.4 a,c2 7^0.243
6.5 Analytical cosmological Solutions
off(R,DR.UkR) gravity.253
xvi Contents
6.5.1 Higher order point-like Lagrangians for cosmology.253
6.5.2 The Noether symmetry approach for higher
order gravities.256
6.6 Conclusions.260
7 Cosmology.261
7.1 Big Bang, infiationary, and late-time cosmology in GR.262
7.1.1 The Standard Big Bang model.263
7.1.2 Inflation in the early universe.263
7.1.3 The present-day acceleration.265
7.2 Using cosmography to map the structure of the universe.273
7.2.1 The cosmographic apparatus.274
7.3 Large scale structure and galaxy Clusters.304
7.3.1 The weak-field limit of f(R) gravity and galaxy Clusters. .305
7.3.2 Extended Systems.306
7.3.3 The Cluster mass profiles.307
7.3.4 The galaxy Clusters sample.310
7.3.5 The gas density model.310
7.3.6 Temperature profiles.311
7.3.7 The galaxy distribution model .311
7.3.8 Uncertainties in the mass profiles.314
7.3.9 Fitting the mass profiles.314
7.3.10 Results.316
7.3.11 Outlooks.321
7.4 Testing cosmological modeis with observations.326
7.4.1 Toward a new cosmological Standard model.327
7.4.2 Methods to constrain modeis.331
7.4.3 Data samples for constraining modeis: large
scale structure.336
7.4.4 Testing cosmological modeis: an example.337
7.5 Conclusions.345
8 From the early to the present universe.347
8.1 Quantum cosmology.347
8.1.1 Noether symmetries in quantum cosmology.350
8.1.2 Scalar-tensor quantum cosmology.352
8.1.3 The quantum cosmology of fourth order gravity.355
8.1.4 Quantum cosmology with gravity of order
higher than fourth.359
8.2 Inflation in ETGs.362
8.2.1 Scalar-tensor gravity: extended
and hyperextended inflation.362
8.2.2 Inflation with quadratic corrections.365
8.3 Cosmological perturbations.366
8.3.1 Scalar perturbations.367
8.3.2 Gravitational wave perturbations.376
Contents xvii
8.4 Constraints on ETGs from primordial nucleosynthesis.381
8.5 The present universe: f(R) gravity as an alternative
to dark energy.384
8.5.1 Background universe.385
8.5.2 Perturbations.388
8.6 Conclusions.389
A Physical constants and astrophysical and cosmological parameters.391
A. 1 Physical constants.391
A.2 Conversion factors.392
A.3 Astrophysical and cosmological quantities.392
A.4 Planck scale quantities.393
B The Noether symmetry approach to f(R) gravity.395
B. 1 The field equations and the Noether vector for spherically
Symmetrie /(R) gravity .395
B.2 Noether symmetries in metric /(R) cosmology.396
C The weak-field limit of metric/(/?) gravity.399
References.401
Index.425 |
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| spelling | Capozziello, Salvatore ca. 20./21. Jh. Verfasser (DE-588)142835277 aut Beyond Einstein gravity a survey of gravitational theories for cosmology and astrophysics Salvatore Capozziello ; Valerio Faraoni Dordrecht [u.a.] Springer 2011 XIX, 428 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Fundamental theories of physics 170 Kosmologie (DE-588)4114294-9 gnd rswk-swf Gravitationstheorie (DE-588)4158117-9 gnd rswk-swf Gravitationstheorie (DE-588)4158117-9 s Kosmologie (DE-588)4114294-9 s DE-604 Faraoni, Valerio Verfasser (DE-588)136483240 aut Fundamental theories of physics 170 (DE-604)BV000012461 170 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3523501&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021190282&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Capozziello, Salvatore ca. 20./21. Jh Faraoni, Valerio Beyond Einstein gravity a survey of gravitational theories for cosmology and astrophysics Fundamental theories of physics Kosmologie (DE-588)4114294-9 gnd Gravitationstheorie (DE-588)4158117-9 gnd |
| subject_GND | (DE-588)4114294-9 (DE-588)4158117-9 |
| title | Beyond Einstein gravity a survey of gravitational theories for cosmology and astrophysics |
| title_auth | Beyond Einstein gravity a survey of gravitational theories for cosmology and astrophysics |
| title_exact_search | Beyond Einstein gravity a survey of gravitational theories for cosmology and astrophysics |
| title_full | Beyond Einstein gravity a survey of gravitational theories for cosmology and astrophysics Salvatore Capozziello ; Valerio Faraoni |
| title_fullStr | Beyond Einstein gravity a survey of gravitational theories for cosmology and astrophysics Salvatore Capozziello ; Valerio Faraoni |
| title_full_unstemmed | Beyond Einstein gravity a survey of gravitational theories for cosmology and astrophysics Salvatore Capozziello ; Valerio Faraoni |
| title_short | Beyond Einstein gravity |
| title_sort | beyond einstein gravity a survey of gravitational theories for cosmology and astrophysics |
| title_sub | a survey of gravitational theories for cosmology and astrophysics |
| topic | Kosmologie (DE-588)4114294-9 gnd Gravitationstheorie (DE-588)4158117-9 gnd |
| topic_facet | Kosmologie Gravitationstheorie |
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