The Scalar-Tensor Theory of Gravitation

Half-title......Page 3
Series-title......Page 4
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 13
Conventions and notation......Page 16
Other special symbols......Page 17
1 Introduction......Page 19
1.1 What is the scalar–tensor theory of gravitation?......Page 20
1.2.1 The scalar field arising from the size of compactified internal space......Page 27
1.2.2 The dilaton from string theory......Page 30
1.2.3 The scalar field in a brane world......Page 34
1.2.4 The scalar field in the assumed two-sheeted structure of space-time......Page 40
1.3.1 The weak equivalence principle......Page 43
1.3.2 The value of Omega and mass of the scalar field......Page 46
1.3.3 Conformal transformation......Page 47
1.3.4 Mach’s principle and Dirac’s suggestion for time-dependent G......Page 49
1.3.5 Does the scalar–tensor theory have any advantage over simple scalar theories?......Page 52
2 The prototype Brans–Dicke model......Page 55
2.1 The Lagrangian......Page 56
2.2 Field equations......Page 58
2.3 The weak-field approximation......Page 61
2.4 The parameterized post-Newtonian approximation......Page 65
2.5 A spinor field as matter......Page 71
2.6 The mechanism of mixing......Page 75
3 Conformal transformation......Page 79
3.1 What is a conformal transformation?......Page 80
3.2 Nonminimal coupling......Page 84
3.3 Coupling to matter......Page 89
3.4 The geodesic in the E frame......Page 92
4.1 How has the cosmological constant re-emerged?......Page 95
4.2 The standard theory with Lambda......Page 100
4.3 The prototype BD model without Lambda......Page 102
4.4.1 Solution in the J frame......Page 106
4.4.2 Solution in the E frame......Page 109
4.4.3 A proposed revision and remarks......Page 119
5 Models of an accelerating universe......Page 123
5.1 Dark energy......Page 124
5.2 Quintessence......Page 128
5.3 Quintessence in the brane world......Page 133
5.3.1 A scalar field in the brane world......Page 134
5.3.2 Quintessence in the brane world......Page 136
5.4.1 Hesitation behavior......Page 142
5.4.2 A two-scalar model......Page 146
5.4.3 Qualitative features unique to the two-scalar model......Page 157
6 Quantum effects......Page 163
6.1 Scale invariance......Page 165
6.2 The dilaton as a Nambu–Goldstone boson......Page 169
6.3.1 The coupling to matter of Sigma, a self-coupled scalar field......Page 173
6.3.2 The coupling to matter of Sigma, scalar QED......Page 178
6.4 Non-Newtonian gravity......Page 186
6.5 A consequence of the suspected occurrence of the scalar field in the Maxwell term......Page 195
6.6 Time-variability of the fine-structure constant......Page 197
6.6.1 Electromagnetic coupling of Phi......Page 198
6.6.2 The behavior of the scalar field......Page 202
Appendix A The scalar field from Kaluza–Klein theory......Page 205
Appendix B The curvature scalar from the assumed two-sheeted space-time......Page 210
Appendix C The field equation of gravity n the presence of nonminimal coupling......Page 213
Appendix D The law of conservation of matter......Page 216
Appendix E Eddington’s parameters......Page 218
Appendix F Conformal transformation of a spinor field......Page 222
Appendix G Conformal transformation of the curvature scalar......Page 227
Appendix H A special choice for conformal invariance......Page 232
Appendix J The matter energy–momentum nonconservation law in the E frame......Page 234
Appendix K A modification to the Lambda term......Page 235
Appendix L Einstein’s equation in the brane world......Page 237
Appendix M Dilatation current......Page 241
Appendix N Loop integrals in continuous dimensions......Page 243
Appendix O A conformal frame in which particle masses are finally constant......Page 245
References......Page 248
Index......Page 255