Cover -- Half-title -- Series-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- Conventions and notation -- Symbols used multiply -- Other special symbols -- 1 Introduction -- 1.1 What is the scalar-tensor theory of gravitation? -- 1.2 Where does the scalar field come from? -- 1.2.1 The scalar field arising from the size of compactified internal space -- 1.2.2 The dilaton from string theory -- 1.2.3 The scalar field in a brane world -- 1.2.4 The scalar field in the assumed two-sheeted structure of space-time -- 1.3 Comments -- 1.3.1 The weak equivalence principle -- 1.3.2 The value of Omega and mass of the scalar field -- 1.3.3 Conformal transformation -- 1.3.4 Mach's principle and Dirac's suggestion for time-dependent G -- 1.3.5 Does the scalar-tensor theory have any advantage over simple scalar theories? -- 2 The prototype Brans-Dicke model -- 2.1 The Lagrangian -- 2.2 Field equations -- 2.3 The weak-field approximation -- 2.4 The parameterized post-Newtonian approximation -- 2.5 A spinor field as matter -- 2.6 The mechanism of mixing -- 3 Conformal transformation -- 3.1 What is a conformal transformation? -- 3.2 Nonminimal coupling -- 3.3 Coupling to matter -- 3.4 The geodesic in the E frame -- 4 Cosmology with Lambda -- 4.1 How has the cosmological constant re-emerged? -- 4.2 The standard theory with Lambda -- 4.3 The prototype BD model without Lambda -- 4.4 The prototype BD model with Lambda -- 4.4.1 Solution in the J frame -- 4.4.2 Solution in the E frame -- 4.4.3 A proposed revision and remarks -- 5 Models of an accelerating universe -- 5.1 Dark energy -- 5.2 Quintessence -- 5.3 Quintessence in the brane world -- 5.3.1 A scalar field in the brane world -- 5.3.2 Quintessence in the brane world -- 5.4 Scalar-tensor theory -- 5.4.1 Hesitation behavior -- 5.4.2 A two-scalar model.

5.4.3 Qualitative features unique to the two-scalar model -- 6 Quantum effects -- 6.1 Scale invariance -- 6.2 The dilaton as a Nambu-Goldstone boson -- 6.3 The contribution from loops -- 6.3.1 The coupling to matter of Sigma, a self-coupled scalar field -- 6.3.2 The coupling to matter of Sigma, scalar QED -- 6.4 Non-Newtonian gravity -- 6.5 A consequence of the suspected occurrence of the scalar field in the Maxwell term -- 6.6 Time-variability of the fine-structure constant -- 6.6.1 Electromagnetic coupling of Phi -- 6.6.2 The behavior of the scalar field -- Appendix A The scalar field from Kaluza-Klein theory -- Appendix B The curvature scalar from the assumed two-sheeted space-time -- Appendix C The field equation of gravity n the presence of nonminimal coupling -- Appendix D The law of conservation of matter -- Appendix E Eddington's parameters -- Appendix F Conformal transformation of a spinor field -- Appendix G Conformal transformation of the curvature scalar -- Appendix H A special choice for conformal invariance -- Appendix J The matter energy-momentum nonconservation law in the E frame -- Appendix K A modification to the Lambda term -- Appendix L Einstein's equation in the brane world -- Appendix M Dilatation current -- Appendix N Loop integrals in continuous dimensions -- Appendix O A conformal frame in which particle masses are finally constant -- References -- Index.