Cosmology in Scalar-Tensor Gravity

1. Scalar-Tensor Gravity.- 1 Introduction.- 2 Brans-Dicke theory.- 3 Brans-Dicke cosmology in the Jordan frame.- 4 The limit to general relativity.- 5 Relation to Kaluza-Klein theory.- 6 Brans-Dicke theory from Lyra’s geometry.- 7 Scalar-tensor theories.- 7.1 Effective Lagrangians and Hamiltonians.- 8 Motivations for scalar-tensor theories.- 9 Induced gravity.- 10 Generalized scalar-tensor theories.- 11 Conformal transformation techniques.- 11.1 Conformal transformations.- 11.2 Brans-Dicke theory.- 11.3 Kaluza-Klein cosmology.- 11.4 Scalar-tensor theories.- 11.5 Generalized scalar-tensor theories.- 12 Singularities of the gravitational coupling.- 2. Effective Energy-Momentum Tensors and Conformal Frames.- 1 The issue of the conformal frame.- 1.1 The first viewpoint.- 1.2 The second viewpoint.- 1.3 The third viewpoint.- 1.4 Other viewpoints.- 1.5 Einstein frame or Jordan frame?.- 1.6 Energy conditions in relativistic theories.- 1.7 Singularity theorems and energy conditions.- 2 Effective energy-momentum tensors.- 2.1 Time-dependence of the gravitational coupling.- 2.2 Conservation equations for the various Tab(J) [øø].- 3. Gravitational Waves.- 1 Introduction.- 2 Einstein frame scalar-tensor waves.- 2.1 Gravitational waves in the Einstein frame.- 2.2 Corrections to the geodesic deviation equation.- 3 Gravitational lensing by scalar-tensor gravitational waves.- 3.1 Jordan frame analysis.- 3.2 Einstein frame analysis.- 3.3 Propagation of light through a gravitational wave background.- 4. Exact Solutions of Scalar-Tensor Cosmology.- 1 Introduction.- 2 Exact solutions of Brans-Dicke cosmology.- 2.1 K = 0 FLRW solutions.- 2.1.1 The O’Hanlon and Tupper solution.- 2.1.2 The Brans-Dicke dust solution.- 2.1.3 The Nariai solution.- 2.1.4 Other solutions with cosmological constant.- 2.1.5 Generalizing Nariai’s solution.- 2.1.6 Phase space analysis for K = 0 and V(ø) = 0.- 2.1.7 Phase plane analysis for K = 0 and V(ø) = Aø.- 2.2 K = ±1 solutions and phase space for V = 0.- 2.3 Phase space for any K and V = m2ø2/2.- 2.3.1 The Dehnen-Obregon solution.- 2.4 Bianchi models.- 2.4.1 Bianchi V universes.- 3 Exact solutions of scalar-tensor theories.- 5. The Early Universe.- 1 Introduction.- 2 Extended inflation.- 2.1 The original extended inflationary scenario.- 2.2 Alternatives.- 3 Hyperextended inflation.- 4 Real inflation?.- 5 Constraints from primordial nucleosynthesis.- 6. Perturbations.- 1 Introduction.- 2 Scalar perturbations.- 3 Tensor perturbations.- 7. Nonminimal Coupling.- 1 Introduction.- 1.1 Generalized inflation.- 1.2 Motivations for nonminimal coupling.- 1.3 Which value of.- 2 Effective energy-momentum tensors.- 2.1 Approach à la Callan-Coleman-Jackiw.- 2.2 Effective coupling.- 2.3 A mixed approach.- 2.4 Discussion.- 2.5 Energy conditions in FLRW cosmology.- 2.6 Nonminimal coupling and gravitational waves.- 3 Conformal transformations.- 4 Inflation and ? 0: the unperturbed universe.- 4.1 Necessary conditions for generalized inflation.- 4.1.1 Specific potentials.- 4.2 The effective equation of state with nonminimal coupling.- 4.3 Critical values of the scalar field.- 5 The slow-roll regime of generalized inflation.- 5.1 Derivation of the stability conditions.- 5.2 Slow-roll parameters.- 6 Inflation and ? 0: perturbations.- 6.1 Density perturbations.- 6.2 Tensor perturbations.- 7 Conclusion.- 8. The Present Universe.- 1 Present acceleration of the universe and quintessence.- 1.1 Coupled quintessence.- 1.2 Multiple field quintessence.- 1.3 Falsifying quintessence models.- 2 Quintessence with nonminimal coupling.- 2.1 Models using the Ratra-Peebles potential.- 2.2 Necessary conditions for accelerated expansion.- 2.3 Doppler peaks with nonminimal coupling.- 3 Superquintessence.- 3.1 An exact superaccelerating solution.- 3.2 Big Smash singularities.- 4 Quintessence in scalar-tensor gravity.- 5 Conclusion.- References.