# Scalar-Tensor Theories of Gravity and Their Cosmological Applications.

Name: Olesya Galkina

Type: PhD thesis

Publication date: 22/12/2020

Advisor:

Name | Role |
---|---|

Júlio César Fabris | Advisor * |

Examining board:

Name | Role |
---|---|

Davi Cabral Rodrigues | Internal Examiner * |

Felipe Tovar Falciano | External Examiner * |

Gilberto Medeiros Kremer | External Examiner * |

Humberto Belich Junior | Internal Examiner * |

Ilia Chapiro | External Examiner * |

Júlio César Fabris | Advisor * |

Júnior Diniz Toniato | External Examiner * |

Summary: The main subjects of the thesis concern the most known scalar-tensor theory - Brans-Dicke theory, and cosmological models considered in the gravity in the presence of Born-Infeld type scalar fields, which in the present times are often called tachyons. We introduce the general solutions for the scale factor and the scalar field for the FriedmannLemaîtreRobertsonWalker flat universe in Brans-Dicke theory. It is usually expected that the violation of the energy conditions is required in order to have classical bounce solutions, even in the nonminimal coupling case: in this situation, phantom fields would appear in the Einstein frame. We show that for the case of the radiative fluid in BransDicke theory it is possible to obtain nonsingular solutions preserving the energy conditions even in the Einstein frame. Then we present a particular

solution of Brans-Dicke theory with matter content described by a stiff

matter barotropic perfect fluid. It is argued in the literature if BransDicke theory reduces to general relativity in the limit ꞷ → ꝏ if the scalar field goes as ϕ α 1 / ω. We show that the power of time dependence of our particular solution for stiff matter does not depend on ꞷ, and there is no general relativity limit even though we have ϕ α 1 / ω. Finally, we present some cosmological models considered in the gravity in the presence of Born-Infeld type scalar fields, revealing the big brake and other sudden future singularities and the effects of transformations of matter fields. Also, we consider a particular cosmological model describing the smooth transformation between the standard and phantom scalar fields. In both cases we try to find whether is it possible to conserve some kind of notion of particle corresponding to a chosen quantum field present in the universe when the latter approaches the

singularity.