New effective theories of gravitation and their phenomenological consequences

TL;DR

This thesis explores modified theories of gravity based on affine structure changes, analyzing their stability, singularities, black hole solutions, and proposing a non-local extension to improve their physical viability.

Contribution

It introduces new effective theories of gravitation with affine structure modifications and proposes a non-local extension to address instabilities and singularities.

Findings

Stability conditions for modified gravity theories

Existence of alternative black hole solutions

Non-local extension reduces instabilities and singularities

Abstract

This thesis focuses on modifications on Einstein's theory of General Relativity, which could explain the current problems in gravitation and cosmology. More specifically, modifications of the affine structure of the spacetime, which is the structure that tells us how to perform derivatives, are studied. These theories appear when imposing that the system must be invariant under the action of the local Poincar\'e group. Within these theories, their stability, the conditions for the appearance of singularities, the movement of fermions, and if it is possible to find different Black Hole solutions than in Einstein's theory, is explored. Moreover, a non-local extension of the mentioned modification is proposed, which can make the theory free of instabilities and singularities at the linear limit.