Modified Actions for Gravity: Theory and Phenomenology

TL;DR

This thesis explores various modified gravity theories as alternatives to General Relativity, analyzing their theoretical foundations, cosmological implications, and observational viability to address unresolved issues in cosmology and quantum gravity.

Contribution

It provides a comprehensive analysis of multiple classes of modified gravity theories, their dynamical equivalences, and their potential to solve key cosmological problems.

Findings

Modified gravity theories can address dark energy and dark matter issues.

Certain theories satisfy observational and stability criteria.

The study highlights future directions beyond trial-and-error approaches.

Abstract

This thesis is devoted to the study of gravitational theories which can be seen as modifications or generalisations of General Relativity. The motivation for considering such theories, stemming from Cosmology, High Energy Physics and Astrophysics is thoroughly discussed (cosmological problems, dark energy and dark matter problems, the lack of success so far in obtaining a successful formulation for Quantum Gravity). The basic principles which a gravitational theory should follow, and their geometrical interpretation, are analysed in a broad perspective which highlights the basic assumptions of General Relativity and suggests possible modifications which might be made. A number of such possible modifications are presented, focusing on certain specific classes of theories: scalar-tensor theories, metric f(R) theories, Palatini f(R) theories, metric-affine f(R) theories and Gauss--Bonnet theories. The characteristics of these theories are fully explored and attention is payed to issues of dynamical equivalence between them. Also, cosmological phenomenology within the realm of each of the theories is discussed and it is shown that they can potentially address the well-known cosmological problems. A number of viability criteria are presented: cosmological observations, Solar System tests, stability criteria, existence of exact solutions for common vacuum or matter configurations etc. Finally, future perspectives in the field of modified gravity are discussed and the possibility for going beyond a trial-and-error approach to modified gravity is explored.