Alternative Formulations of Gravity

Abstract

In this work will review some of the different alternative formulations of gravitation. Formulations inspired by the MacDowell-Mansouri formulation of gravity, which make an attempt to express General Relativity as a gauge theory will be revised. In addition, the conditions in the symmetry breaking in the MacDowell-Mansouri action will be analyzed. This symmetry breaking allows to obtain the action of General Relativity from the MacDowell-Mansouri action, modulo additional terms, known as topological invariants, which do not affect the equations of motion of the theory. On the other hand, alternative approaches to gravity which consider the gravitational interaction as an emerging phenomenon of thermodynamics have become relevant. From the point of view of these approaches, gravity, being an emergent interaction, lacks a quantum description, which would explain the well-known problem of the adequacy of a quantum theory of gravitation. Using the ideas of emergent gravity, through a modified entropy-area relationship, we will present a model that adds corrections to the Newtonian gravitational force. These corrections can be used to explain the anomaly of the rotation curves of galaxies, a phenomenon attributed mainly to dark matter. Finally, taking these same ideas to the cosmological scenario, we will find a modified Friedmann equation, whose solution exhibits a behavior in accordance with the usual Friedmann-Robertson-Walker cosmological model for small times, while, for large times, this solution behaves like a universe dominated by dark energy. With this, we will find an effective cosmological constant in terms of the free parameter of the model. From this perspective, a plausible entropic origin of the cosmological constant is proposed.