Polynomial affine model of gravity in three-dimensions

TL;DR

This paper investigates a three-dimensional polynomial affine gravity model that extends general relativity by excluding the metric, analyzing torsion and nonmetricity effects through cosmological solutions and emergent metrics.

Contribution

It introduces a novel 3D polynomial affine gravity framework and classifies cosmological solutions based on torsion and nonmetricity effects.

Findings

Classified cosmological solutions using a decision tree approach

Derived explicit solutions with emergent metrics from the connection

Explored the role of torsion and nonmetricity in gravity models

Abstract

In this work, we explore a three-dimensional formulation of the polynomial affine model of gravity, which is a model that extends general relativity by relaxing the equivalence principle through the exclusion of the metric from the set of fundamental fields. In particular, in an attempt to gain insight of the role of the torsion and nonmetricity in the gravitational models, we consider homogeneous and isotropic cosmological models, for which their solutions are classified in a \emph{decisions tree}. We also show a few of these explicit solutions that allow the definition of (alternative/emergent) metrics derived from the connection.