Anisotropic singularities in chiral modified gravity

TL;DR

This paper explores a family of chiral modified gravity theories that modify General Relativity in high Weyl curvature regions, resolving singularities like Kasner and introducing bounce solutions with regular connections and new asymptotic regions.

Contribution

It introduces a new parametrisation of chiral modified gravity theories, demonstrating singularity resolution and bounce solutions within this framework.

Findings

Kasner singularity is resolved in certain modified theories.

Solutions exhibit a bounce, avoiding singularities.

A new asymptotic de Sitter region appears behind the bounce.

Abstract

In four space-time dimensions, there exists a special infinite-parameter family of chiral modified gravity theories. All these theories describe just two propagating polarizations of the graviton. General Relativity with an arbitrary cosmological constant is the only parity-invariant member of this family. We review how these modified gravity theories arise within the framework of pure-connection formulation. We introduce a new convenient parametrisation of this family of theories by using certain set of auxiliary fields. Modifications of General Relativity can be arranged so as to become important in regions with large Weyl curvature, while the behaviour is indistinguishable from GR where Weyl curvature is small. We show how the Kasner singularity of General Relativity is resolved in a particular class of modified gravity theories of this type, leading to solutions in which the fundamental connection field is regular all through the space-time. There arises a new asymptotically De Sitter region `behind' the would-be singularity, the complete solution thus being of a bounce type.