On Resolutions of Cosmological Singularities in Higher-Spin Gravity

TL;DR

This paper investigates how higher-spin gravity theories in three dimensions can resolve cosmological singularities, such as the big bang, through gauge transformations that remove initial singularities in the metric.

Contribution

It extends a singularity resolution scheme to higher-spin fields and demonstrates the existence of gauge transformations that eliminate singularities in spin-3 and spin-4 cases within Chern-Simons formulations.

Findings

Existence of gauge transformations removing singularities

Resolution scheme extended to spin-4 fields

Singularities can be gauge artifacts in higher-spin gravity

Abstract

We study the resolution of certain cosmological singularity in the context of higher-spin three-dimensional gravity. We consider gravity coupled to a spin-3 field realized as Chern-Simons theory with gauge group $SL(3,\mathbb{C})$. In this context we elaborate and extend a singularity resolution scheme proposed by Krishnan and Roy. We discuss the resolution of a big-bang singularity in the case of gravity coupled to a spin-4 field realized as Chern-Simons theory with gauge group $SL(4,\mathbb{C})$. In all these cases we show the existence of gauge transformations that do not change the holonomy of the Chern-Simons gauge potential and lead to metrics without the initial singularity. We argue that such transformations always exist in the context of gravity coupled to a spin-N field when described by Chern-Simons with gauge group $SL(N,\mathbb{C})$.