On Resolutions of Cosmological Singularities in Higher-Spin Gravity

TL;DR

The paper investigates cosmological singularities in three-dimensional higher-spin gravity and proposes that holonomy-preserving gauge transformations in the Chern-Simons formulation can render Big Bang singularities non-singular. Using explicit spin-3 and spin-4 constructions, the authors build gauge deformations that preserve holonomy while modifying the metric to eliminate singularities, deriving concrete trace and determinant constraints that count the available degrees of freedom. They generalize the framework to spin-N, arguing for a large, computable space of holonomy-preserving deformations (2(N^2-N-3) complex parameters) capable of removing cosmological singularities. The results suggest that higher-spin cosmology mildly alters the asymptotic structure and supports the view that certain singularities may be gauge artifacts, with potential implications for holography and early-universe physics.

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 $SL(N,\mathbb{C})$.