Higher Spin Resolution of a Toy Big Bang

TL;DR

This work analyzes cosmological singularities in $dS_3$ through a higher-spin lens by formulating de Sitter gravity as a $SL(3,\mathbb{C})$ Chern-Simons theory. Using holonomies to classify bulk solutions, the authors construct a class of holonomy-preserving spin-3 gauge transformations that desingularize a quotient cosmology, yielding a regular, finite-curvature geometry with nontrivial spin-3 fields. The resolution hinges on a flatness-constrained, holonomy-preserving deformation parameterized by constant coefficients, which can modify asymptotics away from the standard Fefferman-Graham form. This bulk demonstration of cosmological singularity resolution in a toy higher-spin theory highlights the power of higher-spin gauge redundancies in altering spacetime structure and has potential implications for time-dependent backgrounds beyond standard general relativity.

Abstract

Diffeomorphisms preserve spacetime singularities, whereas higher spin symmetries need not. Since three dimensional de Sitter space has quotients that have big-bang/big-crunch singularities and since dS_3-gravity can be written as an SL(2,C) Chern-Simons theory, we investigate SL(3,C) Chern-Simons theory as a higher-spin context in which these singularities might get resolved. As in the case of higher spin black holes in AdS_3, the solutions are invariantly characterized by their holonomies. We show that the dS_3 quotient singularity can be de-singularized by an SL(3,C) gauge transformation that preserves the holonomy: this is a higher spin resolution the cosmological singularity. Our work deals exclusively with the bulk theory, and is independent of the subtleties involved in defining a CFT_2 dual to dS_3 in the sense of dS/CFT.