Higher Spin Cosmology

TL;DR

This work constructs higher spin cosmologies in 2+1 dimensional de Sitter space using the $SL(3,\mathbb{C})$ Chern-Simons formulation, introducing spin-3 charges on Kerr-dS$_3$- and quotient-type backgrounds. Thermodynamics of cosmological horizons is made consistent by holonomy (integrability) conditions, which correspond to the integrability of a boundary CFT partition function and reproduce Gibbons-Hawking results in the spin-2 limit. A Maldacena-inspired Wick rotation relates the de Sitter configurations to higher spin AdS$_3$ black holes, such that the on-shell CS action and thermodynamics match under dS/AdS identifications, including the spin-3 sector. The analysis unifies metric and CS perspectives, showing that horizon thermodynamics for higher spin dS$_3$ is governed by holonomy data and maps cleanly to Euclidean AdS thermodynamics, thereby strengthening the dS/CFT intuition for higher spins and providing a concrete computational framework. Overall, the paper demonstrates a controlled holographic link between higher spin cosmologies in de Sitter space and higher spin black holes in AdS$_3$, with explicit holonomy constraints, charge relations, and on-shell actions that reproduce known spin-2 limits and extend to spin-3 dynamics.

Abstract

We construct cosmological solutions of higher spin gravity in 2+1 dimensional de Sitter space. We show that a consistent thermodynamics can be obtained for their horizons by demanding appropriate holonomy conditions. This is equivalent to demanding the integrability of the Euclidean boundary CFT partition function, and reduces to Gibbons-Hawking thermodynamics in the spin-2 case. By using a prescription of Maldacena, we relate the thermodynamics of these solutions to those of higher spin black holes in AdS_3.