Cosmic evolution from phase transition of 3-dimensional flat space

TL;DR

The paper identifies a thermodynamic phase transition in three-dimensional gravity between hot flat space and flat space cosmology, showing that at high temperature HFS becomes thermodynamically unstable and tunnels to FSC. By analyzing smooth Euclidean saddles and their on-shell actions in Einstein gravity (and extending to TMG), it derives a critical temperature ${T_c = 1/(2\pi r_0) = \Omega/(2\pi)}$ at which FSC dominates; FSC entropy matches the Bekenstein–Hawking value and a Cardy-like count in a Galilean CFT. A flat-space analogue of the AdS$_3$/CFT$_2$ S-transformation relates FSC and HFS, providing a field-theoretic interpretation of the phase transition. The results generalize to TMG (with a modified Tc) and point to broader implications for flat-space holography and higher-dimensional extensions.

Abstract

Flat space cosmology spacetimes are exact time-dependent solutions of 3-dimensional gravity theories, such as Einstein gravity or topologically massive gravity. We exhibit a novel kind of phase transition between these cosmological spacetimes and the Minkowski vacuum. At sufficiently high temperature (rotating) hot flat space tunnels into a universe described by flat space cosmology.