Mixmasters in Wonderland: Chaotic dynamics from Carroll limits of gravity

TL;DR

This paper shows that the Carroll limit of general relativity effectively captures the chaotic mixmaster dynamics near spacelike singularities, providing a new ultra-local framework for studying complex cosmological behaviors.

Contribution

It establishes that leading-order Carroll gravity accurately models BKL dynamics and cosmological billiards, offering a tractable approach to ultra-local gravitational phenomena.

Findings

Carroll limit reproduces mixmaster chaotic behavior

Leading-order Carroll gravity models BKL dynamics

Potential applications in inhomogeneous cosmologies and AdS/CFT

Abstract

We demonstrate that the Carroll limit of general relativity coupled to matter captures the chaotic mixmaster dynamics of near-singularity limits. Zooming in on the behavior of general relativity close to spacelike singularities reveals rich and solvable ultra-local Belinski-Khalatnikov-Lifshitz (BKL) dynamics, which we show to be captured by a Carroll limit. Specifically, building on recent work on geometric Carroll expansions of general relativity, we establish that leading-order Carroll gravity, with suitable matter coupling, accurately describes well-known cosmological billiards behavior. Since the Carroll limit implements the ultra-local limit off shell, this opens up the door to a wide range of possible tractable applications, including spatially inhomogeneous setups and the emergence of spikes at late times. This further suggests that Carroll gravity, along with its subleading corrections, could serve as a valuable tool for studying deep infrared physics in AdS/CFT.