Searching for butterflies in dS JT gravity

TL;DR

This work addresses chaos in quantum gravity in de Sitter space by studying bulk out-of-time-ordered correlators in $dS_2$ JT gravity. It introduces a diffeomorphism-invariant framework with invariant bulk points and bulk operator reconstruction, then proposes that gravitational ordering is encoded on multiple Schwarzian sheets via analytic continuation across the Schwarzian sector. Using Schwarzian perturbation theory, the authors show maximal chaos with Lyapunov exponent $\lambda_L = 2\pi/\beta$ and a scrambling time $t_* \sim (\beta/2\pi)\log(1/(G\ell))$, with results in line with shockwave expectations. The findings provide a concrete route to quantify chaos in cosmological horizons and offer a bridge to AdS insights and alternative cosmological observables through a diffeomorphism-invariant bulk formulation.

Abstract

We investigate out of time ordered correlators in the bulk of dS JT gravity, using Schwarzian perturbation theory, and propose that these out of time ordered correlators are encoded on the second sheet of the gravitational path integral, different sheets corresponding to different gravitational operator orderings. Implementing this in practice, we establish maximal chaos, in agreement with shockwave intuition.