Butterfly velocity and chaos suppression in de Sitter space

TL;DR

This paper investigates how de Sitter space curvature and temperature affect chaos in holographic conformal field theories, revealing chaos suppression and the restoring role of chemical potential, with analogies to Schwinger effect and black hole formation.

Contribution

It demonstrates the degeneracy of butterfly velocity in de Sitter space and explores how chemical potential can restore chaos, providing new insights into chaos dynamics in curved spacetime.

Findings

Butterfly velocity degenerates for all H and T values.

Chemical potential can restore butterfly velocity.

Analogies drawn with Schwinger effect and black hole formation.

Abstract

In this note, we study the holographic CFT in the de Sitter static patch at finite temperature $T$ and chemical potential. We find that butterfly velocity $v_B$ in such field theory degenerates for all values of the Hubble parameter $H$ and $T$. We interpret this as a chaos disruption caused by the interplay between the expansion of chaotic correlations constrained by $v_B$ and effects caused by de Sitter curvature. The chemical potential restores healthy butterfly velocity for some range of temperatures. Also, we provide some analogy of this chaos suppression with the Schwinger effect in de Sitter and black hole formation from shock wave collision.