Volume complexity of dS bubbles

TL;DR

This paper investigates the behavior of holographic volume complexity in asymptotically AdS geometries with de Sitter bubbles, revealing different growth patterns including hyperfast divergence and phase transition-like behavior.

Contribution

It introduces a new analysis of volume complexity in geometries with de Sitter bubbles, highlighting the divergence and phase transition phenomena in holographic complexity.

Findings

Complexity in static bubbles has zero rate, indicating a phase transition.

Extremal surfaces anchored at the boundary and horizon show hyperfast complexity growth.

Behavior differs significantly from pure AdS, especially in static bubble cases.

Abstract

In the framework of the static patch approach to de Sitter holography introduced in [arXiv:2109.14104], the growth of holographic complexity has a hyperfast behaviour, which leads to a divergence in a finite time. This is very different from the AdS spacetime, where instead the complexity rate asymptotically reaches a constant value. We study holographic volume complexity in a class of asymptotically AdS geometries which include de Sitter bubbles in their interior. With the exception of the static bubble case, the complexity obtained from the volume of the smooth extremal surfaces which are anchored just to the AdS boundary has a similar behaviour to the AdS case, because it asymptotically grows linearly with time. The static bubble configuration has a zero complexity rate and corresponds to a discontinuous behaviour, which resembles a first order phase transition. If instead we consider extremal surfaces which are anchored at both the AdS boundary and the de Sitter stretched horizon, we find that complexity growth is hyperfast, as in the de Sitter case.