Holographic Complexity in dS$_{d+1}$

TL;DR

This paper investigates holographic complexity in de Sitter spacetime using three approaches, revealing universal behaviors, divergences at finite times, and a linear growth regime after regulation.

Contribution

It introduces a cutoff surface to regulate divergences and demonstrates universal behavior and linear growth in holographic complexity in de Sitter space.

Findings

Holographic complexity exhibits hyperfast growth and divergence at finite critical time.

A cutoff surface regularizes divergence, leading to linear growth.

Universal behavior observed across different holographic complexity approaches.

Abstract

We study the CV, CA, and CV2.0 approaches to holographic complexity in $(d+1)$-dimensional de Sitter spacetime. We find that holographic complexity and corresponding growth rate presents universal behaviour for all three approaches. In particular, the holographic complexity exhibits `hyperfast' growth [arXiv:2109.14104] and appears to diverge with a universal power law at a (finite) critical time. We introduce a cutoff surface to regulate this divergence, and the subsequent growth of the holographic complexity is linear in time.