De Sitter Complexity Grows Linearly in the Static Patch

TL;DR

This paper proposes a new holographic complexity measure for de Sitter static patches, showing it grows linearly over time and indicating a finite-dimensional, chaotic quantum system description.

Contribution

It introduces a novel extremal volume prescription for dS complexity with a clear reference state, resolving previous ambiguities.

Findings

Complexity grows linearly at late times.

Complexity is proportional to the horizon's degrees of freedom.

Supports a finite-dimensional, chaotic quantum system model for dS static patch.

Abstract

The observable universe has undergone periods of expansion that are well approximated by de Sitter (dS) space. Still lacking is a quantum mechanical description of dS, both globally and when restricted to the static patch. We develop a novel prescription for computing holographic complexity in the dS static patch to determine its microscopic features. Specifically, we propose that the natural candidate for dS complexity is the volume of extremal timelike surfaces restricted to the static patch, anchored to the cosmological horizon or an observer worldline. Our anchoring prescription provides a clear definition of a reference state, overcoming a common ambiguity in prior definitions of de Sitter holographic complexity. The late-time growth of our complexity functional is linear and proportional to the number of degrees of freedom associated to the cosmological horizon, and therefore does not exhibit hyperfast growth. Our results imply the dS static patch is characterized by a quantum mechanical system, with a finite dimensional Hilbert space whose evolution is governed by a chaotic Hamiltonian.