The Rise of Cosmological Complexity: Saturation of Growth and Chaos

TL;DR

This paper investigates the growth of circuit complexity in cosmological models, revealing bounds and chaotic behavior in expanding and contracting universes, with implications for understanding cosmic chaos and complexity saturation.

Contribution

It introduces a novel analysis of cosmological complexity using squeezed states, establishing bounds on complexity growth and identifying conditions for chaos in FLRW backgrounds.

Findings

Complexity growth is linearly unbounded in certain cosmological regimes.

A universal bound on complexity growth rate is identified, similar to chaos bounds.

De Sitter space exhibits the maximal complexity growth rate among expanding backgrounds.

Abstract

We compute the circuit complexity of scalar curvature perturbations on FLRW cosmological backgrounds with fixed equation of state $w$ using the language of squeezed vacuum states. Backgrounds that are accelerating and expanding, or decelerating and contracting, exhibit features consistent with chaotic behavior, including linearly growing complexity. Remarkably, we uncover a bound on the growth of complexity for both expanding and contracting backgrounds $\lambda \leq \sqrt{2} \ |H|$, similar to other bounds proposed independently in the literature. The bound is saturated for expanding backgrounds with an equation of state more negative than $w = -5/3$, and for contracting backgrounds with an equation of state larger than $w = 1$. For expanding backgrounds that preserve the null energy condition, de Sitter space has the largest rate of growth of complexity (identified as the Lyapunov exponent), and we find a scrambling time that is similar to other estimates up to order one factors.