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arXiv · 2005.10854

The Rise of Cosmological Complexity: Saturation of Growth and Chaos

Arpan Bhattacharyya·Saurya Das·S. Shajidul Haque·Bret Underwood
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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.

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Arpan Bhattacharyya, Saurya Das, S. Shajidul Haque, Bret Underwood. 2020-05-21. The Rise of Cosmological Complexity: Saturation of Growth and Chaos. https://doi.org/10.1103/physrevresearch.2.033273

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