The Rise of Cosmological Complexity: Saturation of Growth and Chaos

• URL: http://arxiv.org/abs/2005.10854v1
• Date: Thu, 21 May 2020 18:37:28 GMT
• Title: The Rise of Cosmological Complexity: Saturation of Growth and Chaos
• Authors: Arpan Bhattacharyya, Saurya Das, S. Shajidul Haque, Bret Underwood
• Abstract summary: We find a bound on the growth of complexity for both expanding and contracting backgrounds. For expanding backgrounds that preserve the null energy condition, de Sitter space has the largest rate of growth of complexity.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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