The Rise of Cosmological Complexity: Saturation of Growth and Chaos

Understand

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 $w = 1$.