  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.
