Squeezed vacua play a prominent role in quantum field theory in curved spacetime. Instabilities and resonances that arise from the coupling in the field to the background geometry, result in a large squeezing of the vacuum. In this talk, I discuss the
relation between squeezing and Lyapunov exponents of the system. In particular, I derive a new formula for the rate of growth of the entanglement entropy expressed as the sum of the Lyapunov exponents. As an example, we illustrate these features for the Schwinger effect.

[Slides]