Squeezed vacua play a prominent role in quantum field theory in curved spacetime. Resonances in the coupling of the field to the background result in large squeezing of the vacuum. In this talk, I discuss the relation between squeezing and entanglement. In particular, I study the entanglement production during reheating when the rapidly oscillating inflaton field leads to parametric resonance of certain matter field modes. I derive a new formula for the rate of growth of the entanglement entropy associated to a detector probing local degrees of freedom of the matter field.

[Slides]