  Entanglement entropy (EE) of a spatial region quantifies correlations between
the region and its surroundings. For a free scalar in the adiabatic vacuum in
de Sitter space the EE is known to remain low, scaling as the surface area of
the region. Here, we study the evolution of entanglement after the universe
transitions from de Sitter to flat space. We concentrate on the case of a
massless minimally coupled scalar. We find numerically that, after the de
Sitter stage ends, the EE and the R\'enyi entropy rapidly grow and saturate at
values obeying the volume law. The final state of the subsystem (region) is a
partially thermalized state reminiscent of a generalized Gibbs ensemble. We
comment on application of our results to the question of when and how
cosmological perturbations decohere.
