We consider quantum decoherence and entropy increase in early universe cosmology. We first study decoherence in a discrete bipartite quantum system for which a single qubit gets entangled with an environment and the entropy increase is correlated with the decay of the off-diagonal terms of the reduced density matrix. We compare this system with continuous systems relevant for cosmology for which there is a natural external intervention, corresponding to the time-dependent separation between the sub- and super-horizon inflationary fluctuations. We find, in this case, that the off-diagonal terms of the density matrix, in a field basis, do not decay as sometimes assumed in cosmological set-ups. Nevertheless, following a recent treatment in terms of open Effective Field Theories (EFTs), we compute the entanglement entropy for a Gaussian state and show that it actually increases monotonically (S>0) during the accelerated phases (a>0 with a (t) the scale factor). We generalise this result to include non-Gaussian states and briefly discuss the relevance of computing the von Neumann entropy as compared to the thermodynamic entropy.
Céspedes et al. (Mon,) studied this question.