  We examine environmental decoherence of cosmological perturbations in order
to study the quantum-to-classical transition and the impact of noise on
entanglement during inflation. Given an explicit interaction between the system
and environment, we derive a quantum master equation for the reduced density
matrix of perturbations, drawing parallels with quantum Brownian motion, where
we see the emergence of fluctuation and dissipation terms. Although the master
equation is not in Lindblad form, we see how typical solutions exhibit
positivity on super-horizon scales, leading to a physically meaningful density
matrix. This allows us to write down a Langevin equation with stochastic noise
for the classical trajectories which emerge from the quantum system on
super-horizon scales. In particular, we find that environmental decoherence
increases in strength as modes exit the horizon, with the growth driven
essentially by white noise coming from local contribution to environmental
correlations. Finally, we use our master equation to quantify the strength of
quantum correlations as captured by discord. We show that environmental
interactions have a tendency to decrease the size of the discord and that these
effects are determined by the relative strength of the expansion rate and
interaction rate of the environment. We interpret this in terms of the
competing effects of particle creation versus environmental fluctuations, which
tend to increase and decrease the discord respectively.
