  We discuss the possible role of isocurvature perturbations for the quantum
decoherence of the curvature perturbation during inflation. We point out that
if the inflaton trajectory in field space is curved, the adiabatic mode is
generically coupled to the isocurvature mode and thus tracing out the latter
can cause the curvature perturbation to decohere. We explicitly investigate
this suggestion in a model of inflation with two decoupled massive fields and
find that decoherence is effective for a wide range of mass ratios. In
particular, we calculate the entanglement entropy for this model and show that
it grows after horizon exit, providing a quantitative measure for decoherence.
