A cosmological open quantum system
  We derive the evolution equation for the density matrix of a UV- and IR-
limited band of comoving momentum modes of the canonically normalized scalar
degree of freedom in two examples of nearly de Sitter universes. Including the
effects of a cubic interaction term from the gravitational action and tracing
out a set of longer wavelength modes, we find that the evolution of the system
is non-Hamiltonian and non-Markovian. We find linear dissipation terms for a
few modes with wavelength near the boundary between system and bath and
nonlinear dissipation terms for all modes. The non-Hamiltonian terms persist to
late times when the scalar field dynamics is such that the curvature
perturbation continues to evolve on super-Hubble scales.
