A cosmological open quantum system

TL;DR

This paper derives the evolution of a limited set of scalar modes in nearly de Sitter universes, revealing non-Hamiltonian and non-Markovian dynamics with dissipation effects, relevant for understanding quantum cosmological systems.

Contribution

It introduces a novel derivation of the density matrix evolution for scalar modes in cosmology, highlighting non-Hamiltonian and non-Markovian effects due to gravitational interactions.

Findings

Non-Hamiltonian and non-Markovian evolution of scalar modes

Presence of linear and nonlinear dissipation terms

Persistence of non-Hamiltonian effects at late times

Abstract

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.