Time-convolutionless cosmological master equations: Late-time resummations and decoherence for non-local kernels

TL;DR

This paper demonstrates that non-Markovian effects in cosmological models can cause secular divergences, which can be resummed using the time-convolutionless master equation, revealing the importance of non-local kernels in late-time decoherence.

Contribution

It introduces a non-perturbative resummation method for non-Markovian effects in cosmological master equations, clarifying the role of local and non-local kernels in system-environment interactions.

Findings

Secular divergences originate from non-Markovian memory kernels.

Time-convolutionless formalism effectively resums these divergences.

The dominance of local or non-local kernels depends on the system-environment coupling.

Abstract

We revisit a simple toy model of two scalar fields in de Sitter space, playing the roles of "system" and "environment" degrees of freedom, which interact with each other. We show that there are secular divergences in physically relevant observables which arise solely from the non-Markovian part of the memory kernel, contrary to popular belief that secular growth typically comes from local terms in evolution equations. Nevertheless, we show that these terms can still be non-perturbatively resummed, using the time-convolutionless master equation formalism, which improves upon previous approximations. At the same time, there are other physical quantities in the same model that are dominated by local terms in the memory kernel. Therefore, we conclude that, for cosmological backgrounds, either the dissipation or the noise kernel can end up being dominated by non-local terms depending on the nature of the system-environment coupling.