Boltzmann equation in de Sitter space

TL;DR

This paper derives a Boltzmann equation for an interacting scalar field in de Sitter space, revealing how particle production and unitarity influence the cosmological constant's screening effect.

Contribution

It introduces a novel derivation of a Boltzmann equation within the Schwinger-Keldysh formalism for de Sitter space, addressing infra-red divergences and horizon effects.

Findings

Particle production is balanced by unitarity within the horizon.

Inside horizon, screening of the cosmological constant diminishes over time.

Outside horizon, screening effect grows over time.

Abstract

In a time dependent background like de Sitter space, Feynman-Dyson perturbation theory breaks down due to infra-red divergences. We investigate an interacting scalar field theory in Schwinger-Keldysh formalism. We derive a Boltzmann equation from a Schwinger-Dyson equation inside the cosmological horizon. Our solution shows that the particle production is compensated by the reduction of the on-shell states due to unitarity. Although the degrees of freedom inside the horizon leads to a small and diminishing screening effect of the cosmological constant, there is a growing screening effect from those outside the horizon.