IR divergences and kinetic equation in de Sitter space. (Poincare patch; Principal series)

TL;DR

This paper demonstrates that IR loop corrections in de Sitter space scalar QFT involve particle creation effects, leading to a kinetic equation that sums leading IR contributions, differing from simple mass renormalization.

Contribution

It provides an explicit derivation of the kinetic equation from Dyson-Schwinger equations for scalar fields in de Sitter space, highlighting the role of particle creation in IR corrections.

Findings

Loop IR corrections involve particle creation, not just mass renormalization.

Kinetic equation emerges for certain harmonics where particle number dominates.

Solution sums all leading IR contributions to the two-point function.

Abstract

We explicitly show that the one loop IR correction to the two--point function in de Sitter space scalar QFT does not reduce just to the mass renormalization. The proper interpretation of the loop corrections is via particle creation revealing itself through the generation of the quantum averages $<a^+_p a_p>$, $<a_p a_{-p}>$ and $<a^+_p a^+_{-p}>$, which slowly change in time. We show that this observation in particular means that loop corrections to correlation functions in de Sitter space can not be obtained via analytical continuation of those calculated on the sphere. We find harmonics for which the particle number $<a^+_p a_p>$ dominates over the anomalous expectation values $<a_p a_{-p}>$ and $<a^+_p a^+_{-p}>$. For these harmonics the Dyson--Schwinger equation reduces in the IR limit to the kinetic equation. We solve the latter equation, which allows us to sum up all loop leading IR contributions to the Whiteman function. We perform the calculation for the principle series real scalar fields both in expanding and contracting Poincare patches.