Massive scalar field in de Sitter spacetime: a two-loop calculation and a comparison with the stochastic approach

TL;DR

This paper performs a detailed two-loop calculation of long-wavelength correlation functions of massive scalar fields in de Sitter spacetime, comparing results with stochastic and Hartree-Fock approaches to assess their accuracy.

Contribution

It provides the first two-loop computation of the two-point function in this context and clarifies the differences between stochastic and diagrammatic resummation methods.

Findings

Stochastic approach includes sunset diagrams, matching the two-loop results.

Hartree-Fock approximation resums only cactus diagrams, missing sunset contributions.

Long-wavelength commutator expectation value is zero for both spacelike and timelike separations.

Abstract

We examine long-wavelength correlation functions of massive scalar fields in de Sitter spacetime. For the theory with a quartic self-interaction, the two-point function is calculated up to two loops. Comparing our results with the Hartree-Fock approximation and with the stochastic approach shows that the former resums only the cactus type diagrams, whereas the latter contains the sunset diagram as well and produces the correct result. We also demonstrate that the long-wavelength expectation value of the commutator of two fields is equal to zero both for spacelike and timelike separated points.