Renormalization of the 2PI Hartree-Fock approximation on de Sitter background in the broken phase

TL;DR

This paper investigates the infrared effects of light scalar fields in de Sitter space using the 2PI effective action, demonstrating a renormalization scheme at the Hartree-Fock level and analyzing phase structure and backreaction.

Contribution

It introduces a renormalization prescription within the 2PI Hartree-Fock approximation for de Sitter space, addressing IR divergences nonperturbatively.

Findings

MS-like renormalization scheme is feasible at Hartree-Fock level

Infinite series of counterterms are required for renormalization

Phase structure and quantum backreaction are explicitly calculated

Abstract

The infrared effects for light minimally coupled scalar fields with quartic self-interaction in de Sitter space is investigated using the 2PI effective action formalism. This formalism partially resums infinite series of loop diagrams, and enables us to circumvent the IR divergence problem for a massless minimally coupled scalar field in de Sitter space. It is anticipated that nonperturbative infrared effects generate a curvature-induced mass and self-regulate the IR divergence. However, due to its nonperturbative nature, the renormalization prescription is a nontrivial task. To calculate physical quantities, an appropriate renormalization prescription is required. In this paper, we will show that the MS-like scheme is possible at the Hartree-Fock truncation of the 2PI effective action, and infinite series of divergent terms are needed as counterterms. The phase structure and the quantum backreaction to Einstein's field equation are calculated.