The Hartree approximation in curved spacetimes revisited I: the effective potential in de Sitter

TL;DR

This paper revisits the Hartree approximation for quantum scalar fields with  interaction in curved spacetimes, providing a consistent nonperturbative renormalization and analyzing the effective potential in de Sitter space.

Contribution

It introduces a consistent nonperturbative renormalization scheme for the Hartree approximation in curved spacetimes, applied specifically to the effective potential in de Sitter space.

Findings

Renormalized equations are independent of the regularization scale.

Results show strong dependence on the renormalization procedure.

Application to de Sitter space reveals insights into spontaneous symmetry breaking.

Abstract

We consider a quantum scalar field with {\lambda}{\phi}^4 interaction in curved spacetimes. The quantum effects are taken into account nonperturbatively using the Hartree approximation to the 2PI effective action. Although this approximation has been considered in many previous works, we reconsider it using a consistent nonperturbative renormalization procedure, which we extend to general curved spacetimes. We obtain the renormalized equations for the mean field and for the propagator of the fluctuations, showing explicitly their independence on the arbitrary scale introduced by the regularization scheme. We apply our results to the particular case of de Sitter spacetime and discuss spontaneous symmetry breaking. The results depend strongly on the renormalization procedure.