Quantum backreaction in evolving FLRW spacetimes

TL;DR

This paper investigates quantum fluctuations of a scalar field in evolving FLRW spacetimes, analyzing backreaction effects during different cosmological phases, and clarifies how coupling, curvature, and evolution influence quantum effects.

Contribution

It provides exact solutions and numerical analysis of quantum backreaction in dynamic FLRW backgrounds, including effects of nonminimal coupling and spatial curvature.

Findings

Backreaction energy density grows logarithmically in quasi-de Sitter space.

Infrared divergences are absent with appropriate initial conditions or curvature.

Backreaction increases in contracting phases or with negative nonminimal coupling.

Abstract

Quantum fluctuations of a nonminimally coupled scalar field in D-dimensional homogeneous and isotropic background are calculated within the operator formalism in curved models with time evolutions of the scale factor that allow smooth transitions between contracting and expanding and between decelerating and accelerating regimes. The coincident propagator is derived and used to compute the one-loop backreaction from the scalar field. The inflationary infrared divergences are absent in Bunch-Davies vacuum when taking into account a preceding cosmological era or spatial curvature which can be either positive or negative. It is found that asymptotically, the backreaction energy density in the minimally coupled case grows logarithmically with the scale factor in quasi-de Sitter space, and in a class of models decays in slow-roll inflation and grows as a power-law during super-inflation. The backreaction increases generically in a contracting phase or in the presence of a negative nonminimal coupling. The effects of the coupling and renormalization scale upon the quantum fluctuations together with the novel features due to nontrivial time evolution and spatial curvature are clarified with exact solutions and numerical examples.