The graviton one-loop effective action in cosmological space-times with constant deceleration

TL;DR

This paper calculates the one-loop quantum corrections to Friedmann equations in cosmological space-times with constant deceleration, focusing on graviton and scalar field fluctuations, and finds the corrections are small and non-secular.

Contribution

It provides a method to compute infrared finite graviton and scalar propagators in FLRW backgrounds and derives the quantum corrections to Friedmann equations including these effects.

Findings

Quantum corrections are suppressed by H^2/m_p^2.

No secular growth in the one-loop corrections.

Infrared divergences are managed using recent finite propagator constructions.

Abstract

We consider the quantum Friedmann equations which include one-loop vacuum fluctuations due to gravitons and scalar field matter in a FLRW background with constant $\epsilon=-{\dot{H}}/{H^2}$. After several field redefinitions, to remove the mixing between the gravitational and matter degrees of freedom, we can construct the one loop correction to the Friedmann equations. Due to cosmological particle creation, the propagators needed in such a calculation are typically infrared divergent. In this paper we construct the graviton and matter propagators, making use of the recent construction of the infrared finite scalar propagators calculated on a compact spatial manifold in \cite{Janssen:2008px}. The resulting correction to the Friedman equations is suppressed with respect to the tree level contribution by a factor of $H^2/m_p^2$ and shows no secular growth.