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

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 ϵ=-H˙/H2. 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 Janssen et al. (2008) [1]. The resulting correction to the Friedman equations is suppressed with respect to the tree level contribution by a factor of H2/mp2 and shows no secular growth.