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

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.

37 pages, 1 figure. Revised version, including a proper treatment of the infrared sector

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• Late-time backreaction from inflationary fluctuations of a non-minimally coupled massless scalar
• Quantum backreaction in evolving FLRW spacetimes
• Symmetry breaking and the Goldstone theorem in de Sitter space
• Regulating the infrared by mode matching: A massless scalar in expanding spaces with constant deceleration
• Quantum Correlators in Friedmann Spacetimes -The omnipresent de Sitter and the invariant vacuum noise
• Quantum Spacetime Instability and Breakdown of Semiclassical Gravity
• Instability of De Sitter Spacetime induced by Quantum Conformal Anomaly
• Stationary Phase Approximation and Instanton-like States for Cosmological In-In Path Integrals
• When tadpoles matter: One-loop corrections for spectator Higgs in inflation
• Abelian Higgs model in power-law inflation: the propagators in the unitary gauge