Gravitons on de Sitter modified by quantum fluctuations of a nonminimally coupled massive scalar

Abstract

We investigate the one loop contributions to the graviton self-energy from a nonminimally coupled massive scalar perturbatively on a de Sitter background space-time. We assume a positive effective mass. We canonically quantize the scalar field and derive the de Sitter invariant Chernikov-Tagirov propagator. The graviton is defined as a small perturbation around a de Sitter background and the two one loop Feynman diagrams contributing to the graviton self-energy are computed through the effective action. We find that the diagram contributing to the nonlocal part of the graviton self-energy is proportional to the connected energy-momentum tensor correlator, where the expectation value is with respect to the de Sitter invariant Bunch-Davies vacuum. We employ dimensional regularization. The connected energy-momentum correlator is calculated and only partially renormalized due to the many divergences present. The second diagram is a local contribution to the graviton self-energy and is renormalized by the inverse gravitational constant and cosmological constant counterterms. The renormalized graviton self-energy can be used to quantum correct the linearized Einstein equation enabling us to investigate if nonminimally coupled massive scalars, produced during inflation, have an effect on dynamical gravitons and the force of gravity at one loop order. The connected energy-momentum correlator has importance on its own as it is the variance of the expectation value of the energy-momentum tensor and is needed to answer whether or not the expectation value of the energy-momentum tensor is a good description for backreaction.