One-loop corrections to gravitational potentials in de Sitter space induced by a massive scalar.

Abstract

The origin of large scale structure in the universe is one of the most important problems in cosmology. Quantum matter interacting with gravity during inflation is thought to cause these fluctuations in matter density that seed the universe’s large scale structure. We consider slow-roll inflation by a scalar matter field. As such, it is important to understand how gravity is affected by this inflationary field at quantum level.

We model the classical interaction through a de Sitter background spacetime, corresponding to an exponentially expanding universe. The quantum matter effects are to 1-loop order captured in the graviton self energy, which we calculate and renormalise using dimensional regularisation. For the inflationary field, we consider a massive non-minimally coupled inflaton scalar. The self-energy is then decomposed in a spin-0 and spin-2 basis, after which the structure functions are given concisely and covariantly in terms of both the squared and coincident scalar propagator; extending existing research for a massless minimally coupled scalar. The result can be used to calculate the quantum matter corrections to the stress-energy tensor and the graviton propagator.