One-loop quantum backreaction slows down inflation.

Abstract

We consider the one-loop quantum backreaction on a spatially flat, homogeneous and isotropic background with a small, positive deceleration parameter driven by a single minimally coupled inflaton field. The one-loop effect is calculated in a fully fixed gauge where the coordinate systems of subsequent constant time hypersurfaces coincide and matter field fluctuations vanish. This gauge has been chosen with an eye on future works in the stochastic approach to inflation. The main result is a nonvanishing backreaction sourced exclusively by scalar interactions, which induces a negative, logarithmic correction to the scale factor; thus, slowing down the universe's growth during inflation. The logarithmic behaviour is consistent with Weinberg's theorem. Curiously, the backreaction is inversely proportional to the first geometric slow-roll parameter; thus, it diverges in the de Sitter limit. Most likely this is a gauge artefact. Future research will have have to reveal whether this dependence survives in other gauges and whether there are any significant late time manifestations of the backreaction.