Back-Reaction Is For Real

Abstract

We demonstrate the existence of a secular back-reaction on inflation using a simple scalar model. The model consists of a massless, minimally coupled scalar with a quartic self-interaction which is a spectator to $Λ$-driven inflation. To avoid problems with coincident propagators, and to make the scalars interact more like gravitons, we impose a covariant normal ordering prescription which has the effect of removing tadpole graphs. This version of the theory exhibits a secular slowing at three loop order due to interactions between virtual infrared scalars which are ripped apart by the inflating background. The effect is quantified using an invariant observable and all orders bounds are given. We also argue that, although stochastic effects can have either sign, the slowing mechanism is superimposed upon them.