Leading log solution for inflationary Yukawa theory

Abstract

We generalize Starobinski\ifmmode \breve{\imath}\else \u{\i}\fi{}'s stochastic technique to the theory of a massless, minimally coupled scalar interacting with a massless fermion in a locally de Sitter geometry. The scalar is an ``active'' field that can engender infrared logarithms. The fermion is a passive field that cannot cause infrared logarithms but which can carry them, and which can also induce new interactions between the active fields. The procedure for dealing with passive fields is to integrate them out, then stochastically simplify the resulting effective action following Starobinski\ifmmode \breve{\imath}\else \u{\i}\fi{}. Because Yukawa theory is quadratic in the fermion this can be done explicitly using the classic solution of Candelas and Raine. We check the resulting stochastic formulation against an explicit two loop computation. We also derive a nonperturbative, leading log result for the stress tensor. Because the scalar effective potential induced by fermions is unbounded below, backreaction from this model might dynamically cancel an arbitrarily large cosmological constant.