Gravitons Enhance Fermions during Inflation

Abstract

We solve the effective Dirac equation for massless fermions during inflation in the simplest gauge, including all one loop corrections from quantum gravity. At late times the result for a spatial plane wave behaves as if the classical solution were subjected to a time dependent field strength renormalization of Z_2(t) = 1 - \frac{17}{4 \pi} G H^2 \ln(a) + O(G^2). We show that this also follows from making the Hartree approximation, although the numerical coefficients differ.