The fermion propagator in cosmological spaces with constant deceleration

We calculate the fermion propagator in Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetimes with constant deceleration q = epsilon - 1, epsilon = - (H) over dot/H-2 for excited states. For fermions whose mass is generated by a scalar field through a Yukawa coupling m = gY phi, we assume phi proportional to H. We first solve the mode functions by splitting the spinor into a direct product of helicity and chirality spinors. We also allow for non-vacuum states. We normalize the spinors using a consistent canonical quantization and by requiring orthogonality of particle and anti-particle spinors. We apply our propagator to calculate the one-loop effective action and renormalize using dimensional regularization. Since the Hubble parameter is now treated dynamically, this paves the way to study the dynamical backreaction of fermions on the background spacetime.