Fermion Propagator in Cosmological Spaces with Constant Deceleration
  We calculate the fermion propagator in FLRW spacetimes with constant
deceleration $q=\epsilon-1$, $\epsilon=-\dot{H}/H^{2}$ for excited states. For
fermions whose mass is generated by a scalar field through a Yukawa coupling
$m=g_{\mathrm{\scriptscriptstyle{Y}}} \phi$, we assume $\phi \propto H$. We
first solve for the mode functions by splitting the spinor into a direct
product of helicity and chirality spinors. We also allow for non-vacuum states.
We normalise the spinors using a consistent canonical quantisation and by
requiring orthogonality of particle and anti-particle spinors. We apply our
propagator to calculate the one loop effective action and renormalise using
dimensional regularisation. Since the Hubble parameter is now treated
dynamically, this paves the way to study the dynamical backreaction of fermions
on the background spacetime.
