On the Theory of Fermionic Preheating
  In inflationary cosmology, the particles constituting the Universe are created after inflation due to their interaction with moving inflaton field(s) in the process of preheating. In the fermionic sector, the leading channel is out-of equilibrium particle production in the non-perturbative regime of parametric excitation, which respects Pauli blocking but differs significantly from the perturbative expectation. We develop theory of fermionic preheating coupling to the inflaton, without and with expansion of the universe, for light and massive fermions, to calculate analytically the occupation number of created fermions, focusing on their spectra and time evolution. In the case of large resonant parameter $q$ we extend for rermions the method of successive parabolic scattering, earlier developed for bosonic preheating. In an expanding universe parametric excitation of fermions is stochastic. Created fermions very quickly, within tens of inflaton oscillations, fill up a sphere of radius $\simeq q^{1/4}$ in monetum space. We extend our formalism to the production of superheavy fermions and to `instant' fermion creation. 
Patrick B. Greene (Toronto U.), Lev Kofman (CITA)