  Out-of-equilibrium fermions can be created in the early Universe by
non-perturbative parametric effects, both at preheating or during the thermal
era. An anisotropic stress is developed in the fermion distribution, acting as
a source of a stochastic background of gravitational waves (GW). We derive a
general formalism to calculate the spectrum of GW produced by an ensemble of
fermions, which we apply to a variety of scenarios after inflation. We discuss
in detail the regularization of the source, i.e. of the unequal-time-correlator
of the fermions' transverse-traceless anisotropic stress. We discuss how the GW
spectrum builds up in time and present a simple parametrization of its final
amplitude and peak frequency. We find that fermions may generate a GW
background with a significant amplitude at very high frequencies, similarly to
the case of preheating with scalar fields. A detection of this GW background
would shed light about the physics of the very early Universe, but new
technology at high frequencies is required, beyond the range accessible to
currently planned detectors.
