  We present analytic results for the gravitational wave power spectrum induced
in models where the inflaton is coupled to a fermionic pseudocurrent. We show
that although such a coupling creates helically polarized fermions, the
polarized component of the resulting gravitational waves is parametrically
suppressed with respect to the non-polarized one. We also show that the
amplitude of the gravitational wave signal associated to this production cannot
exceed that generated by the standard mechanism of amplification of vacuum
fluctuations. We previously found that this model allows for a regime in which
the backreaction of the produced fermions allows for slow-roll inflation even
for a steep inflaton potential, and still leads to Gaussian primordial scalar
perturbations. The present analysis shows that this regime also results in a
gravitational wave signal compatible with the current bounds.
