  We estimate fermion loop corrections to the two-point correlation function of
primordial tensor perturbations in a slow-roll inflationary background. We
particularly compute an explicit term of one-loop correction from a massless
fermion, and then extend to the complete Interaction Hamiltonian. After that,
we study one-loop corrections contributed by a massive fermion to primordial
tensor fluctuations. The loop correction arisen from a massless fermion field
contains logarithms and thus may constrain the validity of perturbation theory
in inflationary cosmology, but the situation could be relaxed once the
fermion's mass is taken into account. Another one-loop diagram for a massive
fermion which involves one vertex is constrained by a UV cutoff as expected by
quantum field theory. Our result shows that loop corrections of a fermion field
have the same sign as those of a scalar field, and thus implies that the
inclusion of fermion loop corrections may not help to alleviate the issue of IR
divergence in inflationary cosmology.
