IR Divergence in Inflationary Tensor Perturbations from Fermion Loops

TL;DR

This paper calculates fermion loop corrections to primordial tensor perturbations during inflation, revealing that fermion loops do not mitigate IR divergence issues and depend on fermion mass and UV cutoffs.

Contribution

It provides explicit one-loop correction calculations for both massless and massive fermions, extending the understanding of fermion effects in inflationary tensor fluctuations.

Findings

Fermion loop corrections can contain logarithmic terms affecting perturbation validity.

Massive fermions' loop corrections are constrained by UV cutoffs.

Fermion loops have the same sign as scalar loops, not alleviating IR divergence issues.

Abstract

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.