Dark Fermions and Spontaneous $CP$ violation in $SU(2)$-axion Inflation

Remarkably, if $CP$ was spontaneously broken in the physics of inflation, fermions would notice and remember it. Based on that, we present a new (non-thermal) mechanism for generating self-interacting dark Dirac fermions prior to the Hot Big Bang. The non-Abelian gauge fields and axions are well-motivated matter contents for the particle physics of inflation. In this background, we analytical study Dirac fermion doublets charged under the $SU(2)$ gauge field and use point-splitting technique to regularize the currents. We show that the non-trivial $CP$-violating vacuum structure of $SU(2)$-axion models naturally leads to an efficient mechanism for generating massive fermions during inflation. The size of the fermionic backreaction and the density fraction of dark fermions put upper bounds on the fermion's mass. For a GUT scale inflation, the generated dark fermions, only gravitationally coupled to the visible sector, can be as heavy as $m\lesssim 10 TeV$.