Fermion Mass Generation in de Sitter Space
Bjorn Garbrecht, Tomislav Prokopec
TL;DR
This work shows that massless fermions in de Sitter space acquire a dynamical mass at one loop when Yukawa-coupled to a light scalar with $m^2+\xi R_D \ll H^2$. The authors compute the one-loop self-energy, renormalize it, and extract a dominant late-time contribution that leads to an effective fermion mass $m_\psi^2 \simeq \frac{3 f^2 H^4}{8 \pi^2 (m^2+\xi R)}$. They derive a nonlocal, chirality-preserving effective action that reproduces Dirac-like dynamics with this mass, contrasting with a local Dirac mass which would violate chirality. The inflationary dynamics yield mode functions with $\nu_\pm = \tfrac{1}{2}\mp i m_\psi/H$ and particle production described by a Pauli-blocked, quasi-thermal occupation $n_{\mathbf{k}h} \to \frac{1}{e^{2\pi m_\psi/H}+1}$ for infrared modes, while ultraviolet modes display non-thermal scaling. Overall, the mass generation is a generic feature of de Sitter inflation, associated with nonlocal radiative effects rather than a thermal bath, and it has potential implications for early-universe phenomenology and observations.
Abstract
We study the one-loop radiative corrections for massless fermions in de Sitter space induced by a Yukawa coupling to a light, nearly minimally coupled scalar field. We show that the fermions acquire a mass. Next we construct the corresponding (nonlocal) effective fermionic action, which -- in contrast to the case of a massive Dirac fermion -- preserves chirality. Nevertheless, the resulting fermion dynamics is precisely that of a Dirac fermion with a mass proportional to the expansion rate. Our finding supports the view that an observer or a test particle responds to a scalar field in inflation by shifting its energy rather than seeing a thermal bath.