Fermion condensate from torsion in the reheating era after inflation

TL;DR

This paper explores how torsion-induced four-fermion interactions in Einstein-Cartan gravity can lead to fermion condensate formation during the reheating era after inflation, even without fermion-antifermion excess.

Contribution

It demonstrates that nonthermal distributions from preheating can generate fermion condensates via torsion in a simplified 2+1D model, deriving an effective Lagrangian and showing it satisfies the Gross-Pitaevskii equation.

Findings

Fermion condensates can form from nonthermal distributions post-inflation.

The effective Lagrangian describes a gapless propagating mode.

Condensate dynamics follow the Gross-Pitaevskii equation.

Abstract

The inclusion of Dirac fermions in Einstein-Cartan gravity leads to a four-fermion interaction mediated by non-propagating torsion, which can allow for the formation of a Bardeen-Cooper-Schrieffer condensate. By considering a simplified model in 2+1 spacetime dimensions, we show that even without an excess of fermions over antifermions, the nonthermal distribution arising from preheating after inflation can give rise to a fermion condensate generated by torsion. We derive the effective Lagrangian for the spacetime-dependent pair field describing the condensate in the extreme cases of nonrelativistic and massless fermions, and show that it satisfies the Gross-Pitaevski equation for a gapless, propagating mode.