A one-loop functional derivation gives the local effective action and FLRW energy-momentum tensor for a scalar-channel NJL condensate in curved spacetime, reproducing flat-space mean-field results in the constant-condensate limit.
Fermion condensate from torsion in the reheating era after inflation
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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.
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Four-Fermion Condensates in Curved Spacetimes: A Functional Approach
A one-loop functional derivation gives the local effective action and FLRW energy-momentum tensor for a scalar-channel NJL condensate in curved spacetime, reproducing flat-space mean-field results in the constant-condensate limit.