Cosmology constrains gravitational four-fermion interaction
  If torsion exists, it generates gravitational four-fermion interaction (GFFI). This interaction gets dominating on the Planck scale. If one confines to the regular, axial-axial part of this interaction, the results do not comply with the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology for the spatial flat or closed Universe. In principle, the anomalous, vector-vector interaction could restore the agreement. 
I.B. Khriplovich and A.S. Rudenko
astro-ph.CO gr-qc