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.