Fermion condensates induced by axial interactions and cosmological implications

We reveal the presence of a new source of axial current due to the condensed vacuum generated by the spin-spin interaction. To show this, we consider a quartic Dirac Lagrangian containing a spin-spin interaction term, possibly originating from torsion in Einstein-Cartan-like theories. We use a mean field approach to analyze the quantized theory. We show that the diagonalization of the field Hamiltonian defines a new vacuum state, energetically favored with respect to the free vacuum. Such a vacuum, which is a condensate of particle-antiparticle pairs, is characterized by a nontrivial expectation value of the axial current operator. The new source of axial current, here obtained, can have effects both at the atomic level and at the astrophysical-cosmological level depending on the origin of the spin-spin interaction term. The condensate spontaneously breaks Lorentz symmetry, therefore it implies the possibility of CPT violation in the early universe. Furthermore the condensate induces a new source term in the gravitational field equations and may affect the dark sector of the Universe at cosmological level.