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.