Cosmology of fermionic dark energy coupled to curvature

A formulation of cosmology driven by fermions $\psi $ is studied. Assumption that the expectation value of the fermion bilinear is non-zero simplifies the homogeneous solution of the Dirac equations and connects the spinor field with the scale parameter of the universe. With coupling between the Einstein term and spinor field $1 - \frac{\xi }{6} (\bar{\psi }\psi )^{-l}$, the possibility for a late time interaction emerges. In that way, the early universe agrees with $\Lambda $CDM model, but for the late universe the new integrating term dominates.