  From a variational action with non-minimal coupling with a scalar field and
classical scalar and fermionic interaction, cosmological field equations can be
obtained. Imposing a FLRW metric the equations lead directly to a cosmological
model consisting of two interacting fluids, where the scalar field fluid is
interpreted as dark energy and the fermionic field fluid is interpreted as dark
matter. Several cases were studied analytically and numerically. An important
feature of the non-minimal coupling is that it allows crossing the barrier from
a quintessence to phantom behavior. The insensitivity of the solutions to one
of the parameters of the model permits it to find an almost analytical solution
for the cosmological constant type of universe.
