  The article represents a research of the cosmological evolution of fermion
statistical systems with fantom scalar interaction where "kinetic" term's
contribution to the total energy of a scalar field is negative. As a result of
analytical and numerical simulation of such systems it has been revealed a
existence of four possible scenarios depending on parameters of the system and
initial conditions. Among these scenarios there are scenarios with an early,
intermediate and late non-relativistic stages of the cosmological evolution,
all of which also have necessary inflation stage.
