The article represents a research of the cosmological evolution of fermionstatistical systems with fantom scalar interaction where "kinetic" term'scontribution to the total energy of a scalar field is negative. As a result ofanalytical and numerical simulation of such systems it has been revealed aexistence of four possible scenarios depending on parameters of the system andinitial 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.
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