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Based on the previously formulated mathematical model of a statistical systemwith scalar interaction of fermions, a cosmological model based on aone-component statistical system of doubly scalar charged degenerate fermionsinteracting with an asymmetric scalar doublet-canonical and phantom scalarfields-is studied. The connection of the presented model with previouslystudied models based on one-component and two-component fermion systems isinvestigated. The asymptotic and limiting properties of the cosmological modelare investigated, it is shown that among all models there is a class of modelswith a finite lifetime. The asymptotic behavior of models near thecorresponding singularities is investigated, a qualitative analysis of thecorresponding dynamical system is carried out, and numerical implementations ofsuch models are constructed. Based on numerical integration, it is shown thatin the presented model there can be transitions from a stable asymptoticallyvacuum state with a zero canonical field and a constant phantom fieldcorresponding to the phase of cosmological compression to a symmetric statecorresponding to the expansion phase. The time interval of the transitionbetween phases is accompanied by oscillations of the canonical scalar field.

gravitation and cosmology/gravitation and cosmology

Cosmological evolution of a statistical system of degenerate scalar  charged fermions with an asymmetric scalar doublet. II. One-component system  of doubly charged fermions