Similarity of cosmological models and its application to the analysis of cosmological evolution

Scale transformations of cosmological models based on a statistical system of degenerate fermions with a scalar Higgs interaction are studied. The similarity properties of cosmological models under scale transformations of their fundamental parameters are revealed. The transformation laws for the coordinates of singular points and eigenvalues of the characteristic matrix of the dynamical system of the cosmological model under its scale transformations are established. With the help of the transformation to new variables, the previously studied dynamical system of scalar-charged fermions is modified to a dynamical system with a nondegenerate characteristic matrix; for its nondegenerate branch, the singular points and eigenvalues of the characteristic matrix are found, which coincide with the corresponding values for the vacuum field model. Examples of numerical simulation of such cosmological models are given.