Dostęp do publikacji jest możliwy w Archiwum UJ

This dissertation is devoted to investigations of dynamics of Friedmann-Robertson-Walker cosmological models with a non-minimally coupled scalar field and a barotropic matter content. Using dynamical systems methods two types of evolution: the complex behaviour and the regular expansion of the universe were studied in details. Different manifestations of the coexistence of chaotic and regular behaviour in the conformally coupled scalar field cosmology were demonstrated. Also, the fragility of cosmological evolution with respect to the value of non-minimal coupling parameter was presented. The full characteristic of the dynamical evolution of a non-minimally coupled scalar field cosmological models was performed. It was shown that the inclusion of both types of matter opens an enormous dynamical complexity of possible evolutional paths of the universe, which are not present in standard cosmological models or in the models filled with a scalar field only. The generic evolutional path, which does not depend on the form of the scalar field potential function, was found. It leads to new and natural possibility of unified description of the cosmological evolution. Within one framework of a non-minimally coupled scalar field cosmology all the major epochs in the history of the universe emerge as critical points of the corresponding dynamical system (a finite scale factor singularity, an inflation (slow-roll and fast-roll), a radiation era, a barotropic matter domination era and finally the present accelerated expansion epoch).