Cosmological models in the nonsymmetric Kaluza-Klein Theory

We consider a dynamics of Higgs’ field in the framework of cosmological models involving the scalar field from Nonsymmetric Kaluza-Klein (Jordan-Thiry) Theory. The field plays here a role of a quintessence field. We consider phase transition in cosmological models of the second and of the first order due to evolution of Higgs’ field. We developed inflationary models including calculation of an amount of inflation. We match some cosmological models, calculating a Hubble parameter and an age of the Universe.