Dynamics of Higgs" Fields and a Quintessence in the Nonsymmetric Kaluza-Klein (Jordan-Thiry) Theory

We consider a dynamics of Higgs' Fields in the framework of cosmological models involving a scalar field from Nonsymmetric Kaluza Klein (Jordan-Thiry) Theory. The scalar field plays here a role of a quintessece field. We consider phase transitions in cosmological models of the second and of the first order due to an evolution of Higgs' field. We develop inflationary models including calculation of an amount of an inflation.