Nonminimal Higgs models, dark matter, and evolution of the universe

The set of sum rules for a wide class of nonminimal Higgs models has been obtained. Difficulties and ways for revealing the possibilities of studying extended Higgs models at colliders have been revealed with the use of these sum rules and recent LHC results. New methods of studying multidoublet Higgs models with various symmetry groups have been applied to solve problems of classification of these groups, breaking of symmetries in vacuum, etc. A method for the determination of masses and spins of dark-matter particles $D$ and their partners via the energy spectrum of a lepton in the $e^+e^-\to DDW^+W^-$ – process has been proposed. The possibility of the existence of strongly interacting dark matter has been revealed. Variants of the evolution of the phase states of the Universe have been analyzed within the inert doublet model.