Non-canonical volume-form formulation of modified gravity theories and cosmology

A concise description is presented in the basic features of the formalism of non-canonical spacetime volume forms and its application in modified gravity theories and cosmology. The well-known unimodular gravity theory appears as a very special case. Concerning the hot issues facing cosmology now, we specifically briefly outline the construction of: (a) unified description of dark energy and dark matter as manifestations of a single material entity—a special scalar field “darkon”; (b) quintessential models of universe evolution with a gravity “inflaton”-assisted dynamical Higgs mechanism—dynamical suppression/generation of spontaneous electroweak gauge symmetry breaking in the “early”/“late” universe; (c) unification of dark energy and dark matter with diffusive interaction among them; and (d) mechanism for suppression of fifth force without fine-tuning.