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A concise description is presented of the basic features of the formalism ofnon-canonical spacetime volume-forms and its application in modified gravitytheories and cosmology. The well known unimodular gravity theory appears as avery special case. Concerning the hot issues facing cosmology now, wespecifically briefly outline the construction of: (a) unified description ofdark energy and dark matter as manifestations of a single material entity -- aspecial scalar field "darkon"; (b) quintessential models of universe evolutionwith a gravity-"inflaton"-assisted dynamical Higgs mechanism -- dynamicalsuppression/generation of spontaneous electroweak gauge symmetry breaking inthe "early"/"late" universe; (c) unification of dark energy and dark matterwith diffusive interaction among them; (d) mechanism for suppression of 5-thforce without fine-tuning.

Non-Canonical Volume-Form Formulation of Modified Gravity Theories and Cosmology