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Employing alternative spacetime volume-forms (generally-covariant integrationmeasure densities) independent of the pertinent Riemannian spacetime metrichave profound impact in general relativity. Although formally appearing as"pure-gauge" dynamical degrees of freedom they trigger a number of remarkablephysically important phenomena such as: (i) new mechanism of dynamicalgeneration of cosmological constant; (ii) new type of "quintessentialinflation" scenario in cosmology; (iii) non-singular initial "emergentuniverse" phase of cosmological evolution preceding the inflationary phase;(iv) new mechanism of dynamical spontaneous breakdown of supersymmetry insupergravity; (v) gravitational electrovacuum "bags". We study in some detailthe properties, together with their canonical Hamiltonian formulation, of aclass of generalized gravity-matter models built with two independentnon-Riemannian volume-forms and discuss their implications in cosmology.

Metric-Independent Volume-Forms in Gravity and Cosmology