Quintessence, unified dark energy and dark matter, and confinement/deconfinement mechanism

We describe a new type of generalized gravity-matter models where f(R) = R + R² gravity couples in a non-conventional way to a scalar "inflaton" field, to a second scalar "darkon" field responsible for dark energy/dark matter unification, as well as to a non-standard nonlinear gauge field system containing a square-root of the ordinary Maxwell Lagrangian, which is responsible for a charge confining/deconfinfing mechanism. The essential non-conventional feature of our models is employing the formalism of non-Riemannian volume forms, i.e. metric- independent non-Riemannian volume elements on the spacetime manifold, defined in terms of auxiliary antisymmetric tensor gauge fields. Although being (almost) pure-gauge degrees of freedom, the non-Riemannian volume-forms trigger a series of important features unavailable in ordinary gravity-matter models. Upon passing to the physical Einstein frame we obtain an effective matter-gauge-field Lagrangian of quadratic "k-essence" type both w.r.t. the "inflaton" and the "darkon", with the following properties: (i) Remarkable effective "inflaton" potential possessing two infinitely large at regions with vastly different heights ("vacuum" energy densities) describing the "early" and "late" Universe; (ii) Nontrivial effective gauge coupling constants running with the "inflaton", in particular, effective "inflaton"- running coupling constant of the square-root Maxwell term, which determines the strength of the charge confienement; (iii) The confinement-strength gauge coupling constant is non-zero in the "late" Universe, i.e., charge confinement is operating, whereas it vanishes in the "early" Universe, i.e., confinement-free epoch; (iv) The unification of dark energy and dark matter is explicitly seen within the FLRW reduction, where they appear as dynamically generated effective vacuum energy density and dynamically induced dust-like matter, correspondingly.