  We describe a new type of generalized gravity-matter models where
$f(R)=R+R^2$ 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,
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 flat 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, 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.
