Vacuum Structure and Gravitational Bags Produced by Metric-Independent Spacetime Volume-Form Dynamics

We propose a new class of gravity-matter-gauge theories in terms of two different non-Riemannian volume-forms independent of the Riemannian metric. The nonlinear gauge field system contains a square-root $\sqrt{-F^2}$ of the standard Maxwell Lagrangian which is known to describe charge confinement in flat spacetime. In the physical Einstein frame we obtain an effective Lagrangian of "k-essence" type with quadratic dependence on the scalar "dilaton" kinetic term X, with a remarkable effective potential possessing two infinitely large flat regions as well as with nontrivial effective gauge coupling constants running with the "dilaton" $\varphi$. Corresponding to the each of the two flat regions we find "vacuum" configurations of the following types: (i) $\varphi = const$ and a non-zero gauge field vacuum $\sqrt{-F^2}\neq 0$, which corresponds to a charge confining phase; (ii) X = const ("kinetic vacuum") and ordinary gauge field vacuum $\sqrt{-F^2}=0$ which supports confinement-free charge dynamics. In one of the flat regions of the effective potential we also find: (iii) X = const ("kinetic vacuum") and a non-zero gauge field vacuum $\sqrt{-F^2}\neq 0$, which again corresponds to a charge confining phase. In all three cases the spacetime metric is de Sitter or Schwarzschild-de Sitter. Both "kinetic vacuums" (ii) and (iii) can exist only within a finite-volume space region below a de Sitter horizon. Extension to the whole space requires matching the latter with the exterior region with a nonstandard Reissner-Nordstroem-de Sitter geometry carrying an additional constant radial background electric field. As a result we obtain two classes of gravitational bag-like configurations with properties, which on one hand partially parallel some of the properties of the solitonic "constituent quark" model and, on the other hand, partially mimic some of the properties of MIT bags in QCD phenomenology.