Effective Einstein Cosmological Spaces for Non-Minimal Modified Gravity

Certain off-diagonal vacuum and nonvacuum configurations in Einstein gravity can mimic physical effects of modified gravitational theories of $f(R,T,R_{\mu \nu }{T}^{\mu \nu })$ type. We prove this statement by constructing exact and approximate solutions which encode certain models of covariant Ho\v rava type gravity with dynamical Lorentz symmetry breaking. Off-diagonal generalizations of de Sitter and nonolonomic $\mathrm{\Lambda }$CDM universes are constructed which are generated through nonlinear gravitational polarization of fundamental physical constants and which model interactions with non-constant exotic fluids and effective matter. The problem of possible matter instability for such off-diagonal deformations in (modified) gravity theories is discussed.