Einstein Spaces Modeling Nonminimal Modified Gravity

Abstract: 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. To prove this statement, exact and approximate solutions are constructed in the review, which encode certain models of covariant Ho\v{r}ava type gravity with dynamical Lorentz symmetry breaking. The corresponding FLRW cosmological dynamics with possible nonholonomic deformations and the reconstruction procedure of certain actions closely related with the standard $\Lambda$CDM universe are studied. Off-diagonal generalizations of de Sitter 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 briefly discussed.