  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 $\Lambda$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.
