Abstract
Off-diagonal vacuum and nonvacuum configurations in the Einstein gravity can mimic physical effects of modified gravitational theories of f(R, T, R μν T μν) type. To prove this statement, exact and approximate solutions are constructed in the paper, which encode certain models of covariant Hořava-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 ΛCDM 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 nonconstant exotic fluids and effective matter. The problem of possible matter instability for such off-diagonal deformations in (modified) gravity theories is briefly discussed.
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