Eur. Phys. J. Plus (2015) 130: 119
https://doi.org/10.1140/epjp/i2015-15119-0

Regular Article

Einstein spaces modeling nonminimal modified gravity

¹ Instituto de Ciencias del Espacio, Consejo Superior de Investigaciones Científicas, ICE-CSIC and IEEC, Campus UAB, Torre C5-Parell-2a planta, 08193, Bellaterra, Barcelona, Spain
² Max-Planck-Institute for Physics, Foehringer Ring 6, D-80805, Muenchen, Germany
³ Inst. Theor. Phys., Lebiniz Univ. Hannover, Appelstrasse 2, D-30167, Hannover, Germany
⁴ Rector’s Department, Alexandru Ioan Cuza University, Alexandru Lapuşneanu street, nr. 14, UAIC - Corpus R, office 323, 700057, Iaşi, Romania

^* e-mail: elizalde@ieec.uab.es

Received: 11 May 2015
Accepted: 20 May 2015
Published online: 25 June 2015

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.