Cyclic and ekpyrotic universes in modified Finsler osculating gravity on tangent Lorentz bundles

We consider models of an accelerating Universe elaborated for Finsler-like gravity theories constructed on tangent bundles to Lorentz manifolds. In the osculating approximation, certain locally anisotropic configurations are similar to those for f(R) gravity. This allows us to generalize a proposal by Nojiri et al (2011 AIP Conf. Proc. 1458 207–21) in order to reconstruct and compare two classes of Einstein–Finsler gravity (EFG) and f(R) gravity theories using modern cosmological data and realistic physical scenarios. We conclude that EFG provides inflation, acceleration and little rip evolution scenarios with realistic alternatives to standard ΛCDM cosmology. The approach is based on a proof that there is a general decoupling property of gravitational field equations in EFG and modified theories which allows us to generate off-diagonal cosmological solutions. (paper)