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We consider models of accelerating Universe elaborated for Finsler likegravity theories constructed on tangent bundles to Lorentz manifolds. In theosculating approximation, certain locally anisotropic configurations aresimilar to those for f(R) gravity. This allows us to generalize a proposal (byNojiri, Odintsov and Saez-Gomez, arXiv: 1108.0767) in order to reconstruct andcompare two classes of Einstein-Finsler gravity, EFG, and f(R) gravity theoriesusing modern cosmological data and realistic physical scenarios. We concludethat EFG provides inflation, acceleration and little rip evolution scenarioswith realistic alternatives to standard Lambda CDM cosmology. The approach isbased on a proof that there is a general decoupling property of gravitationalfield equations in EFG and modified theories which allows us to generateoff-diagonal cosmological solutions.

Cyclic and Ekpyrotic Universes in Modified Finsler Osculating Gravity on Tangent Lorentz Bundles