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Resembling dark energy and modified gravity with Finsler-Randers cosmology

In this article we present the cosmological equivalence between the relativistic Finsler-Randers cosmology, with dark energy and modified gravity constructions, at the background level. Starting from a small deviation from the quadraticity of the Riemannian geometry, through which the local structure of General Relativity is modified and the curvature theory is extended, we extract the modified Friedmann equation. The corresponding extended Finsler-Randers cosmology is very interesting, and it can mimic dark-energy and modified gravity, describing a large class of scale-factor evolutions, from inflation to late-time acceleration, including the phantom regime. In this respect, the non-trivial universe evolution is not attributed to a new scalar field, or to gravitational modification, but it arises from the modification of the geometry itself.