Author(s): S Basilakos APKoure
n this article we present the cosmological equivalence bet ween the relativistic Finsler-Randers cosmology, with dark energy and modified gravity constructi ons, at the background level. Start- ing from a small deviation from the quadraticity of the Riema nnian geometry, through which the local structure of General Relativity is modified and the cur vature theory is extended, we extract the modified Friedmann equation. The corresponding extende d Finsler-Randers cosmology is very interesting, and it can mimic dark-energy and modified gravi ty, describing a large class of scale- factor evolutions, from inflation to late-time acceleratio n, including the phantom regime. In this respect, the non-trivial universe evolution is not attribu ted to a new scalar field, or to gravitational modification, but it arises from the modification of the geome try itself.