Cosmological evolution and dark energy in osculating Barthel-Randers
  geometry
  We consider the cosmological evolution in an osculating point Barthel-Randers
type geometry, in which to each point of the space-time manifold an arbitrary
point vector field is associated. This Finsler type geometry is assumed to
describe the physical properties of the gravitational field, as well as the
cosmological dynamics. For the Barthel-Randers geometry the connection is given
by the Levi-Civita connection of the associated Riemann metric. The generalized
Friedmann equations in the Barthel-Randers geometry are obtained by considering
that the background Riemannian metric in the Randers line element is of
Friedmann-Lemaitre-Robertson-Walker type. The matter energy balance equation is
derived, and it is interpreted from the point of view of the thermodynamics of
irreversible processes in the presence of particle creation. The cosmological
properties of the model are investigated in detail, and it is shown that the
model admits a de Sitter type solution, and that an effective cosmological
constant can also be generated. Several exact cosmological solutions are also
obtained. A comparison of three specific models with the observational data and
with the standard $\Lambda$CDM model is also performed by fitting the observed
values of the Hubble parameter, with the models giving a satisfactory
description of the observations.
