Conformal gravitational theories in Barthel-Kropina-type Finslerian geometry, and their cosmological implications

We consider dark energy models obtained from the general conformal transformation of the Kropina metric, representing an (alpha, beta)-type Finslerian geometry, constructed as the ratio of the square of a Riemannian metric alpha and the one-form beta. Conformal symmetries appear in many fields of physics, and they may play a fundamental role in our understanding of the Universe. We investigate the possibility of obtaining conformal theories of gravity in the osculating Barthel-Kropina geometric framework, where gravitation is described by an extended Finslerian-type model, with the metric tensor depending on both the base space coordinates and a vector field. We show that it is possible to formulate a family of conformal Barthel-Kropina theories in an osculating geometry with second-order field equations, depending on the properties of the conformal factor, whose presence leads to the appearance of an effective scalar field of geometric origin in the gravitational field equations. The cosmological implications of the theory are investigated in detail by assuming a specific relation between the component of the one-form of the Kropina metric and the conformal factor. The cosmological evolution is thus determined by the initial conditions of the scalar field and a free parameter of the model. We analyze in detail three cosmological models corresponding to different values of the theory parameters. Our results show that the conformal Barthel-Kropina model can provide an acceptable description of the observational data, and may represent a theoretically attractive alternative to the standard Lambda CDM cosmology.