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

TL;DR

This paper develops conformal gravity theories within a Finslerian geometric framework, deriving second-order field equations and exploring their potential to model cosmological phenomena as alternatives to standard cosmology.

Contribution

It introduces a family of conformal Barthel-Kropina gravity models with second-order equations, linking conformal symmetry to cosmological scalar fields and observational data.

Findings

Models can fit observational data well

Effective scalar fields emerge from conformal transformations

Potential to serve as alternatives to ΛCDM cosmology

Abstract

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 of the one-form $\beta$. Conformal symmetries do appear in many fields of physics, and they may play a fundamental role in the 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 on 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 could give an acceptable description of the observational data, and may represent a theoretically attractive alternative to the standard $\Lambda$CDM cosmology.