Observational tests of the conformal osculating Barthel-Kropina cosmological model

We consider detailed cosmological tests of dark energy models obtained from the general conformal transformation of the Kropina metric, representing an $(\alpha,\beta)$-type Finslerian geometry. In particular, we restrict our analysis to the osculating Barthel Kropina geometry. The Kropina metric function is defined as the ratio of the square of a Riemannian metric $\alpha$ and of the one-form $\beta$. In this framework, we also consider the role of the conformal transformations of the metric, which allows us to introduce a family of conformal Barthel-Kropina theories in an osculating geometry. The models obtained in this way are described by second-order field equations, in the presence of an effective scalar field induced by the conformal factor. The generalized Friedmann equations of the model are obtained by adopting for the Riemannian metric $\alpha$ the Friedmann Lemaitre Robertson Walker representation. In order to close the cosmological field equations, we assume a specific relationship between the component of the one-form $\beta$ and the conformal factor. With this assumption, the cosmological evolution is determined by the initial conditions of the scalar field and a single free parameter $\gamma$ of the model. The conformal Barthel Kropina cosmological models are compared against several observational datasets, including Cosmic Chronometers, Type Ia Supernovae, and Baryon Acoustic Oscillations, using a Markov Chain Monte Carlo (MCMC) analysis, which allows the determination of $\gamma$. A comparison with the predictions of standard $\Lambda$CDM model is also performed. {Our results indicate that the conformal osculating Barthel Kropina model can be considered as a successful, and simple, alternative to standard cosmological models.