Observational tests of the conformal osculating Barthel-Kropina cosmological model

TL;DR

This paper tests a conformal osculating Barthel–Kropina (COBK) cosmology, a Finsler-geometry-inspired model, against late-time cosmological data using a Markov Chain Monte Carlo analysis. The COBK framework introduces a conformal factor $\phi$ and a single parameter $\gamma$, yielding generalized Friedmann equations that close with a relation between the Kropina one-form and the conformal factor. Using BAO (DESI DR2), Pantheon$^+$ SNe Ia, and Cosmic Chronometers, the study finds COBK provides a competitive (and often favored) fit relative to $\Lambda$CDM, with strong Bayesian evidence in its favor, while not fully resolving the Hubble tension. Cosmographic and dynamical analyses show COBK predicts a slightly different jerk evolution and a sign-changing conformal factor, indicating distinct geometrical dark-energy behavior and offering a viable alternative to standard cosmology. Overall, the COBK model demonstrates that conformal Finslerian geometry can yield accurate late-time cosmology with a transparent parameterization and clear observational signatures.

Abstract

We consider detailed cosmological tests of dark energy models obtained from the general conformal transformation of the Kropina metric, representing an $(α,β)$-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 $α$ and of the one-form $β$. 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 $α$ 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 $β$ 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 $γ$ 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 $γ$. A comparison with the predictions of standard $Λ$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.

Figures (5)

• Figure S1: The constraints on the parameters of the conformal osculating Barthel–Kropina model using DESI DR2, SNe Ia, and CC measurements at the 68% (1 $\sigma$) and 95% (2 $\sigma$) confidence levels.
• Figure S2: The comparative analysis of the conformal osculating Barthel–Kropina model against the $\Lambda$CDM model and the CC measurements, which are represented by blue dots with corresponding green error bars. The left panel shows the evolution of the Hubble function $H(z)$, while the right panel shows the evolution of the Hubble residual $\Delta H(z)$.
• Figure S3: The evolution of the cosmographic parameters of the conformal osculating Barthel–Kropina model compared to the $\Lambda$CDM model. The deceleration parameter $q(z)$ is shown in the left panel, while the jerk parameter $j(z)$ is represented in the right panel.
• Figure S4: The evolution of the matter density in the conformal osculating Barthel–Kropina model as compared to the $\Lambda$CDM model (left panel), and the evolution of the conformal factor $\phi$ (right panel).
• Figure S5: The evolution of the energy density (left panel) and the effective pressure (right panel) for the conformal osculating Barthel–Kropina model.