Amine Bouali

We investigate the cosmological implications of an extended gravitational framework based on biconnection gravity, constructed from the Schr $$\ddot{\textrm{o}}$$ o ¨ dinger connection and its dual. In this approach, the difference between the two connections defines the mutual curvature, which encodes the non-Riemannian geometric degrees of freedom, while their symmetric combination reduces to the Levi-Civita connection and hence reproduces general relativity at the background level. Within this setting, we derive the generalized Friedmann equations for a spatially flat Friedmann–Lemaître–Robertson–Walker Universe. The resulting equations contain additional geometric contributions that may naturally encode an effective dark energy sector induced by the biconnection degrees of freedom. We explore this extra dark energy by adopting five commonly used parametrizations, namely B $$\Lambda $$ Λ CDM, $$\omega $$ ω CDM, Chevallier–Polarski–Linder, Barboza–Alcaniz, and a logarithmic equations of state. These considerations are confronted with recent observational data, including DESI DR2, Pantheon $$^+$$ + , and CC observations. Our analysis shows that the four parameterizations enter the acceleration phase at almost the same redshifts and share the same current value of the Hubble rate. Furthermore, the statistical comparison based on the Akaike, Bayesian, and Deviance Information Criterion shows that Barboza–Alcaniz, and logarithmic parameterizations have strong evidence and are competitive with $$\Lambda $$ Λ CDM. To classify this biconnection gravity in the plethora theoretical models describing the current cosmic acceleration, we examine its implications through cosmographic tools, including the deceleration, jerk, and snap parameters, as well as through the Statefinder analysis and Om ( z ) diagnostic. These diagnostics indicate that the geometric sector generates a dynamical dark energy component that remains observationally close to $$\Lambda $$ Λ CDM at the background level. Indeed, the effective evolution of the biconnection gravity begins initially from a quintessence-like regime and subsequently evolves toward a phantom-like regime. All parameterizations under consideration face this transition in the recent past, except for the $$\omega $$ ω CDM model, which enters the phantom-like regime in the future.

In this paper, we investigate the running vacuum energy (RVE) model within the framework of $f\left(Q\right)$ gravity ($f\left(Q\right)$-RVE). In this context, the modified Friedmann equation can be used to establish a formal analogy with the structure of the RVE. A key feature is that the vacuum equation of state is no longer fixed but receives a dynamical correction proportional to $\dot{H}$ and $\ddot{H}/H$. We consider two cases of $f\left(Q\right)$-RVE, denoted as Model I (parametrized by $\nu$) and Model II (parametrized by $\nu$ and $\alpha$), corresponding to the first and second derivatives of H, respectively. The models are constrained using recent DESI BAO data in combination with ${\mathrm{Pantheon}}^{+}$, cosmic chronometer (CC), and CMB observations. Our analysis shows a deviation of $\nu$ from zero at a significance level of ∼$1.4\sigma$ for Model I, while in Model II, $\nu$ and $\alpha$ deviate from zero at $0.7\sigma$ and $1.3\sigma$, respectively, relative to $\mathrm{\Lambda }$CDM. Furthermore, the statistical comparison based on the Akaike, Bayesian, and Deviance Information Criteria (AIC, BIC, DIC) indicates that Model I remains competitive with $\mathrm{\Lambda }$CDM, while Model II is penalized due to its higher complexity and the sensitivity associated with the additional parameter $\alpha$.

We investigate $f(R,T)$ gravity, where R is the Ricci scalar and T the trace of the energy–momentum tensor, focusing on the subclass defined by $f(R,T)=R+2f\left(T\right)$. Instead of assuming a parametric form, we adopt a non-parametric reconstruction based on genetic algorithms (GA), a machine learning technique that does not rely on predefined models. Using Hubble parameter measurements from cosmic chronometers, baryon acoustic oscillations, and the Dark Energy Spectroscopic Instrument (DESI) data, we reconstruct $H\left(z\right)$ in a model-independent way. This reconstruction allows us to derive both numerical and analytical forms of $f\left(T\right)$ through the modified Friedmann equations. The analytic expression derived via GA provides an excellent fit to the numerical reconstruction. Furthermore, we compare the evolution of the Hubble parameter predicted by our model with that of the standard ΛCDM scenario (Planck), finding a good agreement for $z\lesssim 2$. These results highlight the robustness of GA-based reconstructions and suggest that the functional form of $f(R,T)$ obtained here may serve as a promising tool for further applications in cosmology and astrophysics.

We present a review of recent developments in cosmological models based on Finsler geometry, as well as geometric extensions of general relativity formulated within this framework. Finsler geometry generalizes Riemannian geometry by allowing the metric tensor to depend not only on position but also on an additional internal degree of freedom, typically represented by a vector field at each point of the spacetime manifold. We examine in detail the possibility that Finsler-type geometries can describe the physical properties of the gravitational interaction, as well as the cosmological dynamics. In particular, we present and review the implications of a particular implementation of Finsler geometry, based on the Barthel connection, and of the $(\alpha ,\beta )$ geometries, where $\alpha$ is a Riemannian metric, and $\beta$ is a one-form. For a specific construction of the deviation part $\beta$, in these classes of geometries, the Barthel connection coincides with the Levi–Civita connection of the associated Riemann metric. We review the properties of the gravitational field, and of the cosmological evolution in three types of geometries: the Barthel–Randers geometry, in which the Finsler metric function F is given by $F=\alpha +\beta$, in the Barthel–Kropina geometry, with $F={\alpha }^2/\beta$, and in the conformally transformed Barthel–Kropina geometry, respectively. After a brief presentation of the mathematical foundations of the Finslerian-type modified gravity theories, the generalized Friedmann equations in these geometries are written down by considering that the background Riemannian metric in the Randers and Kropina line elements is of Friedmann–Lemaitre–Robertson–Walker type. The matter energy balance equations are also presented, and they are interpreted from the point of view of the thermodynamics of irreversible processes in the presence of particle creation. We investigate the cosmological properties of the Barthel–Randers and Barthel–Kropina cosmological models in detail. In these scenarios, the additional geometric terms arising from the Finslerian structure can be interpreted as an effective geometric dark energy component, capable of generating an effective cosmological constant. Several cosmological solutions—both analytical and numerical—are obtained and compared against observational datasets, including Cosmic Chronometers, Type Ia Supernovae, and Baryon Acoustic Oscillations, using a Markov Chain Monte Carlo (MCMC) analysis. A direct comparison with the standard $\Lambda$CDM model is also carried out. The results indicate that Finslerian cosmological models provide a satisfactory fit to the observational data, suggesting they represent a viable alternative to the standard cosmological model based on general relativity.