Observational Constraints on Kaluza-Klein Universe in f(ℝ, 𝕃m) Gravity

We present a cosmological investigation of the five-dimensional Kaluza-Klein universe in the context of the [Formula: see text] theory of gravity, where [Formula: see text] is the Ricci scalar and [Formula: see text] is the matter Lagrangian. By adopting a power-law form [Formula: see text], we derive the modified field equations for a perfect fluid distribution in an anisotropic background. A physically motivated relation between the scale factors of the usual and extra dimensions is assumed to simplify the system. The resulting cosmological model yields an analytical expression for the Hubble parameter [Formula: see text], which is then constrained using 43 Hubble parameter measurements through Markov Chain Monte Carlo (MCMC) analysis. Strong agreement between the best-fit parameters and the observational data is indicated by a reduced chi-square value close to unity. To further evaluate the model’s feasibility, we examine the deceleration parameter, the [Formula: see text] diagnostic, and the statefinder parameters [Formula: see text]. These results demonstrate the capability of [Formula: see text] gravity to effectively describe dark energy dynamics in a higher-dimensional cosmological framework.