Higher-Dimensional Cosmology in the Framework of Generalized Chaplygin Gas: an Approximation Method

We present a higher-dimensional cosmological model with a generalized Chaplygin-type gas to explain the late-time acceleration of the Universe. The model admits dimensional reduction and reproduces the standard $4D$ Chaplygin cosmology for $d=0$. Using Hubble-$57$ data, we obtain observational constraints on the model parameters. Due to the highly nonlinear nature of the field equations, the model successfully describes both matter-dominated and accelerating phases of the Universe. By adopting a first-order approximation, we derive exact time-dependent solutions for the scale factors in both ordinary and extra dimensions, along with an exact expression for the flip time. The model approaches the $Λ$CDM scenario at large scale factors and exhibits the desired transition from deceleration to acceleration. The evolution of the deceleration parameter, effective EoS parameter, and jerk parameter is also discussed. The constrained value of the Chaplygin parameter α 1 disfavors the pure Chaplygin gas model $(α= 1)$ and suggests that smaller values of $α$ are favored at late times.