Two-Fluid Scenario for Dark Energy Cosmological Model in Five Dimensional Kaluza-Klein Space Time

In this work, we investigate the evolution of the dark energy equation of state parameter in a five-dimensional Kaluza-Klein homogeneous and isotropic cosmological model filled with a barotropic fluid and a dark fluid. We adopt a special form of the deceleration parameter, q = - (aä/(à2)) = -1 + α/(1+aα) as proposed by Singha and Debnath International Journal of Theoretical Physics, 48, 351 (2009), which facilitates a smooth transition from early-time deceleration to late-time acceleration. Using this form, we solve the Einstein field equations and analyze the dynamics of the universe under both non-interacting and interacting two-fluid scenarios. The physical and geometrical implications of the model are examined in detail. Key cosmological quantities such as the dark energy density ρD, pressure pD, and density parameter ΩD are studied for various spatial curvatures – open, closed, and flat geometries. The solutions obtained are physically viable and in good agreement with current observational data, including those from Type Ia supernovae, the cosmic microwave background, and large-scale structure surveys. Additionally, we evaluate the jerk parameter to assess the model’s deviation from the standard ΛCDM cosmology. The model demonstrates compatibility with the observed late-time accelerated expansion and provides a unified framework that accommodates a wide range of cosmic behaviors through appropriate parameter choices.