Kaluza-Klein model in f(R,T) theory with ?(T): Implications from data-constrained analysis

In this study, we investigate a class of five-dimensional Kaluza-Klein cosmological models within the framework of f(R,T) gravity, where the functional form is chosen as f(R,T) = f(R) + f(T) with f(R) = lambda R and f(T) = lambda T. This formulation leads to a dynamically evolving effective cosmological constant Lambda(T), which depends on the trace of the energy-momentum tensor. Exact solutions to the field equations are derived by assuming a varying deceleration parameter. The resulting cosmological model exhibits a transition from a decelerating to an accelerating expansion phase, in agreement with observational evidence. To constrain the model parameters, we employ recent observational datasets such as Hubble parameter measurements and Type Ia supernovae from the Union 2.1 compilation. A statistical analysis using chi-square minimization provides optimal parameter values. The kinematical and dynamical properties of the model are analyzed. We determine some important cosmological quantities such as the transition redshift, the present-day deceleration and equation of state parameters, and the age of the universe, which align well with observational estimates. Furthermore, the jerk parameter and statefinder parameters are employed to compare the behavior of the model with standard and alternative dark energy scenarios. The findings indicate that our model closely follows the Lambda CDM evolution at late times while allowing for deviations in earlier epochs, resembling quintessence-like behavior at the late phase of the universe.