Analytical and Observational Analysis of Barrow Entropy Based Holographic Dark Energy in <i>f</i> ( <i>R</i> , <i>T</i> ) Theory

In this study, the Barrow Holographic Dark Energy (BHDE) model is investigated within the f(R, T) gravity scope using a Kaluza-Klein metric. The relevant field equations are derived and solved using the Hubble parameter and the BHDE density, thereby determining the fundamental cosmological quantities of the model. To ensure physical viability, the free parameters of the model are constrained using the optimized parameters obtained from a joint statistical analysis of BAO, H(z) and Pantheon datasets. The dynamical evolution of fundamental cosmological quantities, such as the deceleration parameter, equation of state, energy densities, and statefinder diagnostic, is analyzed. The obtained results indicate that the model exhibits a transition from a decelerating to an accelerating expansion phase, and the evolutionary behaviors of the parameters reflect the general dynamics of a dark-energy-dominated universe.