Higher-Dimensional Study of Cosmic Evolution in f(R, T) Gravity with MLE Validation

This study presents the cosmological implications of f (R, T) gravity using an n-dimensional metric inspired by Kaluza-Klein theory. By integrating the curvature scalar R and the trace of the energy-momentum tensor T , we construct a comprehensive model of cosmic evolution. Through a detailed analysis of key parameters, including pressure, energy density, the equation of state (EoS) parameter, and the Hubble parameter across different redshift ranges, our findings reveal groundbreaking insights into the universe’s complex evolution. We identify a critical transition from an early period of rapid expansion to the present era, when dark energy’s influence induced accelerated cosmic growth, marked by a positive deceleration parameter. To ensure observational relevance, the model’s predictions are validated against Hubble parameter datasets using Maximum Likelihood Estimation. The results affirm the consistency of the f (R, T) framework with cosmological observations and highlight the significant influence of higher-dimensional geometry on cosmic evolution, offering new perspectives on structure formation and the universe’s future trajectory. These findings enhance our understanding of how extra dimensions shape the universe’s expansion history and its ultimate fate.