Numerical and Statistical Insights into f (R, T ) Cosmology: GRP, RK4, and MLE Approaches

This study explores the stability of an f (R, T) gravity-based cosmological model using perturbation techniques and numerical methods. Stability conditions are examined by analyzing the growth rate of small perturbations in density and pressure. Furthermore, the Runge-Kutta fourth-order (RK4) method is employed to numerically track the evolution of these perturbations and validate the theoretical predictions. To ensure consistency with observational data, the model is tested against Hubble parameter measurements and the Pantheon Type Ia super-nova dataset using the Maximum Likelihood Estimation (MLE) method. The findings provide deeper insights into the stability of modified gravity models and underscore the significance of combining analytical, numerical, and observational approaches in cosmological studies.