Nonlinear Perturbation Stability of Cosmological Model in f(R,T) Gravity with Maximum Likelihood Approach

This study investigates the nonlinear stability of cosmological model within the framework of [Formula: see text] gravity by employing a time-dependent deceleration parameter [Formula: see text], where [Formula: see text] is Hubble parameter and [Formula: see text] is an arbitrary constant. Utilizing nonlinear perturbation analysis, we derive growth rate parameters governing perturbations evolution and investigate their role in determining system’s stability. The study establishes localized stability conditions for varying ranges of model parameters. Additionally, the Maximum Likelihood Estimation (MLE) method is employed to validate theoretical predictions against observational datasets, including the Hubble parameter and Pantheon Type Ia supernova (SNe Ia) data. The best-fit values indicate consistency with empirical observations, reinforcing the model’s viability. This work provides a comprehensive framework for assessing cosmic evolution under nonlinear perturbations in modified gravity theory.