Cosmographic implications of f (R, T) gravitation

In this paper, we will explore the cosmological implications of the flat Friedmann-Robertson-Walker model within the context of f ( R, T) = R + alpha R-2 + beta ln(T/T-0) gravity, where R is the Ricci scalar, and T is the trace of the energy-momentum tensor. We prove that the generalized Friedmann equation has nonlinear differential equations of the third order when a nonlinear term is introduced into the f (R, T) formula. In redshift space, the modified theory's field equations are converted into a coupled system of first-order differential equations. The current values of q, j, and s, the deceleration, the jerk, and the snap parameters from Planck 2018 are used as initial conditions with Runge-Kutta fourth-order method to solve for the model numerically. Our obtained model successfully explains the phase transition of the universe's expansion (from an early decelerating phase to the late accelerating phase).