FRW Universe in R2 Gravity

We investigate a model of the Friedmann Robertson Walker metric (FRW) universe governed by hybrid expansion law (HEL) a = t(alpha) e(beta t) in R-2 gravity. By Applying, energy and stability conditions in derived model, we check its physical viability. This model is based on f (R, T) = f (R) + f (T); f (R) = R + alpha R-2 and f (T) = T and we have assumed T = 3p > 0. It is important to note that our model gives the current universe observable properties, including acceleration, without introducing dark energy or the cosmological constant. The following are some key features of the resulting model: Throughout the expansion of the cosmos, the jerk parameter has a positive sign, but the deceleration parameter has a negative sign. The current universe's late-time acceleration is confirmed by this. Finally, we may say that f (R, T) gravity can give a considerable amount of information. There is no need for dark energy or the cosmological constant in a cosmic scenario with late time acceleration. As a consequence, one may argue that f (R) = R + alpha R-2 is a dark energy model alternative that must be considered when defining the universe. We also discuss the jerk, lerk and snap parameters.