A Deep Dive into f(R) Gravity Theory

In this paper we have derived the behavior of deceleration parameter with respect to redshift in context of f(R) gravity in vacuum using Taylor expansion of derivative of action. Here we have obtained that the two first terms in Taylor expansion may describe the late time acceleration which is appeared by SNeIa without need of dark energy and dark matter. Also we have derived that any other terms higher than z in Taylor expansion may describe main inflationary epoch in the early Universe. We have shown that f(R) gravity may cover all the dynamical history of the Universe from the beginning to the late time accelerating phase transition.