In this paper we have considered a red-shift based linear correction in derivative of action in the context of vacuum f (R) gravity. Here we have found out that the linear correction may describe the late time acceleration which is appeared by SuperNovae Ia with no need of dark energy. Also we have calculated the asymptotic action for the desired correction. The value of all solutions may reduce to de' Sitter universe in the absence of correction term.
In this paper we study consistent solutions of spherically symmetric space in metric ) (R f gravity theory. Here we inversely obtain a generic action from metric solutions that describe flat rotation curves in spiral galaxies without dark matter. Then we show that obtained solutions are in conformity with Tully-Fisher relation and modified Newtonian dynamics, which are two strong constraints in justification of flat rotation curves in spiral galaxies.
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.
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