Higher derivative f(R) gravity models for an accelerating universe

Abstract

In modified gravity, we investigate the universe’s accelerating expansion in a vacuum. We obtain a highly nonlinear differential equation from the variation of Einstein–Hilbert action with the consideration of a Robertson–Walker metric. Because the differential equations have non-analytic solutions, the expansion phase of the Friedmann–Robertson–Walker universe is studied using numerical approaches. We analyzed the acceleration phases of the cosmos for different periods, cosmic jerk and snap parameters, and their dependencies on the initial values and coupling parameters involved in various [Formula: see text] gravity models. Using a parametric technique, we also give the values of the jerk and snap parameters in different accelerating stages of the universe. Finally, the behavior of the dark energy component is addressed for [Formula: see text] models.

Cosmological dynamics in f(R) gravity models through cosmographic energy conditions

“…Equation (29) is a highly nonlinear differential equation, making it challenging to derive an exact solution due to the time-dependent nature of the known functional forms z and H. We adopt numerical methods to analyze the evolution of dark energy in f (R) gravity, while constraining the coupling constants based on the results obtained from energy conditions. To do so we rewrite the equation (17) for the deceleration parameter (q), cosmic jerk ( j) and cosmic snap (s) as a function of z and H as…”

“…In Einstein Hilbert's action, models such as R 1 [7,8,10] and others [12][13][14] have demonstrated the current scenario of the accelerating universe and show that the cosmos moves through multiple epochs of acceleration and deceleration. The emergence of such phases of the Universe depends on the coupling factors included in the models [15][16][17]. Though these theories offer an alternate explanation for the cosmic acceleration in the absence of dark energy and additional hyperspace, the freedom in constructing diverse functional forms of f (R) poses the question of how to constrain these numerous conceivable f (R)-gravity model from theoretical and empirical viewpoints.…”