Dark Energy Constraints on Red-Shift-Based Gravity

We have studied cosmological dynamics in gravity theory via cosmographic parameters. We have changed variables of field equations from time to red-shift and solved the achieved differential equation analytically for . Then we have used Taylor expansion to find general form of function around the present day value of scalar curvature. By introducing we would simplify our calculations; if we consider as a given function we would restrict our answers of . In this paper we offer a linear form of which leads us to a specific function, where is a constant which depends on the present day value of deceleration parameter. As an example, using Taylor expansion coefficients, we have compared our analytically calculated function with reconstructed function for Dark Energy models. To reconstruct action for Dark Energy models, we have used corresponding of each Dark Energy model for calculating Taylor expansion coefficients. As our function is linear, the Taylor expansion coefficients would be a function of present day value of deceleration parameter.