Reconstructing cosmographic parameters from different cosmological models: case study. Interacting new generalized Chaplygin gas model

In this paper, we present a method to reconstruct cosmographic parameters, $$\{q,j,s,l\}$$ {q,j,s,l} and their evolution from particular cosmological models. In this method inspired by dynamical system approach, we convert the equation of the cosmological model into an equivalent system of first order differential equations which is much easier to solve numerically. Then, we reproduce the cosmographic parameters in terms of these variables. Instead of best fitting the cosmographic parameters with observation directly, we best fit and estimate the parameters and initial conditions of the model by observational, then the cosmographic parameters will be constrained automatically. The advantage of this method is that, it is free of some of shortcomings reconstructing theories with higher-order derivatives. It also enable us to measure not only the current value of cosmographic parameters $$\{q_{0},j_{0},s_{0},l_{0}\}$$ {q0,j0,s0,l0} the past values, $$\{q_{i},j_{i},s_{i},l_{i}\}$$ {qi,ji,si,li} , future values $$\{q_{f},j_{f},s_{f},l_{f}\}$$ {qf,jf,sf,lf} and their evolution. This can be a useful tool to test, compare and distinguish different cosmological models according to the reconstructed cosmographic parameters at different epoch of the universe.