An approach to investigate stability, cosmography and the dark energy dipole: A case study of cosmological models in R1+ϵ

Abstract

In this paper, in a new approach, we study the stability of the dynamical system (DS) of [Formula: see text] in terms of two significant cosmological parameters, deceleration parameter and jerk parameter [Formula: see text]. Other cosmographic parameters such as [Formula: see text] have been obtained in terms of these two parameters. We have obtained critical points ([Formula: see text]), the best fitted current values of cosmographic parameters ([Formula: see text]), best value for model parameter [Formula: see text] and best trajectory of dynamics of system in phase space by simultaneously solving the DS and best fitting the parameter by the SNIa data. By defining modified redshift in anisotropic cosmological model as [Formula: see text] (where [Formula: see text] is a magnitude of anisotropy, [Formula: see text] is direction of privileged axis and [Formula: see text] is the direction of each SNe Ia sample to galactic coordinates), the luminosity distance has been obtained in terms of modified redshift using cosmography method. Using union 2 data, we have found the direction of privileged axis in the galactic coordinate. The results show that the magnitude of anisotropy is about [Formula: see text] and the direction of privileged axis is [Formula: see text]. Also, our results are consistent with other studies in [Formula: see text] confidence level.