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

In this paper, in a new approach, we study the stability of the dynamical system (DS) of R1+epsilon in terms of two significant cosmological parameters, deceleration parameter and jerk parameter {q, j}. Other cosmographic parameters such as (l, s, ...) have been obtained in terms of these two parameters. We have obtained critical points (q(e), j(e)), the best fitted current values of cosmographic parameters (q(0), j(0), l(0), s(0)), best value for model parameter epsilon 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 1 + z(t, (p) over cap) = a(t(0))/a(t) (1 -A((n) over cap . (p) over cap)) (where A is a magnitude of anisotropy, (n) over cap is direction of privileged axis and (p) over cap 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 vertical bar A vertical bar similar or equal to 10(-3) and the direction of privileged axis is (l, b) = (298(+34)(-34), 2(+23)(-23)). Also, our results are consistent with other studies in 1-sigma confidence level.