Searching for cosmological preferred axis using cosmographic approach

Abstract

Recent released Planck data and other astronomical observations show that the universe may be anisotropic on large scales. This hints a cosmological privileged axis in our anisotropic expanding universe. This paper proceeds a modified redshift in anisotropic cosmological model as $ 1+\tilde{z}(t,\hat{\textbf{p}})=\frac{a(t_{0)}}{a(t)}(1-A(\hat{\textbf{n}}.\hat{\textbf{p}}))$ (where $A$ is the magnitude of anisotropy ,$\hat{\textbf{n}}$ is the direction of privileged axis, and $\hat{\textbf{p}}$ is the direction of each SNe Ia sample to galactic coordinates) along with anisotropic parameter $\delta=\frac{A(\hat{\textbf{n}}.\hat{\textbf{p}})}{1+A(\hat{\textbf{n}}.\hat{\textbf{p}})}$. The luminosity distance is expanded with model-independent cosmographic parameters as a function of modified redshift $\tilde{z}$. As the transformation matrix $M(n\times n)$ is obtained to convert the Taylor series coefficients of isotropic luminosity distance to corresponding anisotropic parameters. These results culminate the magnitude of anisotropy about $\mid A\mid \simeq 10^{-3}$ and the direction of preferred axis as $(l,b)=(297^{-34}_{+34},3^{-28}_{+28})$, which are consistent with other studies in $1-\sigma$ confidence level.