Effect of low anisotropy on cosmological models by using supernova data

By using the supernovae type Ia data we study influence of the anisotropy (although low) on the evolution of the universe and compare ${\Lambda}$CDM model with 6 representative parametrizations of the recent Hubble expansion history $H(z)$. To compare these models we use the the maximum likelihood method for find that the best fit dynamical $\omega(z)$ and $q(z)$ obtained from the SNIa dataset. In particular we find the best fit value of $\Lambda$CDM model $(\Omega_{\sigma_0}= 0.013$, $\chi^2_{min}=197.56)$. The analysis shows that by considering the anisotropy, it leads to more best fit parameters in all models (except of SCDM) with SNIa data. We also use two statistical tests such as the usual $\chi^2_{min}/dof$ and p-test to compare different dark energy models. According to both statistical tests and considering anisotropy, the linear parametrization model that is providing the best fit to $\Lambda$CDM model.