Probing the anisotropic expansion from supernovae and GRBs in a model-independent way

In this paper, we study the anisotropic expansion of the universe using type Ia supernovae Union 2.1 sample and 116 long gamma-ray bursts. The luminosity distance is expanded with model-independent cosmographic parameters as a function of $z/(1+z)$ directly. Thus the results are independent of cosmology model. We find a dipolar anisotropy in the direction ($l=309.2^\circ \pm 15.8^\circ$, $b=-8.6^\circ \pm 10.5^\circ$) in galactic coordinates with a significant evidence $97.29\%$ (more than $2~\sigma$). The magnitude is $(1.37\pm 0.57) \times 10^{-3}$ for the dipole, and $(2.6\pm 2.1)\times 10^{-4}$ for the monopole, respectively. This dipolar anisotropy is more significant at low redshift from the redshift tomography analysis. We also test whether this preferred direction is caused by bulk flow motion or dark energy dipolar scalar perturbation. We find that the direction and the amplitude of the bulk flow in our results are approximately consistent with the bulk flow surveys. Therefore, bulk flow motion may be the main reason for the anisotropic expansion at low redshift, but the effect of dipolar distribution dark energy can not be excluded, especially at high redshift.