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.
