Testing the Cosmic Anisotropy with Supernovae Data: Hemisphere
  Comparison and Dipole Fitting
  The cosmological principle is one of the cornerstones in modern cosmology. It
assumes that the universe is homogeneous and isotropic on cosmic scales. Both
the homogeneity and the isotropy of the universe should be tested carefully. In
the present work, we are interested in probing the possible preferred direction
in the distribution of type Ia supernovae (SNIa). To our best knowledge, two
main methods have been used in almost all of the relevant works in the
literature, namely the hemisphere comparison (HC) method and the dipole fitting
(DF) method. However, the results from these two methods are not always
approximately coincident with each other. In this work, we test the cosmic
anisotropy by using these two methods with the Joint Light-Curve Analysis (JLA)
and simulated SNIa datasets. In many cases, both methods work well, and their
results are consistent with each other. However, in the cases with two (or even
more) preferred directions, the DF method fails while the HC method still works
well. This might shed new light on our understanding of these two methods.
