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 data sets. 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.

Figure 1

The pseudocolor map of AL$(l,b)$ obtained by using the HC method to the JLA SNIa data set. The two preferred directions $(23.49°,2.25°)$ and $(299.47°,28.39°)$ are within the red regions. See the text for details.

Figure 2

The marginalized probability distributions of the dipole magnitude $A_D$ and the dipole direction $(l,b)$, obtained by using the DF method to the JLA SNIa data set with the priors ${\mathrm{\Omega }}_{m0}=0.295$ and $A_D\ge 0$. Note that $A_D$ is given in units of ${10}^{-3}$. See the text for details.

Figure 3

The marginalized probability distributions of ${\mathrm{\Omega }}_{m0}$, the dipole magnitude $A_D$, and the dipole direction $(l,b)$, obtained by using the DF method to the JLA SNIa data set without any prior on ${\mathrm{\Omega }}_{m0}$ and $A_D$. See the text for details.

Figure 4

Demonstration of the spatial distributions of the “pole-centralized” (left panel) and “equator-centralized” (right panel) simulated SNIa, before they are rotated to a preset direction. The blue and red points are the SNIa generated with a relatively large and small ${\mathrm{\Omega }}_{m0}$, respectively. See the text for details.

Figure 5

The marginalized probability distributions of ${\mathrm{\Omega }}_{m0}$, the dipole magnitude $A_D$, and the dipole direction $(l,b)$, obtained by using the DF method to the simulated SNIa data set PC1. See the text for details.

Figure 6

The same as in Fig. 5, except for the simulated SNIa data set PC2. See the text for details.

Figure 7

The same as in Fig. 5, except for the simulated SNIa data set EC1. See the text for details.

Figure 8

The same as in Fig. 5, except for the simulated SNIa data set $\mathrm{EC}{2}_d$. See the text for details.

Figure 9

The same as in Fig. 5, except for the simulated SNIa data set $\mathrm{EC}{3}_d$. See the text for details.

Figure 10

Preferred directions $(l,b)$ found in various observational data sets (see Table 1). Note that the three preferred directions in the SPARC Galaxies are labeled by the green points, while the others are labeled by the red points. See the text and Table 1 for details.