The significance of anisotropic signals hiding in the type Ia supernovae

TL;DR

This study investigates anisotropic signals in Type Ia supernovae data using two methods, revealing that the dipole-fitting method is statistically significant, but current data quality limits definitive conclusions about the universe's isotropy.

Contribution

The paper compares two methods for detecting anisotropy in supernova data and models matter density anisotropy as a dipole, providing insights into their statistical significance and biases.

Findings

DF method is statistically significant in detecting anisotropy.

HC method is biased by data distribution in the sky.

Current data quality is insufficient to confirm universe anisotropy.

Abstract

We use two different methods, i.e., dipole-fitting (DF) and hemisphere comparison (HC), to search for the anisotropic signals hiding in the Union2.1 data set. We find that the directions of maximum matter density derived using these two methods are about $114^{\circ}$ away from each other. We construct four Union2.1-like mock samples to test the statistical significance of these two methods. It is shown that DF method is statistically significant, while HC method is strongly biased by the distribution of data points in the sky. Then we assume that the anisotropy of distance modulus is mainly induced by the anisotropy of matter density, which is modeled to be the dipole form $\Omega_M=\Omega_{M0}(1-\cos\theta)$. We fit our model to Union2.1, and find that the direction of maximum matter density is well consistent with the direction derived using DF method, but it is very different from the direction previously claimed. Monte Carlo simulations show that our method is statistically more significant than HC method, although it is not as significant as DF method. The statistical significance can be further improved if the data points are homogeneously distributed in the sky. Due to the low quality of present supernovae data, however, it is still premature to claim that the Universe has any preferred direction.