arXiv2015
We investigate the validity of the Cosmological Principle by mapping the cosmological parameters $H_0$ and $q_0$ through the celestial sphere. In our analysis, performed in a low-redshift regime to follow a model-independent approach, we use two compilations of type Ia Supernovae (SNe Ia), namely the Union2.1 and the JLA datasets. Firstly, we show that the angular distributions for both SNe Ia datasets are statistically anisotropic at high confidence level ($p$-value $<$ 0.0001), in particular the JLA sample. Then we find that the cosmic expansion and acceleration are mainly of dipolar type, with maximal anisotropic expansion [acceleration] pointing towards $(l,b) \simeq (326^{\circ},12^{\circ})$ [$(l,b) \simeq (174^{\circ},27^{\circ})$], and $(l,b) \simeq (58^{\circ},-60^{\circ})$ [$(l,b) \simeq (225^{\circ},51^{\circ})$] for the Union2.1 and JLA data, respectively. Secondly, we use a geometrical method to test the hypothesis that the non-uniformly distributed SNe Ia events could introduce anisotropic imprints on the cosmological expansion and acceleration. For the JLA compilation, we found significant correlations between the celestial distribution of data points and the directional studies of $H_0$ and $q_0$, suggesting that these results can be attributed to the intrinsic anisotropy of the sample. In the case of the Union2.1 data, nonetheless, these correlations are less pronounced, and we verify that the dipole asymmetry found in the $H_0$ analyses coincides with the well-known bulk-flow motion of our local group. From these analyses, we conclude that the directional asymmetry on the cosmological parameters maps are mainly either of local origin or due to celestial incompleteness of current SNe Ia samples.