Probing the isotropy of cosmic acceleration using different supernova samples

Recent studies indicated that an anisotropic cosmic expansion may exist. In this paper, we use three data sets of type Ia supernovae (SNe Ia) to probe the isotropy of cosmic acceleration. For the Union2.1 data set, the direction and magnitude of the dipole are \((l=309.3^{\circ } {}^{+ 15.5^{\circ }}_{-15.7^{\circ }} ,\ b = -8.9^{\circ } {}^{ + 11.2^{\circ }}_{-9.8^{\circ }} )\), and \(\ A=(1.46 \pm 0.56) \times 10^{-3}\) from dipole fitting method. The hemisphere comparison results are \(\delta =0.20,l=352^{\circ },b=-9^{\circ }\). For the Constitution data set, the results are \((l=67.0^{\circ }{}^{+ 66.5^{\circ }}_{-66.2^{\circ }},\ b=-0.6^{\circ }{}^{+ 25.2^{\circ }}_{-26.3^{\circ }})\), and \(\ A=(4.4 \pm 5.0) \times 10^{-4}\) for dipole fitting and \(\delta = 0.56,l=141^{\circ },b=-11^{\circ }\) for hemisphere comparison. For the JLA data set, no significant dipolar or quadrupolar deviation is found. We find previous works using (l, b, A) directly as fitting parameters may get improper results. We also explore the effects of anisotropic distributions of coordinates and redshifts on the results using Monte-Carlo simulations. We find that the anisotropic distribution of coordinates can cause dipole directions and make dipole magnitude larger. Anisotropic distribution of redshifts is found to have no significant effect on dipole fitting results.