Constraints on Cosmological Anisotropy out to z=1 from Supernovae Ia

A combined sample of 79 high and low redshift supernovae Ia (SNe) is used to set constraints on the degree of anisotropy in the Universe out to $z\simeq1$. First we derive the global most probable values of matter density $\Omega_M $, the cosmological constant $\Omega_\Lambda $, and the Hubble constant $H_0$, and find them to be consistent with the published results from the two data sets of Riess et al. 1998 (R98) and Perlmutter et al. 1999 (P99). We then examine the Hubble diagram (HD, i.e., the luminosity-redshift relation) in different directions on the sky by utilising spherical harmonic expansion. In particular, via the analysis of the dipole anisotropy, we divide the sky into the two hemispheres that yield the most discrepant of the three cosmological parameters, and the scatter $\chi^2_{\rm HD}$ in each case. The most discrepant values roughly move along the locus $-4\Omega_M +3 \Omega_{\Lambda} = 1$ (cf. P99), but by no more than $\Delta \approx 2.5$ along this line. For a perfect FRW universe, Monte Carlo realizations that mimic the current set of SNe yield values higher than the measured $\Delta$ in $\sim 1/5$ of the cases. We discuss implications for the validity of the Cosmological Principle, and possible calibration problems in the SNe data sets.