2001MNRAS.323..859K

A combined sample of 79 high- and low-redshift Type Ia supernovae (SNe) is used to set constraints on the degree of anisotropy in the Universe out to z≃1. First, we derive the global most probable values of matter density Ω_M, the cosmological constant Ω_Λ and the Hubble constant H₀, and find them to be consistent with the published results from the two data sets of Riess et al. and Perlmutter et al. We then examine the Hubble diagram (HD, i.e., the luminosity-redshift relation) in different directions on the sky by utilizing 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 χHD2 in each case. The most discrepant values roughly move along the locus -4Ω_M+3Ω_Λ=1 (cf. Perlmutter et al.), but by no more than Δ~2.5 along this line. For a perfect Friedmann-Robertson-Walker universe, Monte Carlo realizations that mimic the current set of SNe yield values higher than the measured Δ in ∼1/5 of the cases (for Ω_M). We discuss implications for the validity of the Cosmological Principle, and possible calibration problems in the SNe data sets.