The quadrupole in the local Hubble parameter: first constraints using Type Ia supernova data and forecasts for future surveys

The cosmological principle asserts that the Universe looks spatially homogeneous and isotropic on sufficiently large scales. Given its fundamental implications, it is important to empirically test its validity. In this paper, we use the Type Ia supernova (SN Ia) magnitude-redshift relation, from both the Pantheon and joint light-curve analysis compilations, to constrain theoretically motivated anisotropies in the Hubble flow. In particular, we constrain the quadrupole in the effective Hubble parameter and the dipole in the effective deceleration parameter. We find no significant quadrupole term regardless of the redshift frame used. Our results are consistent with the theoretical expectation of a quadrupole moment of a few percent at scales of ~100 h^-1 Mpc. We place an upper limit of an $\sim 10{{\%}}$ quadrupole amplitude relative to the monopole, H₀, at these scales. We find that we can detect an $\sim 7{{\%}}$ quadrupole at the 5σ level, for a forecast low-z sample of 1055 SNe Ia. We find the signficance of an exponentially decaying dipole of the deceleration parameter depends on the redshift frame used. In the heliocentric frame, as expected, it is detected at ~3σ significance. In the cosmic microwave background (CMB) rest frame, we find a marginal ~2σ dipole, however, after applying peculiar velocity (PV) corrections, the dipole is insignificant. Finally, we find the best-fitting frame of rest relative to the supernovae to differ from that of the CMB at ~2σ for both compilations, which reduces to <1σ when including PV covariance.