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

Abstract

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 JLA 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 a $\sim 10{{\%}}$ quadrupole amplitude relative to the monopole, H0, at these scales. We find that we can detect a $\sim 7{{\%}}$ 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 corrections, the dipole is insignificant. Finally, we find the best-fit 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 peculiar velocity covariance.

Is the observable Universe consistent with the cosmological principle?

“…34 However, observations from the Nearby Supernova Factory find no evidence for a backside infall behind the Shapley Supercluster [145]. 35 See for example discussion in [147][148][149][150]. Let us stress that variations in the cosmological parameters on the sky [90,91] (supported by [110,161,167]), excesses in the cosmic dipole [111-113, 124-131, 168], anomalous bulk flows [154][155][156][157][158] and anisotropies in scaling relations [110,159,165] constitute current results.…”

Cosmological distances with general-relativistic ray tracing: framework and comparison to cosmographic predictions

“…Recently, several works have constrained a dipole anisotropy in the cosmographic deceleration parameter from SN Ia data by adding a dipole term on top of the usual FLRW cosmography [53][54][55][56]. Dhawan et al [57] presented the first constraints of anisotropies in SN Ia data which were theoretically motivated by the simplified general cosmography [MH21,37], including the first constraints on a quadrupole in the Hubble parameter from SN Ia. While we cannot claim a significant anisotropy in current data, new and improved data sets will allow for much stronger constraints on individual multipoles -as well as more complete hierarchies of multipoles -in near-future analyses [58].…”

“…Methods to alleviate these potential issues could involve allowing for a rapid decay of the anisotropies with redshift [as is considered in, e.g. 53,[55][56][57], or implementing some smoothing of observational data prior to the cosmological fit.…”

Spatially homogeneous universes with late-time anisotropy

“…In this case, the ΛCDM luminosity distance curve falls in the center of the H 0 d L (z) band corresponding to the variation with α 0 , as shown in figure 12. It is, of course, not clear if such a considerable variation with α 0 is consistent with supernova data, although this could be studied in detail [52,53]. However, as we will now argue, the large anisotropy, η 0 = O(1), required for a significant change in the luminosity distance redshift curves, is in conflict with CMB data, at least for solutions of type I.…”