The multipole expansion of the local expansion rate

TL;DR

This paper introduces a new observable, the expansion rate fluctuation, to analyze local universe anisotropies, revealing significant quadrupole contributions and implications for H0 measurements.

Contribution

The paper develops a novel method to analyze anisotropies in the local expansion rate using spherical harmonics, providing new insights into local universe structure.

Findings

Bulk motion of 307 ± 23 km/s aligned with the Local Group velocity

Significant quadrupole contribution indicating shear in gravity

Axisymmetric 3D quadrupole aligned with dipole axis

Abstract

We design a new observable, the expansion rate fluctuation $\eta$, to characterize deviations from the linear relation between redshift and distance in the local universe. We also show how to compress the resulting signal into spherical harmonic coefficients in order to better decipher the structure and symmetries of the anisotropies in the local expansion rate. We apply this analysis scheme to several public catalogs of redshift-independent distances, the Cosmicflows-3 and Pantheon data sets, covering the redshift range $0.01<z<0.05$. The leading anisotropic signal is stored in the dipole. Within the standard cosmological model, it is interpreted as a bulk motion ($307 \pm 23$ km/s) of the entire local volume in a direction aligned at better than $4$ degrees with the bulk component of the Local Group velocity with respect to the CMB. This term alone, however, provides an overly simplistic and inaccurate description of the angular anisotropies of the expansion rate. We find that the quadrupole contribution is non-negligible ($\sim 50\%$ of the anisotropic signal), in fact, statistically significant, and signaling a substantial shearing of gravity in the volume covered by the data. In addition, the 3D structure of the quadrupole is axisymmetric, with the expansion axis aligned along the axis of the dipole. Implications for the determination of the $H_0$ parameter are also discussed.