Multipole expansion of the local expansion rate

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