The anisotropic expansion rate of the local Universe and its covariant cosmographic interpretation

TL;DR

This work probes the local expansion rate anisotropies without assuming a FLRW background by introducing the expansion rate fluctuation field $\eta$ and interpreting its multipoles via covariant cosmography. Using CF4 and Pantheon+, the authors map $\eta$ up to $z\lesssim0.1$, finding a dominant dipole and significant quadrupole aligned along a common axis, with octupole signals at low redshift. The covariant cosmographic analysis connects these multipoles to a small set of generalized CC functions, revealing a strong quadrupole in the covariant Hubble parameter and nonzero dipole/octupole in the deceleration parameter, while remaining largely model-independent and non-perturbative. The results imply a substantial local bulk flow and a need for a covariant, geometry-aware understanding of local spacetime, with future surveys poised to sharpen the axisymmetric picture and test cosmographic predictions.

Abstract

Without making any assumption on the underlying geometry and metric of the local Universe, we provide a measurement of the expansion rate fluctuation field using the Cosmicflows-4 and Pantheon+ samples in the redshift range $0.01 < z < 0.1$ ($30 \,h^{-1}\,\mathrm{Mpc} < R < 300\,h^{-1}\,\mathrm{Mpc}$). The amplitude of the anisotropic fluctuations is found to be of order a few percent relative to the monopole of the expansion rate. We further decompose the expansion rate fluctuation field into spherical harmonic components and analyze their evolution with redshift across the studied redshift range. At low redshift, the dipole is clearly dominant, with an amplitude of $\sim (2.2 \pm 0.15)\times 10^{-2}$, significantly larger than the higher--order modes. As redshift increases, the dipole amplitude steadily decreases, reaching roughly half its value in the highest redshift bin investigated. The quadrupole is also significant, at about half the dipole amplitude, and persists across all redshift bins, with no clear decreasing trend, although uncertainties grow at higher redshift. A nonzero octupole is also detected at low redshift. The dipole, quadrupole, and octupole components are found to be aligned, exhibiting axial symmetry around a common axis ($l = 295^\circ,\, b = 5^\circ$). We interpret the observed fluctuations in the expansion rate within the framework of covariant cosmography. Our results indicate that the multipoles of the expansion rate fluctuation field are primarily driven by a strong quadrupole in the covariant Hubble parameter, together with dipole and octupole contributions from the covariant deceleration parameter. These few parameters suffice to reconstruct the luminosity distance with high precision out to $z \sim 0.1$, in a manner that is model--independent, non--perturbative, and free from assumptions about peculiar velocities.

Figures (21)

• Figure 1: Histograms showing number counts as a function of redshift. CF4TF and CF4FP are presented in the first row, while CF4SN and Pantheon+ are shown in the second row.
• Figure 2: Top row of panels: Sky distribution of CF4 galaxies in Galactic coordinates. Different subsamples, corresponding to distinct redshift ranges, are shown from left to right: CF4a ($0.01 < \tilde{z} < 0.03$, 11978 galaxies), CF4b ($0.03 < \tilde{z} < 0.05$, 12660 galaxies ), CF4c ($0.05 < \tilde{z} < 0.075$, 13678 galaxies), and CF4d ($0.075 < \tilde{z} < 0.1$, 14486 galaxies). Second row of panels: HEALPix-pixelized maps of the expansion rate fluctuation field $\tilde{\eta}$. Third row of panels: Signal-to-noise ratio maps of the fluctuation field (gray pixels indicate empty cells). Bottom four rows of panels: Multipolar decomposition of $\tilde{\eta}$. From top to bottom, the rows show the dipole, quadrupole, octupole, and hexadecapole components.
• Figure 3: Top row of panels: Sky distribution of CF4TF, CF4FP, CF4SN, and Pantheon+ samples in the range $0.01<\tilde{z}<0.05$. Second row of panels: HEALPix-pixelized maps of the expansion rate fluctuation field $\tilde{\eta}$. Bottom two rows of panels: Multipolar decomposition of $\tilde{\eta}$ into dipole ( top) and quadrupole ( bottom).
• Figure 4: Maps of the quadrupole reconstructed in the redshift ranges $0.01 < \tilde{z} < 0.03$ ( first row), $0.03 < \tilde{z} < 0.05$ ( second row), and $0.01 < \tilde{z} < 0.05$ ( third row), using the same SNe but different determinations of their distance moduli: Pantheon+ ( first column), CF4SN$^+$ ( second column), and CF4SN$^-$ ( third column).
• Figure 5: Top row of panels: Sky distribution of CF4TF+CF4SN (combined) and CF4FP samples in the range $0.05<\tilde{z}<0.1$. Second row of panels: HEALPix-pixelized maps of the expansion rate fluctuation field $\tilde{\eta}$. Bottom two rows of panels: Multipolar decomposition of $\tilde{\eta}$ into the dipole ( top) and quadrupole ( bottom).