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

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 (30h -1Mpc <R< 300h -1Mpc). 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 ∼ (2.2 ± 0.15) × 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 detected at low redshift with a signal-to-noise ratio of ∼ 3, but it becomes unconstrained at higher redshift. The dipole, quadrupole, and octupole components are found to be aligned, exhibiting axial symmetry around a common axis (l= 295°,b= 5°). 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 toz∼ 0.1, in a manner that is model-independent, non-perturbative, and free from assumptions about peculiar velocities. Finally, we find that the CMB frame is not locally comoving with the matter fluid, and that a matter fluid element, roughly a spherical region of size in the range 38 ≲R(Mpc) ≲ 100 centered on the observer position, moves relative to the CMB frame with a velocity of 188 ± 22 km/s, along the axis of symmetry.