Prior-free cosmological parameter estimation of Cosmicflows-4

¹ Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany
² Universität Potsdam, Institut für Physik und Astronomie, Karl-Liebknecht-Str. 24-25, 14476 Potsdam, Germany
³ Aix Marseille Université, CNRS/IN2P3, CPPM, Marseille, France

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 29 July 2025
Accepted: 17 February 2026

Abstract

Context. As tracers of the underlying mass distributions, the peculiar velocities of galaxies are valuable probes of the Universe, allowing us to measure the Hubble constant or to map the large-scale structure and its dynamics. The catalogs of peculiar velocities, however, are noisy, scarce, and prone to various interpretation biases.

Aims. We measured the radial and bulk flow directly from the largest available sample of peculiar velocities and did not impose a cosmological prior on the velocity field. Furthermore, a minimum assumption on the shape of the radial flow at large distances enabled us to estimate the local Hubble constant.

Methods. To address these issues, we analyzed the Cosmicflows-4 catalog (CF4), the most extensive catalog of galaxy peculiar velocities, reaching a redshift z = 0.1. Specifically, we constructed a forward-modeling approach assuming only a flat Universe, which reconstructs the radial and bulk flows of the velocity field directly from measurements of peculiar velocities. Our method was tested on a series of 64 simulated catalogs that mimicked the complex selection function of CF4 in space and in magnitude. Based on our mock data, we propose a simulation-based correction method that we applied to the CF4 data.

Results. Our method recovers the radial flow and the direction and magnitude of the bulk flow throughout the covered volume without bias. The incompleteness of the data leads to a systematic amplification of the underlying flow, however, which in turn leads to a systematic overestimation of the amplitude of the bulk flow. By estimating the (cosmic) variance of the density field at large distances from the Lambda Cold Dark Matter (ΛCDM) model, we were able to extract a value of 75.9 ± 1 (stat) km/s/Mpc from the radial inflow. With regard to the bulk flow, a 3σ tension is found with ΛCDM on the supergalactic X direction and on the magnitude of the bulk flow around 140 Mpc/h and 240 Mpc/h. In summary, our work confirms the existing tension on the Hubble constant measured locally and a significant tension in the local bulk flow with ΛCDM predictions. More work is needed to handle all the possible sources of systematic errors inherent to the treating of composite catalogs such as CF4.