Prior-free cosmological parameter estimation of Cosmicflows-4

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. 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. 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. Our method recovers the radial flow and the direction and magnitude of the bulk flow throughout the covered volume without bias. By estimating the (cosmic) variance of the density field at large distances from the $\Lambda$CDM model, we were able to extract a value of $75.9\pm1{\rm (stat) km/s/Mpc}$ from the radial inflow. With regard to the bulk flow, a 3$\sigma$ tension is found with $\Lambda$CDM around $140\ {\rm Mpc/h}$ and $240\ {\rm Mpc/h}$. In summary, our work confirms the existing tension on the Hubble constant measured locally and a significant tension in the local bulk flow with $\Lambda$CDM predictions.