Cross-correlating radial peculiar velocities and CMB lensing convergence

We study, for the first time, the cross correlation between the angular distribution of radial peculiar velocities (PV) and the lensing convergence of cosmic microwave background (CMB) photons. We derive theoretical expectations for the signal and its covariance and assess its detectability with existing and forthcoming surveys. We find that such cross -correlations are expected to improve constraints on different gravitational models by partially breaking degeneracies with the matter density. We identify in the distance-scaling dispersion of the peculiar velocities the most relevant source of noise in the cross correlation. For this reason, we also study how the above picture changes assuming a redshift-independent scatter for the PV, obtained for example using a reconstruction technique. Our results show that the cross correlation might be detected in the near future combining PV measurements from DESI and the convergence map from CMB-S4. Using realistic direct PV measurements we predict a cumulative signal-to-noise ratio of approximately 3.8a using data on angular scales 3 < Q < 200. For an idealized reconstructed peculiar velocity map extending up to redshift z = 0.15 and a smoothing scale of 4 Mpc h-1 we predict a cumulative signal-to-noise ratio of approximately 27a- from angular scales 3 < Q < 200. We conclude that currently reconstructed peculiar velocities have more constraining power than directly observed ones, even though they are more cosmological-model dependent. JCAP05(2023)002

Automated summary

We investigate the cross correlation between radial peculiar velocities (PV) and lensing convergence of cosmic microwave background (CMB) photons for the first time. The theoretical expectations for the signal and its covariance are derived and the detectability with existing and forthcoming surveys is assessed. The study reveals that such cross-correlations can improve constraints on gravitational models by breaking degeneracies with matter density. Additionally, the distance-scaling dispersion of peculiar velocities is identified as the main source of noise in the cross correlation. When assuming a redshift-independent scatter for PV, the study shows that the cross correlation may be detected in the future using PV measurements from DESI and convergence map from CMB-S4.