Cross-correlating radial peculiar velocities and CMB lensing convergence

TL;DR

This paper explores the first theoretical and observational analysis of the cross correlation between radial peculiar velocities and CMB lensing convergence, showing potential for improved gravitational constraints with upcoming surveys.

Contribution

It introduces the first study of the cross correlation between radial peculiar velocities and CMB lensing convergence, assessing its detectability and potential to enhance cosmological constraints.

Findings

Potential detection with DESI and CMB-S4 data at ~3.8 sigma

Idealized reconstructed velocities could reach ~27 sigma detection

Reconstructed velocities provide stronger constraints than direct measurements

Abstract

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 $3.8 \sigma$ using data on angular scales $3 \leq \ell \leq 200$. 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 $ 27 \sigma$ from angular scales $3 \leq \ell \leq200 $. We conclude that currently reconstructed peculiar velocities have more constraining power than directly observed ones, even though they are more cosmological-model dependent.