# Bias to CMB Lensing Reconstruction from Temperature Anisotropies due to Large-Scale Galaxy Motions

## TL;DR

This paper identifies a bias in CMB lensing reconstruction caused by the kinematic Sunyaev-Zel'dovich effect, which can significantly impact future high-precision cosmological measurements if uncorrected.

## Contribution

It quantifies the kSZ-induced bias in CMB lensing reconstruction and highlights its importance for upcoming surveys, proposing polarization-only methods as a mitigation.

## Key findings

- Bias can reach up to 15% in cross-correlations for Stage 4 experiments.
- The bias is mainly due to the non-Gaussianity and cross-correlation of the kSZ effect.
- Reducing the maximum multipole $\,
m max$ mitigates bias but decreases signal-to-noise.

## Abstract

Gravitational lensing of the cosmic microwave background (CMB) is expected to be amongst the most powerful cosmological tools for ongoing and upcoming CMB experiments. In this work, we investigate a bias to CMB lensing reconstruction from temperature anisotropies due to the kinematic Sunyaev-Zel'dovich (kSZ) effect, that is, the Doppler shift of CMB photons induced by Compton-scattering off moving electrons. The kSZ signal yields biases due to both its own intrinsic non-Gaussianity and its non-zero cross-correlation with the CMB lensing field (and other fields that trace the large-scale structure). This kSZ-induced bias affects both the CMB lensing auto-power spectrum and its cross-correlation with low-redshift tracers. Furthermore, it cannot be removed by multifrequency foreground separation techniques because the kSZ effect preserves the blackbody spectrum of the CMB. While statistically negligible for current datasets, we show that it will be important for upcoming surveys, and failure to account for it can lead to large biases in constraints on neutrino masses or the properties of dark energy. For a Stage 4 CMB experiment, the bias can be as large as $\approx$ 15% or 12% in cross-correlation with LSST galaxy lensing convergence or galaxy overdensity maps, respectively, when the maximum temperature multipole used in the reconstruction is $\ell_{\rm max} = 4000$, and about half of that when $\ell_{\rm max} = 3000$. Similarly, we find that the CMB lensing auto-power spectrum can be biased by up to several percent. These biases are many times larger than the expected statistical errors. Reducing $\ell_{\rm max}$ can significantly mitigate the bias at the cost of a decrease in the overall lensing reconstruction signal-to-noise. Polarization-only reconstruction may be the most robust mitigation strategy.