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