Lensing reconstruction from line intensity maps: the impact of
  gravitational nonlinearity
  We investigate the detection prospects for gravitational lensing of
three-dimensional maps from upcoming line intensity surveys, focusing in
particular on the impact of gravitational nonlinearities on standard quadratic
lensing estimators. Using perturbation theory, we show that these
nonlinearities can provide a significant contaminant to lensing reconstruction,
even for observations at reionization-era redshifts. However, we show how this
contamination can be mitigated with the use of a "bias-hardened" estimator.
Along the way, we present an estimator for reconstructing long-wavelength
density modes, in the spirit of the "tidal reconstruction" technique that has
been proposed elsewhere, and discuss the dominant biases on this estimator.
After applying bias-hardening, we find that a detection of the lensing
potential power spectrum will still be challenging for the first phase of
SKA-Low, CHIME, and HIRAX, with gravitational nonlinearities decreasing the
signal to noise by a factor of a few compared to forecasts that ignore these
effects. On the other hand, cross-correlations between lensing and galaxy
clustering or cosmic shear from a large photometric survey look promising,
provided that systematics can be sufficiently controlled. We reach similar
conclusions for a single-dish survey inspired by CII measurements planned for
CCAT-prime, suggesting that lensing is an interesting science target not just
for 21cm surveys, but also for intensity maps of other lines.
