Weak Lensing of Intensity Mapping: the Cosmic Infrared Background
  Gravitational lensing deflects the paths of cosmic infrared background (CIB)
photons, leaving a measurable imprint on CIB maps. The resulting statistical
anisotropy can be used to reconstruct the matter distribution out to the
redshifts of CIB sources. To this end, we generalize the CMB lensing quadratic
estimator to any weakly non-Gaussian source field, by deriving the optimal
lensing weights. We point out the additional noise and bias caused by the
non-Gaussianity and the `self-lensing' of the source field. We propose methods
to reduce, subtract or model these non-Gaussianities. We show that CIB lensing
should be detectable with Planck data, and detectable at high significance for
future CMB experiments like CCAT-Prime. The CIB thus constitutes a new source
image for lensing studies, providing constraints on the amplitude of structure
at intermediate redshifts between galaxies and the CMB. CIB lensing
measurements will also give valuable information on the star formation history
in the universe, constraining CIB halo models beyond the CIB power spectrum. By
laying out a detailed treatment of lens reconstruction from a weakly
non-Gaussian source field, this work constitutes a stepping stone towards lens
reconstruction from continuum or line intensity mapping data, such as the
Lyman-alpha emission, absorption, and the 21cm radiation.
