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 cosmic microwave background (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 toward lens reconstruction from continuum or line intensity mapping data, such as the Lyman-alpha emission, absorption, and the 21 cm radiation.