Lensing Studies with Diffuse Backgrounds

The current weak lensing measurements of the large scale structure are mostly related to statistical study of background galaxy ellipticities. We consider a possibility to extend lensing studies with intrinsically unresolved sources and suggest that spatial fluctuations in the integrated diffuse emission from these sources can be used for a lensing reconstruction. Examples of upcoming possibilities include the diffuse background generated by dusty starburst galaxies at far-infrared wavelengths, first stars and galaxies in near-infrared wavelengths, and the background related to 21 cm emission by neutral gas in the general intergalactic medium prior to reionization. While methods developed to extract lensing information from cosmic microwave background (CMB) temperature and polarization data can be easily modified to study lensing properties using diffuse backgrounds at other wavelengths, we suggest that the lensing extraction from these backgrounds using higher order non-Gaussian clustering information alone may not be the best approach. In contrast to CMB anisotropies, reasons for this include the lack of features in the clustering power spectrum such that the resulting lensing modification to the angular power spectrum of low-redshift diffuse backgrounds, at arcminute angular scales, is insignificant. While the use of low redshift backgrounds for lensing studies will be challenging, due to confusing foregrounds among other reasons, the use of suggested backgrounds will extend the reconstruction of the integrated matter power spectrum out to redshifts of 15 to 30, and will bridge the gap between current and upcoming galaxy lensing studies out to, at most, a redshift of a few and planned weak lensing studies with CMB out to the last scattering surface at a redshift of 1100.