We explore the reconstruction of the gravitational lensing field of the cosmic microwave background in real space showing that very little statistical information is lost when estimators of short range on the celestial sphere are used in place of the
customary estimators in harmonic space, which are nonlocal and in principle require a simultaneous analysis of the entire sky without any cuts or excisions. Because virtually all the information relevant to lensing reconstruction lies on angular scales close to the resolution scale of the sky map, the gravitational lensing dilatation and shear fields (which unlike the deflection field or lensing potential are directly related to the observations in a local manner) may be reconstructed by means of quadratic combinations involving only very closely separated pixels. Even though harmonic space provides a more natural context for understanding lensing reconstruction theoretically, the real space methods developed here have the virtue of being faster to implement and are likely to prove useful for analyzing realistic maps containing a galactic cut and possibly numerous small excisions to exclude point sources that cannot be reliably subtracted.
B-Pol is a medium-class space mission aimed at detecting the primordial gravitational waves generated during inflation through high accuracy measurements of the Cosmic Microwave Background (CMB) polarization. We discuss the scientific background, fea
sibility of the experiment, and implementation developed in response to the ESA Cosmic Vision 2015-2025 Call for Proposals.
