Mass Reconstruction with Cosmic Microwave Background Polarization

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Abstract
Weak gravitational lensing by the intervening large-scale structure of the universe induces high-order correlations in the cosmic microwave background temperature and polarization fields. We construct minimum variance estimators of the intervening mass distribution out of the six quadratic combinations of the temperature and polarization fields. Polarization begins to assist in the reconstruction when E-mode mapping becomes possible on degree-scale fields, i.e., for an experiment with a noise level of ~40 μK arcmin and beam of ~7', similar to the Planck experiment; surpasses the temperature reconstruction at ~26 μK arcmin and 4'; and yet continues to improve the reconstruction until the lensing B-modes are mapped to l ~ 2000 at ~0.3 μK arcmin and 3'. Ultimately, the correlation between the E- and B-modes can provide a high signal-to-noise ratio mass map out to multipoles of L ~ 1000, extending the range of temperature-based estimators by nearly an order of magnitude. We outline four applications of mass reconstruction: measurement of the linear power spectrum in projection to the cosmic variance limit out to L ~ 1000 (or wavenumbers 0.002 k 0.2 in h Mpc-1), cross-correlation with cosmic shear surveys to probe the evolution of structure tomographically, cross-correlation of the mass and temperature maps to probe the dark energy, and the separation of lensing and gravitational wave B-modes.