Model independent variance cancellation in CMB lensing cross-correlations

Cross-correlations of CMB lensing reconstructions with other tracers of matter constrain primordial non-Gaussianity, neutrino masses and structure growth as a function of cosmic time. We formalize a method to improve the precision of these measurements by using a third tracer to remove structure from the lensing reconstructions. Crucially, our method enjoys the variance reduction benefits of a joint-modelling approach without the need to model the cosmological dependence of the ancillary tracer. We present a first demonstration of variance cancellation using data from Planck and the DESI Legacy Surveys, showing a 10-20% reduction in both lensing power and cross-correlation variance using the Cosmic Infrared Background (CIB) or DESI Legacy Survey Luminous Red Galaxies (LRGs) as matter tracers.