CMB lensing power spectrum estimation without instrument noise bias

The power spectrum of cosmic microwave background (CMB) lensing will be measured to sub-percent precision with upcoming surveys, enabling tight constraints on the sum of neutrino masses and other cosmological parameters. Measuring the lensing power spectrum involves the estimation of the connected trispectrum of the four-point function of the CMB map, which requires the subtraction of a large Gaussian disconnected noise bias. This reconstruction noise bias receives contributions both from CMB and foreground fluctuations as well as instrument noise (both detector and atmospheric noise for ground-based surveys). The debiasing procedure therefore relies on the quality of simulations of the instrument noise which may be expensive or inaccurate. We propose a new estimator that makes use of at least four splits of the CMB maps with independent instrument noise. This estimator makes the CMB lensing power spectrum completely insensitive to any assumptions made in modeling or simulating the instrument noise. We show that this estimator, in many practical situations, leads to no substantial loss in signal-to-noise. We provide an efficient algorithm for its computation that scales with the number of splits m as O(m(2)) as opposed to a naive O(m(4)) expectation.

Automated summary

The power spectrum of cosmic microwave background (CMB) lensing will be measured with high precision in upcoming surveys, allowing for constraints on neutrino masses and cosmological parameters. A new estimator is proposed in this study that is robust against assumptions made in modeling or simulating instrument noise, providing efficient computation without substantial loss in signal-to-noise ratio. This new method relies on multiple splits of CMB maps with independent instrument noise to improve the accuracy of lensing power spectrum measurements.