CMB lensing power spectrum estimation without instrument noise bias

TL;DR

This paper introduces a new estimator for CMB lensing power spectrum that eliminates instrument noise bias by using multiple independent noise splits, improving accuracy without significant loss of signal-to-noise.

Contribution

A novel estimator utilizing at least four independent noise splits to remove instrument noise bias in CMB lensing measurements, with an efficient computational algorithm.

Findings

Estimator is insensitive to instrument noise modeling.

No substantial loss in signal-to-noise in practical scenarios.

Algorithm scales as O(m^2), improving computational efficiency.

Abstract

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 $\mathcal{O}(m^2)$ as opposed to a naive $\mathcal{O}(m^4)$ expectation.