Optimal bispectrum estimator and simulations of the the CMB Lensing-ISW non-Gaussian signal

TL;DR

This paper develops optimal tools and simulations for extracting the Lensing-ISW bispectrum signal from future CMB data, improving estimation accuracy and addressing biases in primordial non-Gaussianity measurements.

Contribution

It introduces two methods for simulating L-ISW non-Gaussian maps and implements an optimal estimator analysis, enhancing the accuracy of L-ISW signal extraction from CMB data.

Findings

Estimator approaches the Cramer-Rao bound.

Wiener filtering improves $f_{NL}^{L-ISW}$ estimate by up to 10%.

Proper accounting of L-ISW prevents underestimation of primordial non-Gaussianity errors.

Abstract

In this paper we present the tools to optimally extract the Lensing-Integrated Sachs Wolfe (L-ISW) bispectrum signal from future CMB data. We implement two different methods to simulate the non-Gaussian CMB maps with the L-ISW signal: a non-perturbative method based on the FLINTS lensing code and the separable mode expansion method. We implement the Komatsu, Spergel and Wandelt (KSW) optimal estimator analysis for the Lensing-ISW bispectrum and we test it on the non-Gaussian simulations in the case of a realistic CMB experimental settings with an inhomogeneous sky coverage. We show that the estimator approaches the Cramer-Rao bound and that Wiener filtering the L-ISW simulations gives a slight improvement on the estimate of $f_{NL}^{L-ISW}$ of $\leq 10%$. For a realistic CMB experimental setting accounting for anisotropic noise and masked sky, we show that the linear term of the estimator is highly correlated to the cubic term and it is necessary to recover the signal and the optimal error bars. We also show that the L-ISW bispectrum, if not correctly accounted for, yields an underestimation of the $f_{NL}^{local}$ error bars of $\simeq 4%$. A joint analysis of the non-Gaussian shapes and/or L-ISW template subtraction is needed in order to recover unbiased results of the primordial non-Gaussian signal from ongoing and future CMB experiments.