Optimal bispectrum estimator and simulations of the CMB lensing-integrated Sachs Wolfe non-Gaussian signal

We present the tools to optimally extract the lensing-integrated Sachs Wolfe (L-ISW) bispectrum signal from future cosmic microwave background (CMB) data. We implemented 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 implemented the Komatsu, Spergel, and Wandelt (KSW) optimal estimator analysis for the L-ISW bispectrum and tested it on the non-Gaussian simulations for 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 slightly improves the estimate of f(NL)(L-ISW) by <= 10%. For a realistic CMB experimental setting that accounts 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 similar or equal to 4%. A joint analysis of the non-Gaussian shapes and/or L-ISW template subtraction is needed to recover unbiased results of the primordial non-Gaussian signal from ongoing and future CMB experiments.