Minimizing gravitational lensing contributions to the primordial bispectrum covariance

The next generation of ground-based cosmic microwave background (CMB) experiments aim to measure temperature and polarization fluctuations up to ${\ensuremath{\ell}}_{\mathrm{max}}\ensuremath{\approx}5000$ over half of the sky. Combined with Planck data on large scales, this will provide improved constraints on primordial non-Gaussianity. However, the impressive resolution of these experiments will come at a price. Besides signal confusion from galactic foregrounds, extragalactic foregrounds, and late-time gravitational effects, gravitational lensing will introduce large non-Gaussianity that can become the leading contribution to the bispectrum covariance through the connected four-point function. Here, we compute this effect analytically for the first time on the full sky for both temperature and polarization. We compare our analytical results with those obtained directly from map-based simulations of the CMB sky for several levels of instrumental noise. Of the standard shapes considered in the literature, the local shape is most affected, resulting in a 35% increase of the estimator standard deviation for an experiment such as the Simons Observatory (SO) and a 110% increase for a cosmic-variance limited experiment, including both temperature and polarization modes up to ${\ensuremath{\ell}}_{\mathrm{max}}=3800$. Because of the nature of the lensing four-point function, the impact on other shapes is reduced while still non-negligible for the orthogonal shape. Two possible avenues to reduce the non-Gaussian contribution to the covariance are proposed: First by marginalizing over lensing contributions, such as the Integrated Sachs Wolfe (ISW)-lensing three-point function in temperature, and second by delensing the CMB. We show the latter method can remove almost all extra covariance, reducing the effect to below $<5%$ for local bispectra. At the same time, delensing would remove signal biases from secondaries induced by lensing, such as ISW lensing. We aim to apply both techniques directly to the forthcoming SO data when searching for primordial non-Gaussianity.

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