Minimizing gravitational lensing contributions to the primordial bispectrum covariance

William R. Coulton, P. Daniel Meerburg, David G. Baker, Selim Hotinli, Adriaan J. Duivenvoorden, and Alexander van Engelen

Phys. Rev. D 101, 123504 – Published 4 June 2020

Abstract

The next generation of ground-based cosmic microwave background (CMB) experiments aim to measure temperature and polarization fluctuations up to $ℓ_{\max} \approx 5000$ 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 $ℓ_{\max} = 3800$ . 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.

Received 16 January 2020
Accepted 20 May 2020

DOI:https://doi.org/10.1103/PhysRevD.101.123504

Physics Subject Headings (PhySH)

Cosmic microwave background

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

William R. Coulton¹, P. Daniel Meerburg², David G. Baker ³, Selim Hotinli⁴, Adriaan J. Duivenvoorden ⁵, and Alexander van Engelen^6,7

¹Institute of Astronomy and Kavli Institute for Cosmology, Madingley Road, Cambridge CB3 0HA, United Kingdom
²Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands
³DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
⁴Physics Department, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom
⁵Department of Physics: Joseph Henry Laboratories, Jadwin Hall, Princeton University, Princeton, New Jersey 08542, USA
⁶School of Earth and Space Exploration, Arizona State University, Tempe, Arizona 85287, USA
⁷Canadian Institute of Theoretical Astrophysics, 60 St George Street, Toronto, Ontario M5S 3H8, Canada

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Vol. 101, Iss. 12 — 15 June 2020

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Images

Figure 1
The standard deviation of the estimator ${\hat{f}}_{NL}^{local}$ as a function of maximum scale, for the case of Gaussian unlensed CMB fields, blue curve, when lensing effects are included only via their contribution to the power spectrum, orange curve, and including the non-Gaussian lensing contributions, green curve. We also plot the measurements from our non-Gaussian simulations, red curve. We see that for $ℓ_{\max} ≳ 2000$ the error begins to saturate due to the variance sourced by CMB lensing, which is the subject of this paper, and that including even smaller scales results in an increase in the estimator variance (i.e., a decrease in the constraining power). The upturn occurs as the estimator does not account for the lensing non-Gaussianity and is suboptimally weighting the smallest scales.
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Figure 2
The standard deviation of the estimators ${\hat{f}}_{NL}^{equil}$ and ${\hat{f}}_{NL}^{orth}$ for the case of Gaussian fields (both with and without lensing power) and including the lensing non-Gaussian contributions. Here we see that these configurations are not as affected by lensing as the local configuration.
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Figure 3
The standard deviation of the estimator ${\hat{f}}_{NL}^{local}$ , for a Planck-like experiment and a Simons Observatory–like experiment. The difference between these and Figs. 1 and 2 is the inclusion of instrumental noise and scaling them to the observed sky fractions. This shows that the extra lensing variance, if unmitigated, would remove most of the improvements expected from an SO-like experiment.
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Figure 4
The standard deviation of the estimator ${\hat{f}}_{NL}^{local}$ , with ISW-lensing marginalization. Theoretically, we find that ISW marginalization reduces the contribution of the lensing four-point function to the variance from the level predicted (orange) to the level shown in green. However, when we compare the results from a suite of simulations with ISW marginalization (purple) to a suite of simulations without (red), we see that the variance is only slightly reduced.
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Figure 5
The standard deviation of the estimators $f_{N L}^{local}$ and $f_{N L}^{orth}$ after delensing for an idealized SO-like experiment. As in Fig. 1 we show how the unlensed standard deviation (blue curve) is increased by the additional lensing-induced variance (orange curve). However, we find that, for an SO-like experiment, delensing is able to almost completely remove the contribution of the lensing variance (green curve). This is the case for both the local and the orthogonal shapes.
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