Removing the ISW-lensing bias from the local-form primordial non-Gaussianity estimation

Abstract

The Integrated Sachs-Wolfe (ISW) effect produces a secondarytemperature aniso\\-tropy of the cosmic microwave background (CMB), as CMBphotons travel through time-varying potentials along the line-of-sight. The main contribution comes from redshifts z≲2, where darkenergy leads to a decay of potentials. As the same photons are gravitationally lensed by these decaying potentials, there exists a high degree ofcorrelation between the ISW effect and CMB lensing, leading to a non-zero three-point correlation (bispectrum)of the observed temperature anisotropy. This ISW-lensing bispectrum, whose shape resembles that of the so-called ``local-form'' primordial bispectrum parametrized by fNL, is known to be the largest contamination of fNL. In order to avoid a spurious detection of primordialnon-Gaussianity, we need to remove the ISW-lensing bias. In this work, we investigate three debiasing methods: (I)subtraction of an expected, ensemble average of the ISW-lensingbispectrum; (II) subtraction of a measured ISW-lensing bispectrum; and(III) direct subtraction of an estimated ISW signal from an observedtemperature map. One may use an estimation of theISW map from external non-CMB data or that from the CMB data themselves.As the methods II and III are based on fewerassumptions about the nature of dark energy, they are preferred over themethod I. While the methods I and II yield unbiased estimates offNL with comparable error bars, the method III yields abiased result when the underlying primordialfNL is non-zero and the ISW map isestimated from a lensing potential reconstructed from the observed temperaturemap. One of the sources of the bias is a lensing reconstruction noisebias which is independent of fNL and can be calculated precisely, butother fNL-dependent terms are difficult tocompute reliably. We thus conclude that the method II is the best, model-independent way to remove theISW-lensing bias of fNL, enabling us totest the physics of inflation with smaller systematic errors.