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Cosmic Microwave Background Bispectrum from the Lensing--Rees-Sciama Correlation Reexamined: Effects of Non-linear Matter Clustering

The bispectrum of the cosmic microwave background (CMB) generated by a correlation between a time-dependent gravitational potential and the weak gravitational lensing effect provides a direct measurement of the influence of dark energy on CMB. This bispectrum is also known to yield the most important contamination of the so-called "local-form" primordial bispectrum, which can be used to rule out all single-field inflation models. In this paper, we reexamine the effect of non-linear matter clustering on this bispectrum. We compare three different approaches: the 3rd-order perturbation theory (3PT), and two empirical fitting formulae available in the literature, finding that detailed modeling of non-linearity appears to be not very important, as most of the signal-to-noise comes from the squeezed triangle, for which the correlation in the linear regime dominates. The expected signal-to-noise ratio for an experiment dominated by the cosmic variance up to $l_{\rm max}=1500$ is about 5, which is much smaller than the previous estimates including non-linearity, but agrees with the estimates based on the linear calculation. We find that the difference between the linear and non-linear predictions is undetectable, and does not alter the contamination of the local-form primordial non-Gaussianity.