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The bispectrum of the cosmic microwave background (CMB) generated by acorrelation between a time-dependent gravitational potential and the weakgravitational lensing effect provides a direct measurement of the influence ofdark energy on CMB. This bispectrum is also known to yield the most importantcontamination of the so-called "local-form" primordial bispectrum, which can beused to rule out all single-field inflation models. In this paper, we reexaminethe effect of non-linear matter clustering on this bispectrum. We compare threedifferent approaches: the 3rd-order perturbation theory (3PT), and twoempirical fitting formulae available in the literature, finding that detailedmodeling of non-linearity appears to be not very important, as most of thesignal-to-noise comes from the squeezed triangle, for which the correlation inthe linear regime dominates. The expected signal-to-noise ratio for anexperiment dominated by the cosmic variance up to $l_{\rm max}=1500$ is about5, which is much smaller than the previous estimates including non-linearity,but agrees with the estimates based on the linear calculation. We find that thedifference between the linear and non-linear predictions is undetectable, anddoes not alter the contamination of the local-form primordial non-Gaussianity.

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