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.
