Cosmic microwave background bispectrum from the lensing-Rees-Sciama correlation reexamined: Effects of nonlinear matter clustering

The bispectrum of the cosmic microwave background 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 cosmic microwave background. This bispectrum is also known to yield the most important contamination of the so-called localform primordial bispectrum, which can be used to rule out all single-field inflation models. In this paper, we reexamine the effect of nonlinear matter clustering on this bispectrum. We compare three different approaches: the 3rd-order perturbation theory, and two empirical fitting formulae available in the literature, finding that detailed modeling of nonlinearity 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(max) = 1500 is about 5, which is much smaller than the previous estimates including nonlinearity, but agrees with the estimates based on the linear calculation. We find that the difference between the linear and nonlinear predictions is undetectable, and does not alter the contamination of the localform primordial non-Gaussianity.