CMB ISW-lensing bispectrum from cosmic strings
  We study the effect of weak lensing by cosmic (super-)strings on the
higher-order statistics of the cosmic microwave background (CMB). A cosmic
string segment is expected to cause weak lensing as well as an integrated
Sachs-Wolfe (ISW) effect, the so-called Gott-Kaiser-Stebbins (GKS) effect, to
the CMB temperature fluctuation, which are thus naturally cross-correlated. We
point out that, in the presence of such a correlation, yet another kind of the
post-recombination CMB temperature bispectra, the ISW-lensing bispectra, will
arise in the form of products of the auto- and cross-power spectra. We first
present an analytic method to calculate the autocorrelation of the temperature
fluctuations induced by the strings, and the cross-correlation between the
temperature fluctuation and the lensing potential both due to the string
network. In our formulation, the evolution of the string network is assumed to
be characterized by the simple analytic model, the velocity-dependent one scale
model, and the intercommutation probability is properly incorporated in orderto
characterize the possible superstringy nature. Furthermore, the obtained power
spectra are dominated by the Poisson-distributed string segments, whose
correlations are assumed to satisfy the simple relations. We then estimate the
signal-to-noise ratios of the string-induced ISW-lensing bispectra and discuss
the detectability of such CMB signals from the cosmic string network. It is
found that in the case of the smaller string tension, $G\mu\ll 10^{-7}$\,, the
ISW-lensing bispectrum induced by a cosmic string network can constrain the
string-model parameters even more tightly than the purely GKS-induced
bispectrum in the ongoing and future CMB observations on small scales.
