  We discuss detectability of the nonlinear growth of the large-scale structure
in the cosmic microwave background (CMB) lensing. Lensing signals involved in
CMB anisotropies have been measured from multiple CMB experiments, such as
Atacama Cosmology Telescope (ACT), Planck, POLARBEAR, and South Pole Telescope
(SPT). Reconstructed lensing signals are useful to constrain cosmology via
their angular power spectrum, while detectability and cosmological application
of their bispectrum induced by the nonlinear evolution are not well studied.
Extending the analytic estimate of the galaxy lensing bispectrum presented by
Takada and Jain (2004) to the CMB case, we show that even near term CMB
experiments such as Advanced ACT, Simons Array and SPT3G could detect the CMB
lensing bispectrum induced by the nonlinear growth of the large-scale
structure. In the case of the CMB Stage-IV, we find that the lensing bispectrum
is detectable at $\gtrsim 50\sigma$ statistical significance. This precisely
measured lensing bispectrum has rich cosmological information, and could be
used to constrain cosmology, e.g., the sum of the neutrino masses and the
dark-energy properties.
