  The Sunyaev-Zel'dovich (SZ) effects are produced by the interaction of cosmic
microwave background (CMB) photons with the ionized and diffuse gas of
electrons inside galaxy clusters integrated along the line of sight. The two
main effects are the thermal SZ (tSZ) produced by thermal pressure inside
galaxy clusters and the kinetic SZ (kSZ) produce by peculiar motion of galaxy
clusters compared to CMB rest-frame. The kSZ effect is particularly challenging
to measure as it follows the same spectral behavior as the CMB, and
consequently can not be separated from the CMB using spectral considerations.
In this paper, we explore the feasibility of detecting the kSZ through the
computation of the tSZ-CMB-CMB cross-correlation bispectrum for current and
future CMB experiments. We conclude that next generation of CMB experiments
will offer the possibility to detect at high S/N the tSZ-kSZ-kSZ bispectrum.
This measurement will constraints the intra-cluster dynamics and the velocity
field of galaxy cluster that is extremely sensitive to the growth rate of
structures and thus to dark energy properties. Additionally, we also
demonstrate that the tSZ-kSZ-kSZ bispectrum can be used to break the
degeneracies between the mass-observable relation and the cosmological
parameters to set tight constraints, up to 4\%, on the $Y-M$ relation
calibration.
