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The Sunyaev-Zel'dovich (SZ) effects are produced by the interaction of cosmicmicrowave background (CMB) photons with the ionized and diffuse gas ofelectrons inside galaxy clusters integrated along the line of sight. The twomain effects are the thermal SZ (tSZ) produced by thermal pressure insidegalaxy clusters and the kinetic SZ (kSZ) produce by peculiar motion of galaxyclusters compared to CMB rest-frame. The kSZ effect is particularly challengingto measure as it follows the same spectral behavior as the CMB, andconsequently can not be separated from the CMB using spectral considerations.In this paper, we explore the feasibility of detecting the kSZ through thecomputation of the tSZ-CMB-CMB cross-correlation bispectrum for current andfuture CMB experiments. We conclude that next generation of CMB experimentswill offer the possibility to detect at high S/N the tSZ-kSZ-kSZ bispectrum.This measurement will constraints the intra-cluster dynamics and the velocityfield of galaxy cluster that is extremely sensitive to the growth rate ofstructures and thus to dark energy properties. Additionally, we alsodemonstrate that the tSZ-kSZ-kSZ bispectrum can be used to break thedegeneracies between the mass-observable relation and the cosmologicalparameters to set tight constraints, up to 4\%, on the $Y-M$ relationcalibration.

Constraining galaxy cluster velocity field with the tSZ-kSZ-kSZ bispectrum