  We investigate the galaxy bispectrum induced by the nonlinear gravitational
evolution as a possible probe to constrain degenerate higher-order scalar
tensor (DHOST) theories. We find that the signal obtained from the leading
kernel of second-order density fluctuations is partially hidden by the
uncertainty in the nonlinear galaxy bias, and that the kernel of second-order
velocity fields instead provides unbiased information on the modification of
gravity theory. Based on this fact, we propose new phenomenological
time-dependent functions, written as a combination of the coefficients of the
second-order kernels, which is expected to trace the higher-order growth
history. We then present approximate expressions for these variables in terms
of parameters that characterize the DHOST theories. We also show that the
resultant formulae provides new constraints on the parameter space of the DHOST
theories.
