Cosmological evolution of viable models in the generalized scalar-tensor
  theory
  We investigate the parameter distributions of the viable generalized
scalar-tensor theory with conventional dust matter after GW170817 in a
model-independent way. We numerically construct the models by computing the
time evolution of a scalar field, which leads to a positive definite
second-order Hamiltonian and are consistent with the observed Hubble parameter.
We show the model parameter distributions in the degenerate higher-order
scalar-tensor (DHOST) theory, and its popular subclasses, e.g., Horndeski and
GLPV theories, etc.. We find that 1) the Planck mass run rate, $\alpha_M$, is
insensitive to distinguish the theories. 2) the kinetic-braiding parameter,
$\alpha_B$, clearly discriminates the models from those of the Horndeski
theory, 3) the parameters for the higher-order theories, $\alpha_H$ and
$\beta_1$, are relatively smaller in magnitude (by several factors) than
$\alpha_M$ and $\alpha_B$, but can still be used for discriminating the
theories except for the GLPV theory. Based on the above three facts, we propose
a minimal set of parameters that sensibly distinguishes the subclasses of DHOST
theories, ($\alpha_M$, $\alpha_B-\alpha_M/2$, $\beta_1$).
