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 the models 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, ${\alpha }_B$, marginally discriminates the models from those of the Horndeski theory in some range; and (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, (${\alpha }_M$, ${\alpha }_B-{\alpha }_M/2$, ${\beta }_1$).

• Received 6 December 2019
• Revised 21 February 2020
• Accepted 29 May 2020

DOI:https://doi.org/10.1103/PhysRevD.102.024003