Constraints on scalar-tensor theory of gravity by the recent
  observational results on gravitational waves
  The speed of gravitational waves provides us a new tool to test alternative
theories of gravity. The constraint on the speed of gravitational waves from
GW170817 and GRB170817A is used to test some classes of Horndeski theory. In
particular, we consider the coupling of a scalar field to Einstein tensor and
the coupling of the Gauss-Bonnet term to a scalar field. The coupling strength
of the Gauss-Bonnet coupling is constrained to be in the order of $10^{-15}$.
In the Horndeski theory we show that in order for this theory to satisfy the
stringent constraint on the speed of GWs the mass scale $M$ introduced in the
non-minimally derivative coupling is constrained to be in the range
$10^{15}\text{GeV}\gg M \gtrsim 2\times 10^{-35}$GeV taking also under
consideration the early times upper bound for the mass scale $M$. The large
mass ranges require no fine-tuning because the effect of non-minimally
derivative coupling is negligible at late times.
