  Scalar-tensor theories have shown promise in many sectors of cosmology.
However, recent constraints from the speed of gravitational waves have put
severe limits on the breadth of models such classes of theories can realize. In
this work, we explore the possibility of a string-like Horndeski Lagrangian
that is equipped with two dilaton fields. This is an interesting low-energy
effective string theory that has a healthy general relativity limit. The
evolution of a two-dilation coupled cosmology is not well-known in the
literature. We explore the tensor perturbations in order to assess the behavior
of the model again the speed of gravitational wave constraint. Our main result
is that this model exhibits of a class of cosmological theories that is
consistent with this observational constraint.
