Propagation of Tensor Perturbation in Horndeski-like Gravity

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 Horndeski Lagrangian that is equipped with two dilaton fields. The evolution of a two-dilaton coupled cosmology is not well known in the literature. We explore the tensor perturbations in order to assess the behavior of the model against the speed of the gravitational wave constraint. Our main result is that this model exhibits a class of cosmological theories that is consistent with this observational constraint.