Propagating gravitational waves in teleparallel Gauss-Bonnet gravity

Gravitational waves offer a key insight into the viability of classes of gravitational theories beyond general relativity. The observational constraints on their speed of propagation can provide strong constraints on generalized classes of broader gravitational frameworks. In this work, we reconsider the general class of Gauss-Bonnet theories in the context of teleparallel gravity, where the background geometry is expressed through torsion. We perform tensor perturbations on a flat Friedmann--Lema\^{\i}tre--Robertson--Walker background, and derive the gravitational wave propagation equation. We find that gravitational waves propagate at the speed of light in these classes of theories. We also derive the distance-duality relationship for radiation propagating in the gravitational wave and electromagnetic domains.