With the development of next-generation gravitational waves detectors, we aim to measure and infer data on a broader range of the energy and redshift spectrum. However, in this range, deviations...Show moreWith the development of next-generation gravitational waves detectors, we aim to measure and infer data on a broader range of the energy and redshift spectrum. However, in this range, deviations from theories that predict a non-standard propagation speed for GWs are expected to become non negligible anymore. Moreover, it has been shown that the presence of inhomogeneities and structures in our universe does affect the GWs observables: with the forecasted level of precision of future detectors, such corrections can not be ignored. In this work we set in the frame of quartic scalar-tensor theories of gravity to study such relativistic effects with the presence of an extra scalar degree of freedom. Due to the complexity of the full theory, we opted for a phenomenological approach to describe the dispersion relation and amplitude evolution of the metric perturbation. Using this technique, we evaluated the relativistic corrections to frequency and direction of propagation of the GWs wave-vector. On the other hand, it was not possible to analytically calculate the relativistic corrections to the tensor amplitude even using the parametric approach, as a consequence of the elevated number of terms in the amplitude evolution equation. Nevertheless, after selecting from such equation the transverse-traceless modes, we were able to find, using the N-P formalism, which types of term can actually contribute to the evolution of the physical modes.Show less
