Propagation and emission of gravitational waves in the weak-field limit within the Palatini formalism

In the era of gravitational waves physics, when detections of wave fronts are increasing in number, sensitivity, frequencies and distances, gravitational physics has entered a period of maximum activity and brilliance. This has open a new window where General Relativity can be challenged in both weak as strong-field regimes. In this paper, we focus on the analysis of gravitational waves propagation and emission in the weak-field regime for gravitational theories within the Palatini formalism. Our results show that gravitational waves propagation in vacuum matches General Relativity predictions as well as the functional form of the multipolar expansion when considering weak sources. However, a rescaling of the gravitational constant arises, which affects the energy radiated by the gravitational waves emission.