Impact of f(R) gravity on gravitational waves propagation

We explore the propagation of gravitational waves (GWs) in context of metric f(R) gravity under weak field approximation. We observe that the scalar degree of freedom arising from f(R) gravity modifies the wave equation for GWs leading to additional scalar modes of polarization. The background matter distribution influences GWs propagation affecting their speed. Our study also focuses on the observational constraints which limit the detection of these deviations in GWs signals from General Relativity (GR), thus providing insights into the challenges of testing extended gravity theories.