Constraints on extended gravity models through gravitational wave emission

Using recent experimental results of detection of gravitational waves from the binary black hole signals by Advanced LIGO and Advanced Virgo, we investigate the propagation of gravitational waves in the context of fourth order gravity nonminimally coupled to a massive scalar field. Gravitational radiation admits extra massive modes of oscillation and we assume that the amplitude of these modes is comparable to that of the massless mode. We derive the propagation equation and effective mass for each degree of freedom and we infer, from the current observational data, constraints on the free parameters of the gravity models we considered. In particular, for $f(R)=R-R^2/R_0 $, the constraint obtained from the speed of gravitational waves is not compatible with the one set by Solar System tests, which implies that amplitude of the massive modes could not be detectable with current experiments on Earth