Modified gravitational waves across galaxies from macroscopic gravity

We analyze the propagation of gravitational waves in a medium containing bounded subsystems ("molecules") able to induce significant macroscopic gravity effects We establish a precise constitutive relation between the average quadrupole and the amplitudes of a vacuum gravitational wave, via the geodesic deviation equation. Then we determine the modified equation for the wave inside the medium and the associated dispersion relation. A phenomenological analysis shows that anomalous polarizations of the wave emerge with an appreciable experimental detectability if the medium is identified with a typical galaxy. Both the modified dispersion relation (wave velocity less than the speed of light) and anomalous oscillations modes could be detectable by the incoming LISA or pulsar timing array experiments, having the appropriate size to see the concerned wavelengths (larger than the molecular size) and the appropriate sensitivity to detect the expected deviation from vacuum general relativity.