Probing Screening and the Graviton Mass with Gravitational Waves

Gravitational waves can probe fundamental physics, leading to new constraints on the mass of the graviton. Previous tests, however, have neglected the effect of screening, which is typically present in modified theories that predict a non-zero graviton mass. We here study whether future gravitational wave observations can constrain the graviton mass when screening effects are taken into account. We first consider model-independent corrections to the propagation of gravitational waves due to screened massive graviton effects. We find that future observation can place constraints on the screening radius and the graviton mass of ${\cal{O}}(10^{2})$--${\cal{O}}(10^{4})$ Mpc and ${\cal{O}}(10^{-22})$--${\cal{O}}(10^{-26})$ eV respectively. We also consider screening effects in two specific theories, ghost-free massive gravity and bigravity, that might not realize these types of propagation modifications, but that do provide analytic expressions for screening parameters relevant to our analysis allowing for more concrete results. However, the constraints we are able to place are small. The reason for this is that second- and third-generation detectors are sensitive to graviton masses that lead to very small screening radii in these particular models. The effect of screening, however, can become important as constraints on the graviton mass are improved through the stacking of multiple observations in the near future.