Landau damping for gravitational waves in parity-violating theories

We discuss how tensor polarizations of gravitational waves can suffer Landau damping in the presence of velocity birefringence, when parity symmetry is explicitly broken. In particular, we analyze the role of the Nieh-Yan and Chern-Simons terms in modified theories of gravity, showing how the gravitational perturbation in collisionless media can be characterized by a subluminal phase velocity, circumventing the well-known results of General Relativity and allowing for the appearance of the kinematic damping. We investigate in detail the connection between the thermodynamic properties of the medium, such as temperature and mass of the particles interacting with the gravitational wave, and the parameters ruling the parity violating terms of the models. In this respect, we outline how the dispersion relations can give rise in each model to different regions of the wavenumber space, where the phase velocity is subluminal, superluminal or does not exist. Quantitative estimates on the considered models indicate that the phenomenon of Landau damping is not detectable given the sensitivity of present-day instruments.