Gravitational waves in Einstein-{\AE}ther theory and generalized TeVeS theory after GW170817

In this paper, the polarization contents of Einstein-\ae ther theory and the generalized TeVeS theory are studied. The Einstein-\ae ther theory has five polarizations, while the generalized TeVeS theory has six. In particular, transverse and longitudinal breathing polarization are mixed. The~possibility of using pulsar timing arrays to detect the extra polarizations in Einstein-\ae{}ther theory was also investigated. The analysis showed that different polarizations cannot be easily distinguished by using pulsar timing arrays in this theory. For generalized TeVeS theory, one of the propagating modes travels much faster than the speed of light due to the speed bound set by GW170817. In some parameter subspaces, the strong coupling does not take place, so this theory is excluded.