Gravitational Waves in Einstein-\AE ther Theory and Generalized T$e$V$e$S Theory after GW170817.
In this work, the polarization contents of Einstein-\ae ther theory and the Generalized T$e$V$e$S theory are discussed, as both theories have a normalized timelike vector field. The linearized equations of motion about the flat spacetime background are derived using the gauge invariant variables to easily separate physical degrees of freedom. The plane wave solutions are then found, and the polarizations are identified by examining the geodesic deviation equations. It shows that both theories contain six polarizations: plus, cross, vector-$x$, vector-$y$, transverse breathing and longitudinal polarizations. We also discuss the experimental tests of the extra polarizations in Einstein-\ae ther theory using pulsar timing arrays with the gravitational wave speed bound derived from the observations on GW 170817 and GRB 170817A. It turns out that it is difficult to use pulsar timing arrays to distinguish different polarizations in Einstein-\ae ther theory. The same speed bound also forces one of the propagating modes in the Generalized T$e$V$e$S theory to travel much faster than the speed of light, so the Generalized T$e$V$e$S theory is excluded.
Publisher URL: http://arxiv.org/abs/1801.03382
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