Gravitational Waves in Einstein-{\AE}ther Theory and Generalized T$e$V$e$S Theory after GW170817

摘要

In this work, the polarization contents of Einstein-\ae ther theory and theGeneralized T$e$V$e$S theory are discussed, as both theories have a normalizedtimelike vector field. The linearized equations of motion about the flatspacetime background are derived using the gauge invariant variables to easilyseparate physical degrees of freedom. The plane wave solutions are then found,and the polarizations are identified by examining the geodesic deviationequations. It shows that both theories contain six polarizations: plus, cross,vector-$x$, vector-$y$, transverse breathing and longitudinal polarizations. Wealso discuss the experimental tests of the extra polarizations in Einstein-\aether theory using pulsar timing arrays with the gravitational wave speed boundderived from the observations on GW 170817 and GRB 170817A. It turns out thatit is difficult to use pulsar timing arrays to distinguish differentpolarizations in Einstein-\ae ther theory. The same speed bound also forces oneof the propagating modes in the Generalized T$e$V$e$S theory to travel muchfaster than the speed of light, so the Generalized T$e$V$e$S theory isexcluded.