Gravitational waves in Einstein-æther and generalized TeVeS theory after GW170817

Abstract

In this work, we discuss the polarization contents of Einstein-aether theory and the generalized tensor-vector-scalar (TeVeS) theory, as both theories have a normalized timelike vector field. We derive the linearized equations of motion around the flat spacetime background using the gaugeinvariant variables to easily separate physical degrees of freedom. We find the plane wave solutions are then found, and identify the polarizations by examining the geodesic deviation equations.We find that there are five polarizations in Einstein-aether theory and six polarizations in the generalized TeVeS theory. In particular, the transverse breathing mode is mixed with the pure longitudinal mode. We also discuss the experimental tests of the extra polarizations in Einsteinaether theory using pulsar timing arrays combined with the gravitational-wave speed bound derived from the observations on GW 170817 and GRB 170817A. It turns out that it might be difficult to use pulsar timing arrays to distinguish different polarizations in Einstein-aether theory. The same speed bound also forces one of the propagating modes in the generalized TeVeS theory to travel much faster than the speed of light. Since the strong coupling problem does not exist in some parameter subspaces, the generalized TeVeS theory is excluded in these parameter subspaces. *

The Polarizations of Gravitational Waves

“…[33] also discussed the constraints that the generalized TeVeS theory should satisfy. Similarly to Einstein-aether theory, it is also constrained by the solar system test (i.e., the constraints on α 1 and α 2 2 ), the absence of the gravitational Cherenkov radiation, and the recent GW speed bound [45], etc.…”

“…Ref. [33] discussed the conditions for the strong coupling to take place. The analysis showed that in some parameter regions, the strong coupling does not happen, so this theory should be excluded.…”

“…Linearizing the equations of motion (g µν = η µν + h µν and u µ = u µ + v µ ), and using the gauge-invariant variables defined in Ref. [33], one obtains the following equations of motion…”

“…The experimental constraints and the implications for the future experimental tests of these theories can be found in Refs. [33,61].…”

“…In fact, it cannot be used to identify the polarizations in Einstein-aether theory [29] or generalized Tensor-Vector-Scalar (TeVeS) theory [30][31][32], as the local Lorentz invariance is violated in both theories [33].…”