Gravitational Waves in Einstein-Æther Theory and Generalized TeVeS Theory after GW170817

Shaoqi Hou,Yungui Gong

doi:10.3390/universe4080084

Abstract

In this paper , the polarization contents of Einstein-æther theory and the generalized TeVeS theory are studied. The Einstein-æther 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-æther 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.

Highlights

The Laser Interferometer Gravitational-Wave Observatory (LIGO) Scientific and Virgo collaborations have detected gravitational waves since 14 September 2015 [1,2,3,4,5,6]
Gravitational Waves in Einstein-Æther Theory In Einstein-æther theory, gravity is mediated by the metric tensor, gμν, and the normalized timelike æther field uμ
Polarizations of gravitational waves: If the matter fields minimally couple with gμν only, the polarization content of GWs is determined by the linearized geodesic deviation equation ẍ j = d2 x j /dt2 = − Rtjtk xk with x j being the deviation vector

Summary

Introduction

The Laser Interferometer Gravitational-Wave Observatory (LIGO) Scientific and Virgo collaborations have detected gravitational waves since 14 September 2015 [1,2,3,4,5,6]. Observations led to a very stringent constraint on the speed of GWs , which constrains many alternative theories of gravity. The generalized tensor-vector-scalar (TeVeS) theory [17] contain several extra degrees of freedom (d.o.f.), so it predicts many extra polarizations. The identification of these extra polarizations and their detection are the main topics of this paper. For a discussion on the GWs of black holes according to Einstein-æther theory, please refer to Refs. In this paper , we first present the GW solutions in Einstein-æther theory, where we solve the equations of motion. We discuss the constraints on the theory, and after that, the possible detection by pulsar timing arrays.

Gravitational Waves in Einstein-Æther Theory

Gravitational Waves in the Generalized TeVeS Theory

Conclusions