Abstract
The gravitational wave provides a new method to examine General Relativity and its alternatives in the high speed, strong field regime. Alternative theories of gravity generally predict more polarizations than General Relativity, so it is important to study the polarization contents of theories of gravity to reveal the nature of gravity. In this talk, we analyze the polarization contents of Horndeski theory and f(R) gravity. We find out that in addition to the familiar plus and cross polarizations, a massless Horndeski theory predicts an extra transverse polarization, and there is a mix of pure longitudinal and transverse breathing polarizations in the massive Horndeski theory and f(R) gravity. It is possible to use pulsar timing arrays to detect the extra polarizations in these theories. We also point out that the classification of polarizations using Newman–Penrose variables cannot be applied to massive modes. It cannot be used to classify polarizations in Einstein-æther theory or generalized Tensor-Vector-Scalar (TeVeS) theory, either.
Highlights
The gravitational wave (GW) was detected by the Laser Interferometer Gravitational-WaveObservatory (LIGO) Scientific and Virgo collaborations, which further supports General Relativity (GR) [1,2,3,4,5,6]
Our analysis showed that the extra polarization state is the transverse breathing mode if the scalar field is massless, and it is a mix of the transverse breathing and the longitudinal modes if the scalar field is massive [21]. f ( R) gravity [22] is equivalent to a scalar-tensor theory of gravity [23,24]
Each theory predicts at least one extra polarization states due to the additional d.o.f. provided by it
Summary
The gravitational wave (GW) was detected by the Laser Interferometer Gravitational-Wave. Ψ4 represents the plus and the cross polarizations, Φ22 donates the transverse breathing polarization, Ψ3 corresponds to the vector-x and vector-y polarizations, and Ψ2 is for the longitudinal polarization This classification can be applied to any metric theory of gravity which respects the local Lorentz invariance and predicts null GWs, such as Brans–Dicke theory, the simplest scalar-tensor theory [19]. In this theory, there are plus and cross modes Ψ4 due to the massless graviton, and there exists the transverse breathing mode Φ22 induced by the massless scalar field [17].
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