Waveform of gravitational waves in the general parity-violating gravities

TL;DR

This paper investigates how parity violation in various gravity theories affects gravitational waveforms during propagation, revealing modifications in phase, amplitude, and velocity that can be tested through circular polarization mode comparisons.

Contribution

It provides a unified framework to analyze parity violation effects on gravitational waves across multiple gravity theories, including Chern-Simons and Hořava-Lifshitz gravity.

Findings

Parity violation causes birefringence in GW amplitude and phase.

Modifications depend on both parity-violating and conserving terms.

Waveform deviations from GR can be used to test parity symmetry.

Abstract

As an extension of our previous work [J.Qiao, T.Zhu, W.Zhao & A.Wang, arXiv:1909.03815], in this article, we calculate the effects of parity violation on gravitational-wave (GW) waveforms during their propagation in the most general parity-violating gravities, including Chern-Simons modified gravity, ghost-free scalar-tensor gravity, symmetric teleparallel equivalence of GR theory, Ho\v{r}ava-Lifshitz gravity and so on. For this purpose, we consider the GWs generated by the coalescence of compact binaries and concentrate on the imprints of the parity violation in the propagation of GWs. With a unified description of GW in the theories of parity-violating gravity, we study the effects of velocity and amplitude birefringence on the GW waveforms. Decomposing the GWs into the circular polarization modes, the two birefringence effects exactly correspond to the modifications in phase and amplitude of GW waveforms respectively. We find that, for each circular polarization mode, the amplitude, phase and velocity of GW can be modified by both the parity-violating terms and parity-conserving terms in gravity. Therefore, in order to test the parity symmetry in gravity, we should compare the difference between two circular polarization modes, rather than measuring an individual mode. Combining two circular modes, we obtain the GW waveforms in the Fourier domain, and obtain the deviations from those in General Relativity. The GW waveforms derived in this paper are also applicable to the theories of parity-conserving gravity, which have the modified dispersion relations (e.g. massive gravity, double special relativity theory, extra-dimensional theories, etc), or/and have the modified friction terms (e.g. nonlocal gravity, gravitational theory with time-dependent Planck mass, etc).