Inspiral gravitational waveforms from compact binary systems in Horndeski gravity

TL;DR

This paper investigates gravitational waveforms from binary systems in a subclass of Horndeski gravity, highlighting how scalar fields influence wave polarizations and energy loss, and exploring observable deviations from General Relativity.

Contribution

It develops a framework to compute scalar and tensor gravitational waveforms in Horndeski theories, connecting ppE parameters to scalar charges and analyzing deviations from GR in specific models.

Findings

Scalar modes induce breathing and longitudinal polarizations.

The waveform reduces to GR if scalar mass exceeds orbital frequency.

Deviations from GR are detectable in neutron star-black hole binaries.

Abstract

In a subclass of Horndeski theories with the speed of gravity equivalent to that of light, we study gravitational radiation emitted during the inspiral phase of compact binary systems. We compute the waveform of scalar perturbations under a post-Newtonian expansion of energy-momentum tensors of point-like particles that depend on a scalar field. This scalar mode not only gives rise to breathing and longitudinal polarizations of gravitational waves, but it is also responsible for scalar gravitational radiation in addition to energy loss associated with transverse and traceless tensor polarizations. We calculate the Fourier-transformed gravitational waveform of two tensor polarizations under a stationary phase approximation and show that the resulting waveform reduces to the one in a parametrized post-Einsteinian (ppE) formalism. The ppE parameters are directly related to a scalar charge in the Einstein frame, whose existence is crucial to allow the deviation from General Relativity (GR). We apply our general framework to several concrete theories and show that a new theory of spontaneous scalarization with a higher-order scalar kinetic term leaves interesting deviations from GR that can be probed by the observations of gravitational waves emitted from neutron star-black hole binaries. If the scalar mass exceeds the order of typical orbital frequencies $\omega \simeq 10^{-13}$~eV, which is the case for a recently proposed scalarized neutron star with a self-interacting potential, the gravitational waveform practically reduces to that in GR.