Gravitational waveforms from the quasicircular inspiral of compact binaries in massive Brans-Dicke theory

TL;DR

This paper derives explicit gravitational waveform models for inspiralling binaries in massive Brans-Dicke theory, analyzing scalar and tensor polarizations, and assesses their detectability with future gravitational wave detectors.

Contribution

It provides analytical expressions for scalar polarizations in massive Brans-Dicke theory and explores their mapping to the ppE framework, including constraints from future observations.

Findings

Waveforms can be mapped to the ppE framework when the scalar field is light.

The ppE framework is not applicable when the scalar field is heavy.

Projected constraints on theory parameters are obtained for future ground-based detectors.

Abstract

We study the gravitational waves emitted by an inspiralling compact binary system in massive Brans-Dicke theory. In addition to the two tensor polarizations, which have been obtained in the previous work, we calculate explicitly and analytically the expressions for the time-domain waveforms of the two scalar polarizations. With the stationary phase approximations, we obtain the Fourier transforms of the two tensor polarizations. We find that when the scalar field is light, the waveforms can be mapped to the parametrized post-Einsteinian (ppE) framework and we identify the ppE parameters. However, when the scalar field is heavy, the ppE framework is not applicable. We also obtain the projected constraints on the parameters of this theory by gravitational wave observations of future ground-based detectors. Finally, we apply our result to the model proposed by Damour and Esposito-Far\`{e}se, $f(R)$ gravity, and screened modified gravity.