# Testing Brans-Dicke gravity using the Einstein telescope

## TL;DR

This paper explores how the proposed Einstein Telescope could significantly improve constraints on Brans-Dicke gravity by analyzing gravitational waves from inspiraling compact binaries, surpassing current Solar System limits.

## Contribution

It provides detailed waveform calculations in Brans-Dicke theory and estimates the potential bounds on the coupling constant using third-generation gravitational wave data.

## Key findings

- Constraints on $oldsymbol{ ext{ω}_{ ext{BD}}}$ could exceed current limits by over an order of magnitude.
- Detection of inspiraling binaries up to redshift 5 can tighten bounds on alternative gravity theories.
- Einstein Telescope has the potential to be a powerful tool for testing gravity theories beyond General Relativity.

## Abstract

Gravitational radiation is an excellent field for testing theories of gravity in strong gravitational fields. The current observations on the gravitational-wave (GW) bursts by LIGO have already placed various constraints on the alternative theories of gravity. In this paper, we investigate the possible bounds which could be placed on the Brans-Dicke gravity using GW detection from inspiralling compact binaries with the proposed Einstein Telescope, a third-generation GW detector. We first calculate in details the waveforms of gravitational radiation in the lowest post-Newtonian approximation, including the tensor and scalar fields, which can be divided into the three polarization modes, i.e. "plus mode", "cross mode" and "breathing mode". Applying the stationary phase approximation, we obtain their Fourier transforms, and derive the correction terms in amplitude, phase and polarization of GWs, relative to the corresponding results in General Relativity. Imposing the noise level of Einstein Telescope, we find that the GW detection from inspiralling compact binaries, composed of a neutron star and a black hole, can place stringent constraints on the Brans-Dicke gravity. The bound on the coupling constant $\omega_{\rm BD}$ depends on the mass, sky-position, orbital angle, polarization angle, luminosity distance, redshift distribution and total observed number $N_{\rm GW}$ of the binary systems. Taking into account all the burst events up to redshift $z=5$, we find that the bound could be $\omega_{\rm BD}\gtrsim 10^{6}\times(N_{\rm GW}/10^4)^{1/2}$. Even for the conservative estimation with $10^{4}$ observed events, the bound is still more than one order tighter than the current limit from Solar System experiments. So, we conclude that Einstein Telescope will provide a powerful platform to test alternative theories of gravity.