Testing Scalar-Tensor Gravity with Gravitational-Wave Observations of Inspiralling Compact Binaries

TL;DR

Brans-Dicke scalar-tensor gravity is tested using gravitational-wave observations of inspiralling binaries. The authors develop a matched-filtering framework to bound dipole radiation tied to the BD coupling ${\omega_{\rm BD}}$, showing that neutron-star–black-hole systems can yield bounds stronger than the solar-system limit ${\omega_{\rm BD}>500}$ for favorable masses and signal-to-noise ratio; black-hole–black-hole binaries produce no detectable BD effect, while neutron-star–neutron-star systems require sizable mass differences. For a ${0.7}\,M_\odot$ neutron star and a ${3}\,M_\odot$ black hole, a bound ${\omega_{BD}} \approx 2000$ is achievable, with larger bounds for lighter black holes and stiffer equations of state; space-based detectors could push bounds to ${\omega_{BD}}\gtrsim 5\times10^4$ at low frequencies. Overall, gravitational-wave observations offer a robust probe of strong-field gravity and meaningful constraints on scalar-tensor theories beyond solar-system tests.

Abstract

Observations of gravitational waves from inspiralling compact binaries using laser-interferometric detectors can provide accurate measures of parameters of the source. They can also constrain alternative gravitation theories. We analyse inspiralling compact %binaries in the context of the scalar-tensor theory of Jordan, Fierz, Brans and Dicke, focussing on the effect on the inspiral of energy lost to dipole gravitational radiation, whose source is the gravitational self-binding energy of the inspiralling bodies. Using a matched-filter analysis we obtain a bound on the coupling constant $ω_{\rm BD}$ of Brans-Dicke theory. For a neutron-star/black-hole binary, we find that the bound could exceed the current bound of $ω_{\rm BD}>500$ from solar-system experiments, for sufficiently low-mass systems. For a $0.7 M_\odot$ neutron star and a $3 M_\odot$ black hole we find that a bound $ω_{\rm BD} \approx 2000$ is achievable. The bound decreases with increasing black-hole mass. For binaries consisting of two neutron stars, the bound is less than 500 unless the stars' masses differ by more than about $0.5 M_\odot$. For two black holes, the behavior of the inspiralling binary is observationally indistinguishable from its behavior in general relativity. These bounds assume reasonable neutron-star equations of state and a detector signal-to-noise ratio of 10.

Figures (3)

• Figure 1: Bounds on $\omega_{\rm BD}$ from inspir-al-ling neu-tron--star/-black-hole binaries, plotted against black-hole mass, for various neutron-star masses. Hatched portion indicates black holes with mass less than $3.0 M_\odot$, where identification as a black-hole may be ambiguous. Curves assume ${\cal S}=0.3$ and a signal--to--noise ratio of 10.
• Figure 2: Bounds on $\omega_{\rm BD}$ from inspir-al-ling double neu-tron--star binaries, plotted against mass of neutron stars. For equal masses, dipole radiation is suppressed, and no bound on $\omega_{\rm BD}$ results. Curves assume a linear dependence of sensitivity on mass, with ${\cal S}=0.2 \delta m /M_\odot$, and a signal-to-noise ratio of 10.
• Figure 3: Chirp-mass/reduced--mass param-eter plane, showing location of three different types of compact binaries. Chirp mass is plotted in units of the neutron-star maximum mass.