Light scalar field constraints from gravitational-wave observations of compact binaries

Scalar-tensor theories are among the simplest extensions of general relativity. In theories with light scalars, deviations from Einstein’s theory of gravity are determined by the scalar mass m_s and by a Brans-Dicke-like coupling parameter \omega_{BD}. We show that gravitational-wave observations of nonspinning neutron star-black hole binary inspirals can be used to set lower bounds on \omega_{BD} and upper bounds on the combination m_s/\sqrt{\omega_{BD}}$. We estimate via a Fisher matrix analysis that individual observations with signal-to-noise ratio \rho would yield (m_s/\sqrt{\omega_{BD}})(\rho/10)<10^{-15}, 10^{-16} and 10^{-19} eV for Advanced LIGO, ET and eLISA, respectively. A statistical combination of multiple observations may further improve these bounds.

💡 Research Summary

This paper investigates how gravitational‑wave (GW) observations can constrain light scalar fields that appear in scalar‑tensor extensions of general relativity. In such theories a massive scalar of mass mₛ couples to matter with a Brans‑Dicke‑like parameter ω_BD. The presence of a light scalar modifies the inspiral waveform of compact binaries through an additional dipole radiation channel, which enters at the –1 PN order (or 1.5 PN relative to the leading quadrupole term). The authors focus on non‑spinning neutron‑star–black‑hole (NS‑BH) binaries because the mass asymmetry maximizes the dipole contribution.

A key theoretical ingredient is the scalar‑mass‑induced cutoff frequency f_c ≈ mₛ/(2πħ). For GW frequencies above f_c the scalar radiation is exponentially suppressed, and the waveform reverts to the pure general‑relativistic form. By incorporating this cutoff into the frequency‑domain waveform model, the authors perform a Fisher‑matrix analysis to estimate how accurately the combination (mₛ/√ω_BD) can be measured as a function of the signal‑to‑noise ratio (SNR) ρ.

The results show a simple linear scaling: (mₛ/√ω_BD) < 10⁻¹⁵ eV · (ρ/10) for Advanced LIGO, < 10⁻¹⁶ eV · (ρ/10) for the third‑generation Einstein Telescope, and < 10⁻¹⁹ eV · (ρ/10) for the space‑based eLISA mission. These bounds are orders of magnitude tighter than current Solar‑System tests and binary‑pulsar limits. Moreover, by statistically combining N independent detections, the uncertainty improves by a factor of √N, suggesting that a modest catalog of NS‑BH inspirals could push the lower limit on ω_BD well beyond existing constraints.

The paper discusses several caveats: the analysis assumes non‑spinning, quasi‑circular binaries; higher‑order post‑Newtonian effects, spin‑induced precession, and eccentricity are neglected but could affect parameter correlations. Nevertheless, the study demonstrates that GW astronomy provides a powerful, complementary probe of light scalar fields, and it outlines a clear pathway for future work to incorporate more realistic waveforms and to exploit the full potential of upcoming detector networks.