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 ${\omega }_{\mathrm{BD}}$. We show that gravitational-wave observations of nonspinning neutron star-black hole binary inspirals can be used to set lower bounds on ${\omega }_{\mathrm{BD}}$ and upper bounds on the combination $m_s/\sqrt{{\omega }_{\mathrm{BD}}}$. We estimate via a Fisher matrix analysis that individual observations with signal-to-noise ratio $\rho$ would yield $(m_s/\sqrt{{\omega }_{\mathrm{BD}}})(\rho /10)\lesssim {10}^{-15}$, ${10}^{-16}$, and ${10}^{-19}\mathrm{eV}$ for Advanced LIGO, ET, and eLISA, respectively. A statistical combination of multiple observations may further improve these bounds.

Figure 1

Bounds on $m_s/\sqrt{{\omega }_{\mathrm{BD}}}$ with AdLIGO, AdLIGO ZDHP, ET, Classic LISA, and eLISA/NGO at fixed SNR $\rho =10$.

Figure 2

Bounds from eLISA/NGO at SNR $\rho =10$, compared to Solar System and binary pulsar bounds.

Figure 3

SNR for observations of neutron star-black hole binaries as a function of the black hole mass $M_{\mathrm{BH}}$ for various detectors (AdLIGO, AdLIGO ZDHP, ET, Classic LISA, and eLISA/NGO) at luminosity distance $D_L=200\mathrm{Mpc}$.

Figure 4

Bound on ${\omega }_{\mathrm{BD}}$ obtained and considering a six-parameter Fisher matrix at fixed SNR $\rho =10$. Left: we set $m_s\propto \nu =0$ and consider a six-parameter Fisher matrix. Right: same, but for a seven-parameter Fisher matrix with $\nu \ne 0$.