Constraints on Brans-Dicke gravity from neutron star-black hole merger events using higher harmonics

Brans-Dicke (BD) theory is one of the simplest scalar-tensor theories, with potential applications in dark matter, dark energy, inflation, and primordial nucleosynthesis. The strongest constraint on the BD coupling constant is provided by the Cassini measurement of the Shapiro time delay in the Solar System. Constraints from gravitational wave (GW) events are subject to asymmetric binaries. The third Gravitational-Wave Transient Catalog (GWTC) reports a neutron star-black hole (NSBH) merger event, GW200115, making it possible to constrain BD by GW. With the aid of this source and Bayesian Markov-chain Monte Carlo (MCMC) analyses, we derive a 90% credible lower bound on the modified parameter of scalar-tensor theories as ${\phi }_{-2}>-7.94\times {10}^{-4}$ by using dominant-mode correction. Specific to BD theory, we have the constraint ${\omega }_{\mathrm{BD}}>4.75$. Asymmetric binary systems usually have a significant mass ratio; in such cases, higher harmonic modes cannot be neglected. Our work considers higher harmonic corrections from scalar-tensor theories and provides a tighter constraint of ${\phi }_{-2}>-7.59\times {10}^{-4}$. Transitioning to BD theory, the constraint is ${\omega }_{\mathrm{BD}}>5.06$, with a 6.5% improvement. We also consider a plausible NSBH event, GW190814, which is a highly unequal mass ratio source that exhibits strong evidence for higher-order multipoles. We obtain poorly converged results when using the dominant mode, while getting a constraint of ${\phi }_{-2}>-6.60\times {10}^{-4}$ on scalar-tensor theories when including the higher harmonic modes. This suggests that the difference between the dominant mode and higher modes has a significant impact on our analysis. Furthermore, treating this suspected event as an NSBH event, we find ${\omega }_{\mathrm{BD}}>6.12$ when including the higher harmonic modes. Combining GW200115 and GW190814 and including higher modes, the constraint is improved to ${\omega }_{\mathrm{BD}}>110.55$. This is currently the strongest constraint utilizing GWs, contingent upon GW190814 being an NSBH event. Additionally, we take into account a BD-like theory, known as screened modified gravity, and investigate the coupling constant constraints, both with and without higher-mode corrections, by using data from both GW200115 and GW190814.

Figure 1

Probability density of Bayesian posterior distributions on ${\phi }_{-2}$. The gray line corresponds to the constraint at a 90% credible level by using the dominant-mode (DM) correction, while the red line stands for the constraint at the 90% confidence level by using the correction including the higher mode (HM). The top panel shows the constraints on ${\phi }_{-2}$ from the GW200115 event; the middle and bottom panels are from GW190814, and they show the results corresponding to dominant and higher modes. The absence of a gray line in the middle panel is due to the fact that there is not good convergence in the result when using the dominant mode. We use a logarithmic scale due to the posterior distribution of ${\omega }_{\mathrm{BD}}$ spanning several orders of magnitude.

Figure 2

Probability density of Bayesian posterior distributions on ${\omega }_{\mathrm{BD}}$. The top and bottom panels describe the constraints on ${\omega }_{\mathrm{BD}}$ from GW200115 and GW190814 events, respectively. The gray line corresponds to the constraint on BD at a 90% credible level by using the DM correction, while the red line represents the constraint on BD with 90% probability by using the correction including the HM. The reason for the absence of the gray line in the bottom panel is also the poor convergence of the dominant mode.