Constraining scalar-tensor theories from gravitational wave

Brans-Dicke (BD) theory is one of the simplest scalar-tensor theories, with potential applicationsin dark matter, dark energy, inflation, and primordial nucleosynthesis. The strongest constrainton the BD coupling constant is provided by the Cassini measurement of the Shapiro time delayin the Solar System. Constraints from gravitational wave (GW) events are subject to asymmetricbinaries. The GW230529, which was initially released in O4a, is most likely neutron star-black hole(NSBH) mergers. 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 theoriesas φ−2 > −1.98 × 10−4 by using dominant-mode correction. Specific to BD theory, we have theconstraint ωBD > 25.12. Asymmetric binary systems usually have a significant mass ratio; in suchcases, higher harmonic modes cannot be neglected. Our work considers higher harmonic correctionsfrom scalar-tensor theories and provides a tighter constraint of φ−2 > −1.54 × 10−4. Transitioningto the BD theory, the constraint is ωBD > 32.68, with a 30.1% improvement. Combining GW230529,GW200115 and GW190814 and including higher modes, the constraint is improved to ωBD > 123.75.This is currently the strongest constraint utilizing GWs, contingent upon GW190814 being an NSBHevent. Additionally, we take into account a BD-like theory, known as screened modified gravity(SMG), and investigate the coupling constant constraints, both with and without higher-modecorrections.