Constraining scalar-tensor theories from higher harmonics with GW230529

TL;DR

This work uses GW230529_181500, a likely NSBH event, to constrain scalar-tensor gravity models—specifically Screened Modified Gravity (SMG) and Brans-Dicke (BD) theory—by incorporating higher-harmonic modes in the waveform through the parameterized post-Einsteinian (ppE) formalism. The authors implement a theory-informed phase modification, map SMG and BD corrections to leading dipolar radiation, and perform Bayesian parameter estimation with PyCBC/emcee_pt, analyzing DM and HM contributions and a three-event combination (GW230529, GW200115, GW190814). They report 90% bounds: for GW230529 DM, $\varphi_{-2}$ and $\omega_{BD}$ are constrained to $\varphi_{-2} > -1.98\times 10^{-4}$ and $\omega_{BD} > 25$, improving to $\varphi_{-2} > -1.54\times 10^{-4}$ and $\omega_{BD} > 32.68$ with HM; the three-event combination yields $\varphi_{-2} > -4.26\times 10^{-5}$, $\varphi_{VEV}/M_{Pl} < 7.84\times 10^{-3}$, and $\omega_{BD} > 123.75$, representing the strongest GW-based constraints to date (conditional on GW190814 being NSBH). The results emphasize the importance of higher modes in asymmetric binaries and provide a framework for future GW-era tests of scalar-tensor gravity with more NSBH detections.

Abstract

The Advanced LIGO and Virgo collaborations recently detected a gravitational wave event, GW230529\_181500, during the fourth observing run, which is most plausibly attributed to the merger of a neutron star and a black hole. This observation provides an opportunity to test a class of gravitational theories that deviate from general relativity. In such theories, additional terms contribute to the gravitational wave signal only in cases of asymmetric binaries. This study focuses on two scalar-tensor models within this class of theories: the Screened Modified Gravity and Brans-Dicke theory. These models have potential applications in areas such as dark matter, dark energy, cosmic inflation, and primordial nucleosynthesis. With the GW230529\_181500 and Bayesian Markov-chain Monte Carlo analyses, we derive a 90\% credible lower bound as $ \frac{\varphi_{\rm_{VEV}}}{M_{\rm Pl}}<1.7\times10^{-2}$ and $ω_{\rm BD}>25.12$ by using dominant mode correction. 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 $ \frac{\varphi_{\rm_{VEV}}}{M_{\rm Pl}}<1.5\times10^{-2}$ and $ω_{\rm BD}>32.68$, with a 13.3\% and 30.1\% improvement respectively. Combining GW230529\_181500, GW200115 and GW190814 and including higher modes, the constraint is improved to $\frac{\varphi_{\rm_{VEV}}}{M_{\rm Pl}}<7.84\times10^{-3}$ and $ω_{\rm BD}>123.75$. This is currently the strongest constraint from GWs, contingent upon GW190814 being an NSBH event.

Figures (5)

• Figure 1: Probability density of Bayesian posterior distributions on $\varphi_{-2}$. The blue dashed line corresponds to the 90% credible constraint using the dominant mode correction, while the red solid line denotes the 90% credible constraint using the correction including higher modes. The gray dash-dotted line represents the prior on $\varphi_{-2}$.
• Figure 2: Probability density of Bayesian posterior distributions on $\omega_{\rm_{BD}}$. The blue dashed line corresponds to the constraint on BD at 90% credible level by using the dominant mode correction, while the red solid line represents the constraint on BD with 90% probability by using the correction including higher mode. The gray dash-dotted line represents the prior on $\omega_{\rm_{BD}}$. We use a logarithmic scale due to the posterior distribution of $\omega_{\rm BD}$ spanning several orders of magnitude.
• Figure 3: Probability density of Bayesian posterior distributions on ${\varphi_{\rm_{VEV}}}/{M_{\rm Pl}}$. The blue dashed line corresponds to the constraint at a 90% credible level by using the dominant mode correction, while the red solid line stands for the constraint at the 90% confidence level by using the correction including the higher mode. The gray dash-dotted line represents the prior on ${\varphi_{\rm_{VEV}}}/{M_{\rm Pl}}$.
• Figure 4: Prior including both negative and positive values
• Figure 5: Comparison of results with different PSD choices