Constraining Lorentz and parity violations in gravity with multiband gravitational wave observations

TL;DR

The paper tackles constraining parity- and Lorentz-violating gravity using multi-band gravitational waves. It develops a unified propagation framework with four coefficients ($\bar{\nu}$, $\bar{\mu}$, $\nu_A$, $\mu_A$) linked to energy scales $M_{\rm PV}$ and $M_{\rm LV}$ and power laws $\beta$, and forecasts $1\sigma$ bounds via Fisher information for two representative BBH events across two detector networks (Network A: CE+ET+LISA+Taiji; Network B: CE+ET+LISA+TianQin). The results show that multiband observations yield improvements of several orders of magnitude over single-band plans, with high-frequency modifications constrained by ground-based detectors and low-frequency modifications by space-based detectors; the combination of GW250114-like and GW231123-like signals across the networks demonstrates the strong potential of coordinated future GW observations to perform precision tests of GR over a broad frequency range.

Abstract

This study evaluates the capability of future multi-band observations of gravitational waves emitted from binary black hole coalescences, utilizing joint third-generation ground-based (CE, ET) and space-based (LISA, Taiji, TianQin) detector networks, to constrain parity and Lorentz symmetry violations in the gravitational sector. We model these effects through a parameterized waveform framework that incorporates a set of parameters that quantify potential deviations from general relativity. The frequency-dependence of their effects is described by power-law indices $β$ (i.e., $β_{\bar ν}$, $β_{\bar μ}$, $β_ν$, and $β_μ$). By analyzing events such as a high-signal noise ratio (SNR) "golden event" like GW250114 and a massive binary system like GW231123 (total mass $190-265 M_\odot$) using two networks of ground- and space-based detectors, we demonstrate that multi-band observations can significantly improve the current constraints on Lorentz and parity violations by several order of magnitude, for both high-frequency ($β> 0$) and low-frequency ($β< 0$) modifications. Our Bayesian analysis reveals that while the exceptional SNR of the GW250114-like event yields superior constraints for high-frequency modifications ($β> 0$), the massive nature of GW231123 provides more stringent limits for low-frequency effects ($β< 0$). This work highlights the critical value of future multi-band gravitational wave astronomy for conducting precision tests of general relativity across diverse binary populations.

Figures (2)

• Figure 1: Sensitivity curves of various GW interferometers, plotted alongside the characteristic amplitude of GW250114 and GW231123. The figure illustrates the multi-band nature of the event: the early inspiral phase is observable by space-based detectors, whereas the late inspiral, merger, and ringdown phases fall within the detection band of ground-based instruments.
• Figure 2: Comparison of the 90% credible bounds on the parity-violating energy scale $M_{\rm PV}$ and Lorentz-violating energy scale $M_{\rm LV}$ derived in this work against previous benchmarks. The solid markers represent the multi-band constraints obtained in this work using the high-SNR event GW250114 and the massive binary GW231123. For comparison, we include the current observational limits from the LIGO-Virgo-KAGRA GWTC-3 catalog reported by ref.Zhu:2023rrxWang:2021gqmGong:2023ffbWang:2025fhw, and the forecasted constraints for future ground- and space-based detectors presented by ref.Zhang:2025kcw. The comparison demonstrates that our multi-band strategy, particularly with the inclusion of the massive GW231123 event, yields constraints that significantly improve upon current baselines and are competitive with or superior to single-band future projections in the low-frequency regime.