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

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 $\beta$ (i.e., $\beta_{\bar \nu}$, $\beta_{\bar \mu}$, $\beta_{\nu}$, and $\beta_{\mu}$). 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 ($\beta > 0$) and low-frequency ($\beta < 0$) modifications. Our Bayesian analysis reveals that while the exceptional SNR of the GW250114-like event yields superior constraints for high-frequency modifications ($\beta > 0$), the massive nature of GW231123 provides more stringent limits for low-frequency effects ($\beta < 0$). This work highlights the critical value of future multi-band gravitational wave astronomy for conducting precision tests of general relativity across diverse binary populations.