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

Abstract This study evaluates the capability of future multiband 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 $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> (i.e., $$\beta _{\bar{\nu }}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>β</mml:mi> <mml:mover> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:msub> </mml:math> , $$\beta _{\bar{\mu }}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>β</mml:mi> <mml:mover> <mml:mrow> <mml:mi>μ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:msub> </mml:math> , $$\beta _{\nu }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>β</mml:mi> <mml:mi>ν</mml:mi> </mml:msub> </mml:math> , and $$\beta _{\mu }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>β</mml:mi> <mml:mi>μ</mml:mi> </mml:msub> </mml:math> ). By analyzing events such as a high-signal noise ratio (SNR) “golden event” like GW250114 and a massive binary system like GW231123 (total mass $$190-265 M_\odot $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>190</mml:mn> <mml:mo>-</mml:mo> <mml:mn>265</mml:mn> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:mrow> </mml:math> ) using two networks of ground- and space-based detectors, we demonstrate that multiband observations can significantly improve the current constraints on Lorentz and parity violations by several orders of magnitude, for both high-frequency ( $$\beta &gt; 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>β</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> ) and low-frequency ( $$\beta &lt; 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>β</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> ) modifications. The results reveal that while the exceptional SNR of the GW250114-like event yields superior constraints for high-frequency modifications ( $$\beta &gt; 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>β</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> ), the massive nature of GW231123 provides more stringent limits for low-frequency effects ( $$\beta &lt; 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>β</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> ). This work highlights the critical value of future multiband gravitational wave astronomy for conducting precise tests of general relativity across diverse binary populations.