[Paper Review] Testing Lorentz Invariance of Gravity in the Standard Model Extension with GWTC-3

Rui Niu, Tao Zhu+1 more|arXiv (Cornell University)|Feb 10, 2022

Geophysics and Gravity Measurements4 citations

TL;DR

This study tests Lorentz invariance in gravity using gravitational wave data from the LIGO-Virgo-KAGRA GWTC-3 catalog. By modeling Lorentz-violating effects—such as anisotropy, birefringence, and dispersion—via the Standard Model Extension (SME) at mass dimensions d=5 and d=6, the authors perform full Bayesian inference on 50 confident events, finding no evidence for Lorentz violation and setting 90% credible bounds at ~10⁻¹⁵ m for d=5 and ~10⁻¹⁰ m² for d=6.

ABSTRACT

Successful detection of gravitational waves has presented a new avenue to explore the nature of gravity. With the cumulative catalog of detected events, we can perform tests on General Relativity from various aspects with increasing precision. In this work, we focus on Lorentz symmetry during propagation of gravitational waves. Considering the dispersion relation in the gauge-invariant linearized gravity sector of the Standard-Model Extension, the anisotropy, birefringence, and dispersion effects will be induced during propagation of gravitational waves because of the Lorentz violating modification, and cause dephasings in waveform received by detectors. With the distorted waveform, we perform full Bayesian inference with confident events in the last gravitational wave catalog. We consider two cases associated with the lowest mass dimension $d=5,6$ which are supposed to have the most significant effects, and place the constraints on the expansion coefficients characterizing the Lorentz violating behavior which have 16 independent components for $d=5$ and 18 components for $d=6$. We do not find any evidence for Lorentz violation in the gravitational wave data, the constraints on the coefficients are on the order of $10^{-15}{ m m}$ for $d=5$ and $10^{-10}{ m m^2}$ for $d=6$ respectively.

Motivation & Objective

• To test Lorentz invariance in the gravitational sector using gravitational wave data from the GWTC-3 catalog.
• To constrain Lorentz-violating coefficients in the Standard Model Extension (SME) framework for gravity at mass dimensions d=5 and d=6.
• To perform a full Bayesian inference on 50 confident gravitational wave events to detect deviations from General Relativity due to anisotropy, birefringence, or dispersion effects.
• To improve upon previous approximate methods by using a rigorous statistical framework that allows for identification of deviations if present.

Proposed method

• The study employs the gauge-invariant linearized gravity sector of the SME to model Lorentz-violating modifications to the dispersion relation of gravitational waves.
• It incorporates waveform deformations due to anisotropy, birefringence, and dispersion, derived from the SME Lagrangian at d=5 and d=6.
• Full Bayesian inference is performed using the Bilby software suite, with stochastic sampling over effective parameters to reconstruct posteriors of independent SME coefficients.
• The analysis uses 50 confident events from GWTC-3, selected based on LVK's GR consistency tests, to ensure high signal quality.
• The 'maximal-reach' approach is applied, isolating one component or pair of components at a time while setting others to zero to constrain individual coefficients.
• Constraints are derived from posterior distributions using 90% credible intervals, ensuring robust statistical interpretation.

Experimental results

Research questions

• RQ1 Does gravitational wave propagation exhibit signs of Lorentz violation as predicted by the SME at mass dimensions d=5 and d=6?
• RQ2 Can full Bayesian inference detect deviations from General Relativity in GW waveforms due to anisotropy, birefringence, or dispersion effects?
• RQ3 How do the constraints on SME coefficients from GWTC-3 compare to previous results based on approximate arrival time differences?
• RQ4 What is the sensitivity of current GW detectors to Lorentz-violating effects in the gravity sector?
• RQ5 Can the full Bayesian framework improve upon prior approximate methods in constraining Lorentz-violating coefficients?

Key findings

• No evidence for Lorentz violation is found in the GWTC-3 data, consistent with the predictions of General Relativity.
• The 90% credible upper bounds on the d=5 SME coefficients are on the order of 10⁻¹⁵ m.
• The 90% credible upper bounds on the d=6 SME coefficients are on the order of 10⁻¹⁰ m².
• The constraints are consistent with but slightly weaker than previous results based on approximate arrival time estimation.
• The full Bayesian analysis provides a more rigorous framework than prior approximate methods, enabling potential detection of deviations if they existed.
• The study demonstrates the feasibility of using full Bayesian inference to constrain Lorentz-violating coefficients in the SME gravity sector with current GW data.