Yi-Fan Wang^{1, 2}, Stephanie M. Brown^{1, 2}, Lijing Shao^{3, 4}, Wen Zhao^{5, 6}

_{1. Albert-Einstein-Institut, Max-Planck-Institut for Gravitationsphysik, D-30167 Hannover, Germany 2. Leibniz Universitat Hannover, D-30167 Hannover, Germany 3. Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, China 4. National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China 5. CAS Key Laboratory for Researches in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of China, Chinese Academy of Sciences, Hefei, Anhui 230026, China 6. School of Astronomy and Space Science, University of Science and Technology of China, Hefei 230026, China}

The routine detection of gravitational-wave events from compact binary coalescence has allowed precise tests of gravity in strong field, dynamical field, and high energy regime. To date, a total of 57 gravitational-wave events have been reported by the third Open Gravitational-wave Catalog (3-OGC). In this work, we report the results of testing gravitational-wave birefringence using the events from 3-OGC. Birefringence, an effect where the left- and right-handed polarizations of gravitational waves follow different equations of motion, occurs when the parity symmetry of gravity is broken. This arises naturally in the effective field theory extension of general relativity. Using Bayesian inference with state-of-the-art waveform modeling, we use all events in 3-OGC to constrain the lower limit of energy scale at which parity violation effects emerge. Overall we do not find evidence for a violation of general relativity, and thus we constrain the parity-violating energy scale to $M_\mathrm{PV} > 0.14$ GeV at $90%$ confidence level, which is an improvement over previous results by one order of magnitude. Intriguingly, we find an outlier, GW190521, that supports the existence of birefringence over general relativity with a higher match-filtering signal-to-noise ratio and a natural log Bayes factor of $7.84$. Because the inferred $M_\mathrm{PV}$ from GW190521 is in tension with the combined constraints, we hypothesize that this may be caused by the limitations of the existing waveform approximants, such as systematic errors during merger phase of the waveform, or by the existence of physical effects such as eccentricity which are not taken into account by the current waveform approximants.

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