  We report the results of testing gravitational-wave birefringence using the
largest population of gravitational-wave events currently available.
Gravitational-wave birefringence, which can arise from the effective field
theory extension of general relativity, occurs when the parity symmetry is
broken, causing the left- and right-handed polarizations to propagate following
different equations of motion. We perform Bayesian inference on the 94 events
reported by the 4th-Open Gravitational-wave Catalog (4-OGC) using a
parity-violating waveform. We find no evidence for a violation of general
relativity in the vast majority of events. However, the most massive event,
GW190521, and the second most massive event, GW191109, show intriguing non-zero
results for gravitational-wave birefringence. We find that the probability of
association between GW190521 and the possible electromagnetic (EM) counterpart
reported by Zwicky Transient Facility (ZTF) is increased when assuming
birefringence. Excluding GW190521 and GW191109, the parity-violating energy
scale is constrained to $M_\mathrm{PV} > 0.05$ GeV at $90\%$ credible interval,
which is an improvement over previous results from twelve events by a factor of
five. We discuss the implications of our results on modified gravity and
possible alternative explanations such as waveform systematics. More detections
of massive binary black hole mergers from the upcoming LIGO/Virgo/KAGRA run
will shed light on the true origin of the apparent birefringence.
