New probe of gravitational parity violation through nonobservation of the stochastic gravitational-wave background

Parity violation in the gravitational sector is a prediction of many theories beyond general relativity. In the propagation of gravitational waves, parity violation manifests by inducing amplitude and/or velocity birefringence between right- and left-circularly polarized modes. We study how the stochastic gravitational-wave background can be used to place constraints on these birefringent effects. We consider two model scenarios, one in which we allow birefringent corrections to become arbitrarily large and a second in which we impose stringent theory priors. In the former, we place constraints on a generic birefringent gravitational-wave signal due to the current nondetection of a stochastic background from compact binary events. We find a joint constraint on birefringent parameters κD and κz of O(10-1). In the latter scenario, we forecast constraints on parity-violating theories resulting from observations of the future upgraded LIGO-Virgo-KAGRA network as well as proposed third-generation detectors. We find that third-generation detectors will be able to improve the constraints by at least 2 orders of magnitude, yielding new stringent bounds on parity-violating theories. This work introduces a novel and powerful probe of gravitational parity violation with gravitational-wave data.