New test of modified gravity with gravitational wave experiments

We propose a new strategy to probe nontensorial polarizations in the stochastic gravitational wave (GW) background. Averaging over polarization angles, we find that three-point correlations of the GW signal vanish for tensor and vector modes, while scalar modes generically leave a nonzero imprint. This property makes the GW bispectrum a distinctive and robust diagnostic of scalar polarizations predicted in theories beyond general relativity. We derive the corresponding response functions for ground-based interferometers, pulsar timing arrays, and astrometric observables, and we construct an optimal estimator together with simple Fisher forecasts for pulsar timing sensitivity. As a proof of principle, we show that second-order GWs sourced by primordial magnetogenesis can be characterized by large three-point functions. Our results demonstrate that GW three-point correlations provide a novel observational window on physics beyond general relativity.