We introduce the concept of stationary graviton non-Gaussianity (nG), an observable that can be probed in terms of 3-point correlation functions of a stochastic gravitational wave (GW) background. When evaluated in momentum space, stationary nG corresponds to folded bispectra of graviton nG. We determine 3-point overlap functions for testing stationary nG with pulsar timing array GW experiments, and we obtain the corresponding optimal signal-to-noise ratio. For the first time, we consider 3-point overlap functions including scalar graviton polarizations (which can be motivated in theories of modified gravity); moreover, we also calculate 3-point overlap functions for correlating pulsar timing array with ground based GW detectors. The value of the optimal signal-to-noise ratio depends on the number and position of monitored pulsars. We build geometrical quantities characterizing how such ratio depends on the pulsar system under consideration, and we evaluate these geometrical parameters using data from the IPTA collaboration. We quantitatively show how monitoring a large number of pulsars can increase the signal-to-noise ratio associated with measurements of stationary graviton nG.
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