For a scale-invariant inflationary gravitational wave background with negligible primordial non-Gaussianity, the gravitational wave energy density perturbation is lognormally distributed, δGW = A e^{-ζ} - 1, yielding a specific connected three-point function and an effective f_NL^GW = f_NL - 5/6.
The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background,
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Non-linear effects on the Cosmological Gravitational Wave Background anisotropies
For a scale-invariant inflationary gravitational wave background with negligible primordial non-Gaussianity, the gravitational wave energy density perturbation is lognormally distributed, δGW = A e^{-ζ} - 1, yielding a specific connected three-point function and an effective f_NL^GW = f_NL - 5/6.