Non-Gaussianity of inflationary gravitational waves from the field equation

摘要

We demonstrate equivalence of the in-in formalism and Green's function method for calculating the bispectrum of primordial gravitational waves generated by vacuum fluctuations of the metric. The tree-level bispectrum from the field equation, B-h, agrees with the results obtained previously using the in-in formalism exactly. Characterizing non-Gaussianity of the fluctuations using the ratio B-h/P-h(2) in the equilateral configuration, where P-h is the power spectrum of scale-invariant gravitational waves, we show that it is much weaker than in models with spectator gauge fields. We also calculate the tree-level bispectrum of two right-handed and one left-handed gravitational wave using Green's function, reproducing the results from in-in formalism, and show that it can be as large as the bispectrum of three right-handed gravitational waves.