Non-Gaussianity of Inflationary Gravitational Waves from the Field Equation

TL;DR

This paper confirms the equivalence of two methods for calculating the bispectrum of primordial gravitational waves, finds that non-Gaussianity is weaker than in some models, and explores polarization effects.

Contribution

It demonstrates the equivalence of the in-in formalism and Green's function method for bispectrum calculations and analyzes non-Gaussianity strength and polarization effects.

Findings

Bispectrum calculations agree between methods.

Non-Gaussianity is weaker than in models with spectator gauge fields.

Bispectrum can be large for mixed polarization states.

Abstract

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. Characterising non-Gaussianity of the fluctuations using the ratio $B_h/P^2_h$ 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.