# 3-pt Statistics of Cosmological Stochastic Gravitational Waves

## TL;DR

This paper investigates the three-point correlation function of stochastic gravitational wave backgrounds from various sources, assessing their detectability and proposing a diagrammatic method for calculations, with implications for distinguishing inflationary signals.

## Contribution

It introduces a diagrammatic approach for calculating non-Gaussianities in stochastic gravitational waves and evaluates their potential detectability in different cosmological scenarios.

## Key findings

- The 3-pt signal from inflationary gravitational waves is very small.
- Causal classical mechanisms produce negligible 3-pt correlations in direct detection.
- A strong 3-pt signal could distinguish inflationary B-modes sourced by phase transitions.

## Abstract

We consider the 3-pt function (i.e. the bispectrum or non-Gaussianity) for stochastic backgrounds of gravitational waves. We estimate the amplitude of this signal for the primordial inflationary background, gravitational waves generated during preheating, and for gravitational waves produced by self-ordering scalar fields following a global phase transition. To assess detectability, we describe how to extract the 3-pt signal from an idealized interferometric experiment and compute the signal to noise ratio as a function of integration time. The 3-pt signal for the stochastic gravitational wave background generated by inflation is unsurprisingly tiny. For gravitational radiation generated by purely causal, classical mechanisms we find that, no matter how non-linear the process is, the 3-pt correlations produced vanish in direct detection experiments. On the other hand, we show that in scenarios where the B-mode of the CMB is sourced by gravitational waves generated by a global phase transition, a strong 3-pt signal among the polarization modes could also be produced. This may provide another method of distinguishing inflationary B-modes. To carry out this computation, we have developed a diagrammatic approach to the calculation of stochastic gravitational waves sourced by scalar fluids, which has applications beyond the present scenario.