The four-point correlation function of graviton during inflation

TL;DR

This paper calculates the four-point correlation function of gravitons during inflation using the Einstein-Hilbert action expanded to fourth order, providing insights into gravitational wave interactions in de Sitter space.

Contribution

It introduces a detailed calculation of the graviton four-point function during inflation, including contact and exchange diagrams, and explores properties of n-point functions for polarized gravitons.

Findings

Derived the four-point correlation function of gravitons during inflation.

Analyzed properties of n-point functions for polarized gravitational waves.

Provided a framework for understanding graviton interactions in de Sitter space.

Abstract

We expand the Einstein-Hilbert action with a positive cosmological constant up to the fourth order in terms of gravity fluctuations, and then use the in-in formalism to calculate the four-point correlation function for gravitational waves, including both contact and exchange diagrams, generated during a period of exactly de Sitter expansion. In addition, we also present the general properties of the $n$-point function of graviton in terms of both circularly and linearly polarized states.