On graviton non-Gaussianities during inflation

TL;DR

This paper analyzes the three-point functions of gravitational waves during de Sitter inflation, identifying three possible shapes constrained by symmetries, including parity-violating contributions, and introduces a spinor helicity formalism for polarization states.

Contribution

It provides the most general form of three-point functions for gravitational waves in de Sitter space, including parity-violating shapes, and introduces a spinor helicity formalism for polarization analysis.

Findings

Three shapes of gravitational wave three-point functions are identified.

Parity-violating shape does not contribute to the bispectrum.

A spinor helicity formalism for de Sitter gravitational waves is developed.

Abstract

We consider the most general three point function for gravitational waves produced during a period of exactly de Sitter expansion. The de Sitter isometries constrain the possible shapes to only three: two preserving parity and one violating parity. These isometries imply that these correlation functions should be conformal invariant. One of the shapes is produced by the ordinary gravity action. The other shape is produced by a higher derivative correction and could be as large as the gravity contribution. The parity violating shape does not contribute to the bispectrum [1106.3228, 1108.0175], even though it is present in the wavefunction. We also introduce a spinor helicity formalism to describe de Sitter gravitational waves with circular polarization. These results also apply to correlation functions in Anti-de Sitter space. They also describe the general form of stress tensor correlation functions, in momentum space, in a three dimensional conformal field theory. Here all three shapes can arise, including the parity violating one.