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On graviton non-Gaussianities during inflation

Juan M. Maldacena, Guilherme L. Pimentel

TL;DR

The paper shows that exact de Sitter symmetry restricts the graviton three-point function to two parity-conserving shapes (Einstein and a higher-derivative $W^3$ term), plus a parity-violating wavefunction term that does not affect the bispectrum. It introduces a spinor-helicity formalism for de Sitter to streamline calculations and connects these results to 3D CFT stress-tensor correlators via the wavefunction perspective, deriving conformal Ward identities in momentum space. The authors estimate the relative sizes of Einstein and higher-derivative contributions, noting that higher-derivative corrections can be as large as the Einstein term when the new scale $L$ approaches the Hubble scale, which would probe UV physics during inflation. They further validate the gravity results by comparing with free scalar and fermion stress-tensor correlators, highlighting the role of contact terms and the compatibility with supersymmetry. Overall, the work provides a symmetry-driven classification of graviton non-Gaussianities in de Sitter, with implications for inflationary phenomenology and holographic interpretations.

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.

On graviton non-Gaussianities during inflation

TL;DR

The paper shows that exact de Sitter symmetry restricts the graviton three-point function to two parity-conserving shapes (Einstein and a higher-derivative term), plus a parity-violating wavefunction term that does not affect the bispectrum. It introduces a spinor-helicity formalism for de Sitter to streamline calculations and connects these results to 3D CFT stress-tensor correlators via the wavefunction perspective, deriving conformal Ward identities in momentum space. The authors estimate the relative sizes of Einstein and higher-derivative contributions, noting that higher-derivative corrections can be as large as the Einstein term when the new scale approaches the Hubble scale, which would probe UV physics during inflation. They further validate the gravity results by comparing with free scalar and fermion stress-tensor correlators, highlighting the role of contact terms and the compatibility with supersymmetry. Overall, the work provides a symmetry-driven classification of graviton non-Gaussianities in de Sitter, with implications for inflationary phenomenology and holographic interpretations.

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.

Paper Structure

This paper contains 30 sections, 104 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Direct computation of general three point functions
  3. Setup and review of the computation of the gravitational wave spectrum
  4. Three point amplitudes in flat space
  5. Three-point function calculations
  6. Three point function from the Einstein term
  7. Three point amplitude from $W^3$ in flat space
  8. Three point function from $W^3$ in dS
  9. Estimating the size of the corrections
  10. Spinor helicity variables for de Sitter computations
  11. Gravitational wave correlators in the spinor helicity variables
  12. Gravitational wave correlation function and conformal symmetry
  13. Wavefunction of the universe point of view
  14. Constraints from special conformal transformations
  15. Constraints of special conformal invariance on scalar operators
  16. ...and 15 more sections

Figures (1)

  • Figure 1: The 3-momenta and the auxiliary vectors used to define the polarizations.