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Cosmological Shapes of Higher-Spin Gravity

D. Anninos, V. De Luca, G. Franciolini, A. Kehagias, A. Riotto

Abstract

We explore non-Gaussian features of a massless spin-two field in the Vasiliev theory of higher-spin gravity. The theory contains an infinite tower of interacting gauge fields with increasing spin, and admits four-dimensional asymptotically de Sitter configurations. Using a recent proposal for calculating late-time quantum correlations in Vasiliev theory, we provide an exact formula for the tensor non-Gaussianities of the massless spin-two graviton field. By general symmetry considerations, we relate our result to that produced by a tree-level calculation in a gravitational theory containing an Einstein term and a term cubic in the Weyl tensor. The relative coefficient between the two terms is calculated explicitly, exhibiting a significant contribution from the Weyl cubed term. We discuss potential cosmological implications of our results.

Cosmological Shapes of Higher-Spin Gravity

Abstract

We explore non-Gaussian features of a massless spin-two field in the Vasiliev theory of higher-spin gravity. The theory contains an infinite tower of interacting gauge fields with increasing spin, and admits four-dimensional asymptotically de Sitter configurations. Using a recent proposal for calculating late-time quantum correlations in Vasiliev theory, we provide an exact formula for the tensor non-Gaussianities of the massless spin-two graviton field. By general symmetry considerations, we relate our result to that produced by a tree-level calculation in a gravitational theory containing an Einstein term and a term cubic in the Weyl tensor. The relative coefficient between the two terms is calculated explicitly, exhibiting a significant contribution from the Weyl cubed term. We discuss potential cosmological implications of our results.

Paper Structure

This paper contains 28 sections, 162 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Review of the $Q$-formalism
  3. The free massless spin-$s$ in de Sitter spacetime
  4. Microscopic operator content
  5. Relation to dS/CFT
  6. Two-point correlator of the spin-2 field
  7. Real space
  8. Momentum space
  9. Evaluating the integrals and their regularisation
  10. Final result
  11. The three-point correlator of the spin-2 field
  12. The general structure
  13. Result
  14. The three-point correlator as Einstein plus (Weyl)$^{3}$
  15. The shapes of the graviton three-point correlator
  16. ...and 13 more sections

Figures (3)

  • Figure 1: Pictorial representation of the identification between bulk effective fields and the microscopic bilinear operators. $\mathcal{I}^+$ denotes the future boundary of de Sitter space.
  • Figure 2: Ratios $\mathcal{R}^{\lambda_1,\lambda_2,\lambda_3}(r_2,r_3)$ as defined in Eq. \ref{['ratios']}.
  • Figure 3: Shapes $\mathcal{S}_{\lambda_1,\lambda_2,\lambda_3}(r_2,r_3)$ for the independent combinations of the polarisations.