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Holographic Non-Gaussianity

Paul McFadden, Kostas Skenderis

Abstract

We investigate the non-Gaussianity of primordial cosmological perturbations within our recently proposed holographic description of inflationary universes. We derive a holographic formula that determines the bispectrum of cosmological curvature perturbations in terms of correlation functions of a holographically dual three-dimensional non-gravitational quantum field theory (QFT). This allows us to compute the primordial bispectrum for a universe which started in a non-geometric holographic phase, using perturbative QFT calculations. Strikingly, for a class of models specified by a three-dimensional super-renormalisable QFT, the primordial bispectrum is of exactly the factorisable equilateral form with f_nl^eq=5/36, irrespective of the details of the dual QFT. A by-product of this investigation is a holographic formula for the three-point function of the trace of the stress-energy tensor along general holographic RG flows, which should have applications outside the remit of this work.

Holographic Non-Gaussianity

Abstract

We investigate the non-Gaussianity of primordial cosmological perturbations within our recently proposed holographic description of inflationary universes. We derive a holographic formula that determines the bispectrum of cosmological curvature perturbations in terms of correlation functions of a holographically dual three-dimensional non-gravitational quantum field theory (QFT). This allows us to compute the primordial bispectrum for a universe which started in a non-geometric holographic phase, using perturbative QFT calculations. Strikingly, for a class of models specified by a three-dimensional super-renormalisable QFT, the primordial bispectrum is of exactly the factorisable equilateral form with f_nl^eq=5/36, irrespective of the details of the dual QFT. A by-product of this investigation is a holographic formula for the three-point function of the trace of the stress-energy tensor along general holographic RG flows, which should have applications outside the remit of this work.

Paper Structure

This paper contains 25 sections, 124 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Perturbed domain-walls and cosmologies
  3. Defining the perturbations
  4. Equations of motion
  5. Response functions
  6. The domain-wall/cosmology correspondence
  7. The cosmological bispectrum
  8. Computation using response functions
  9. An example: slow-roll inflation
  10. Holographic 3-point functions
  11. Holographic analysis
  12. Background solutions
  13. Asymptotic analysis
  14. Radial Hamiltonian formulation
  15. 3-point functions
  16. ...and 10 more sections

Figures (2)

  • Figure 1: The 'pseudo'-QFT dual to inflationary cosmology is operationally defined using the domain-wall/cosmology correspondence and standard gauge/gravity duality.
  • Figure 2: 1-loop contribution to $\langle T(\bar{q}_1)T(\bar{q}_2)T(\bar{q}_3)\rangle$.