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Holography for Cosmology

Paul McFadden, Kostas Skenderis

TL;DR

We propose a holographic description of four dimensional single-scalar inflationary universes by mapping cosmologies to Euclidean domain walls and to a three dimensional pseudo-QFT, with cosmological observables obtained from QFT stress-energy correlators via analytic continuation. The approach reproduces standard inflation predictions in the perturbative regime and offers a weakly coupled large-$N$ QFT description when gravity is strongly coupled at early times. It identifies two classes of dual domain-wall solutions, asymptotically AdS and asymptotically power-law, corresponding to de Sitter-like and power-law cosmologies, and demonstrates that a simple holographic model with a single dimensionful parameter and $N \,\sim\ 10^4$ can fit current data, predicting $n_s-1 \,\sim\ O(10^{-2})$ and a small tensor-to-scalar ratio $r$, while $f_{NL}^{local}$ is independent of $N$ at leading order. This holographic phenomenology provides a controlled framework for Planck-scale cosmology with potential observational distinctions from standard slow-roll inflation.

Abstract

We propose a holographic description of four-dimensional single-scalar inflationary universes, and show how cosmological observables, such as the primordial power spectrum, are encoded in the correlation functions of a three-dimensional QFT. The holographic description correctly reproduces standard inflationary predictions in the limit where a perturbative quantization of fluctuations is justified. In the opposite limit, wherein gravity is strongly coupled at early times, we propose a holographic description in terms of perturbative large N QFT. Initiating a holographic phenomenological approach, we show that models containing only two parameters, N and a dimensionful coupling constant, are capable of satisfying the current observational constraints.

Holography for Cosmology

TL;DR

We propose a holographic description of four dimensional single-scalar inflationary universes by mapping cosmologies to Euclidean domain walls and to a three dimensional pseudo-QFT, with cosmological observables obtained from QFT stress-energy correlators via analytic continuation. The approach reproduces standard inflation predictions in the perturbative regime and offers a weakly coupled large- QFT description when gravity is strongly coupled at early times. It identifies two classes of dual domain-wall solutions, asymptotically AdS and asymptotically power-law, corresponding to de Sitter-like and power-law cosmologies, and demonstrates that a simple holographic model with a single dimensionful parameter and can fit current data, predicting and a small tensor-to-scalar ratio , while is independent of at leading order. This holographic phenomenology provides a controlled framework for Planck-scale cosmology with potential observational distinctions from standard slow-roll inflation.

Abstract

We propose a holographic description of four-dimensional single-scalar inflationary universes, and show how cosmological observables, such as the primordial power spectrum, are encoded in the correlation functions of a three-dimensional QFT. The holographic description correctly reproduces standard inflationary predictions in the limit where a perturbative quantization of fluctuations is justified. In the opposite limit, wherein gravity is strongly coupled at early times, we propose a holographic description in terms of perturbative large N QFT. Initiating a holographic phenomenological approach, we show that models containing only two parameters, N and a dimensionful coupling constant, are capable of satisfying the current observational constraints.

Paper Structure

This paper contains 9 sections, 17 equations, 2 figures.

Table of Contents

  1. Introduction.
  2. Domain-wall/cosmology correspondence.
  3. Quantization of perturbations.
  4. Holographic analysis.
  5. (i) Asymptotically AdS domain-walls.
  6. (ii) Asymptotically power-law solutions.
  7. Continuation to the pseudo-QFT.
  8. Beyond the weak gravitational description.
  9. Conclusions.

Figures (2)

  • Figure 1: The 'pseudo'-QFT dual to inflationary cosmology is operationally defined using the correspondence of cosmologies to domain-walls and standard gauge/gravity duality.
  • Figure 2: The straight line is the leading order prediction of holographic models with a single dimensionful coupling constant for the correlation of the running $\alpha_s$ and the scalar tilt $n_s$. The data show the $68\%$ and $95\%$ CL constraints (marginalizing over tensors) at $q = 0.002\, \mathrm{Mpc}^{-1}$, and are taken from Fig. 4 of Komatsu:2008hk. As new data appear the allowed region should shrink to a point, which is predicted to lie close to the line.