The Holographic Universe

TL;DR

The paper develops a holographic description of inflationary cosmology by mapping four-dimensional universes to three-dimensional QFT duals via domain-wall correspondences. It shows that standard inflationary predictions are recovered when gravity is weak, while a new class of strongly gravitating early-universe models can be analyzed through a weakly coupled 3D QFT, yielding nearly scale-invariant spectra and distinctive running of the scalar index. Cosmological observables are computed from QFT 2-point (and higher-point) functions through explicit holographic dictionaries, including precise formulas for power spectra in terms of $\mathrm{Im}\,A(-i q)$ and $\mathrm{Im}\,B(-i q)$, and by analytic continuation to a pseudo-QFT. The framework provides a UV-complete, large-$N$ description with concrete predictions for non-Gaussianities and spectral running, offering a potential route to observational signatures of holography in the early universe.

Abstract

We present a holographic description of four-dimensional single-scalar inflationary universes in terms of a three-dimensional quantum field theory. The holographic description correctly reproduces standard inflationary predictions in their regime of applicability. In the opposite case, wherein gravity is strongly coupled at early times, we propose a holographic description in terms of perturbative QFT and present models capable of satisfying the current observational constraints while exhibiting a phenomenology distinct from standard inflation. This provides a qualitatively new method for generating a nearly scale-invariant spectrum of primordial cosmological perturbations.

Figures (5)

• 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: Using holography it is possible to describe the generation of primordial cosmological perturbations during an early time epoch in which the gravitational description is strongly coupled. At later times we envision a smooth transition to a conventional hot big bang description in which gravity is weakly coupled. (Figure adapted from xfig).
• Figure 3: 1-loop contribution to $\langle T_{ij}(\bar{q})T_{kl}(-\bar{q})\rangle$. We sum over the contributions from gauge fields, scalars and fermions, with each diagram yielding a contribution of order $\sim \bar{N}^2\bar{q}^3$.
• Figure 4: Diagram topologies contributing at 2-loop order. Each diagram consists of an overall factor of $\bar{N}^3 g_{\mathrm{YM}}^2$ multiplying an integral with superficial degree of divergence two. After dimensional regularization and renormalization, the integrals evaluate to $\sim \bar{q}^2 \ln (\bar{q}/\bar{q}_*)$, and so overall each diagram yields a contribution to the stress tensor 2-point function of order $\sim \bar{N}^3 g_{\mathrm{YM}}^2\bar{q}^2 \ln (\bar{q}/\bar{q}_*)$, or equivalently $\sim \bar{N}^2\bar{q}^3 g_{\mathrm{eff}}^2 \ln (\bar{q}/\bar{q}_*)$.
• Figure 5: 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 $q_0 = 0.002\, \mathrm{Mpc}^{-1}$, 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.