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Planckian Birth of the Quantum de Sitter Universe

J. Ambjorn, A. Gorlich, J. Jurkiewicz, R. Loll

TL;DR

Planckian Birth of the Quantum de Sitter Universe shows that a nonperturbative, Lorentzian sum-over-geometries implemented via causal dynamical triangulations yields an emergent four-dimensional de Sitter background. The background fluctuations are sizeable yet semiclassical and are well described by a mini-superspace action, allowing the extraction of Newton's constant $G$ from lattice data; the four-volume scaling fixes $\ell_{Pl}=\sqrt{G}$ and yields $\ell_{Pl} \approx 0.47 a$ with the universes spanning $17$–$28$ Planck lengths. This provides a concrete, background-independent realization of quantum cosmology, and points to future work on sub-Planckian regimes, matter coupling, and connections with renormalization group scenarios such as asymptotic safety.

Abstract

We show that the quantum universe emerging from a nonperturbative, Lorentzian sum-over-geometries can be described with high accuracy by a four-dimensional de Sitter spacetime. By a scaling analysis involving Newton's constant, we establish that the linear size of the quantum universes under study is in between 17 and 28 Planck lengths. Somewhat surprisingly, the measured quantum fluctuations around the de Sitter universe in this regime are to good approximation still describable semiclassically. The numerical evidence presented comes from a regularization of quantum gravity in terms of causal dynamical triangulations.

Planckian Birth of the Quantum de Sitter Universe

TL;DR

Planckian Birth of the Quantum de Sitter Universe shows that a nonperturbative, Lorentzian sum-over-geometries implemented via causal dynamical triangulations yields an emergent four-dimensional de Sitter background. The background fluctuations are sizeable yet semiclassical and are well described by a mini-superspace action, allowing the extraction of Newton's constant from lattice data; the four-volume scaling fixes and yields with the universes spanning – Planck lengths. This provides a concrete, background-independent realization of quantum cosmology, and points to future work on sub-Planckian regimes, matter coupling, and connections with renormalization group scenarios such as asymptotic safety.

Abstract

We show that the quantum universe emerging from a nonperturbative, Lorentzian sum-over-geometries can be described with high accuracy by a four-dimensional de Sitter spacetime. By a scaling analysis involving Newton's constant, we establish that the linear size of the quantum universes under study is in between 17 and 28 Planck lengths. Somewhat surprisingly, the measured quantum fluctuations around the de Sitter universe in this regime are to good approximation still describable semiclassically. The numerical evidence presented comes from a regularization of quantum gravity in terms of causal dynamical triangulations.

Paper Structure

This paper contains 4 sections, 14 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Macroscopic de Sitter universe
  3. Fluctuations around de Sitter space
  4. Discussion

Figures (3)

  • Figure 1: Background geometry $\langle N_3(i)\rangle$: MC measurements (for fixed $N_4=362.000$) and best fit (\ref{['n1']}) yield indistinguishable curves at given plot resolution. The bars indicate the average size of quantum fluctuations.
  • Figure 2: Analyzing the quantum fluctuations of Fig. \ref{['fig1']}: diagonal entries $F(t,t)^{1/2}$ of the scaling function $F$ from (\ref{['n7f']}), for $N_4=$ 45.500, 91.000, 181.000 and 362.000.
  • Figure 3: Comparing the highest eigenvector of $C(t,t')$ and the lowest eigenvector of $M^{-1}(t,t')$.