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Spectral Dimension of the Universe

J. Ambjorn, J. Jurkiewicz, R. Loll

Abstract

We measure the spectral dimension of universes emerging from nonperturbative quantum gravity, defined through state sums of causal triangulated geometries. While four-dimensional on large scales, the quantum universe appears two-dimensional at short distances. We conclude that quantum gravity may be "self-renormalizing" at the Planck scale, by virtue of a mechanism of dynamical dimensional reduction.

Spectral Dimension of the Universe

Abstract

We measure the spectral dimension of universes emerging from nonperturbative quantum gravity, defined through state sums of causal triangulated geometries. While four-dimensional on large scales, the quantum universe appears two-dimensional at short distances. We conclude that quantum gravity may be "self-renormalizing" at the Planck scale, by virtue of a mechanism of dynamical dimensional reduction.

Paper Structure

This paper contains 4 sections, 16 equations, 1 figure.

Table of Contents

  1. Quantum gravity as an ultraviolet regulator?
  2. The spectral dimension
  3. Measuring the spectral dimension
  4. Discussion

Figures (1)

  • Figure 1: The data points along the central curve show the spectral dimension $D_S(\sigma)$ of the universe as function of the diffusion time $\sigma$. Superimposed is a best fit, the continuous curve $D_S(\sigma) = 4.02\!-\! 119/(54\!+\!\sigma)$. The two outer curves quantify the error bars, which increase linearly with $\sigma$, due to (\ref{['ja1']}). (Measurements taken for a quantum universe with 181.000 four-simplices.)