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-di- mensional at short distances. We conclude that quantum gravity may be “self- renormalizing” at the Planck scale, by virtue of a mechanism of dynamical dimen- sional reduction.