The Spectral Dimension of the Universe is Scale Dependent

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.

Figure 1

The data points along the central curve show the spectral dimension $D_S(\sigma )$ of the universe as a 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 (8). (Measurements taken for a quantum universe with 181.000 four-simplices.)