Fractal Geometry of Quantum Spacetime at Large Scales

TL;DR

This paper investigates the fractal geometry of quantum spacetime at large scales, revealing a Hausdorff dimension greater than 4 influenced by the Gauss-Bonnet term, with implications for cosmology and dark matter.

Contribution

It introduces a covariant diffusion approach to determine the fractal dimension of quantum spacetime and links it to the trace anomaly coefficient, providing a new perspective on large-scale universe behavior.

Findings

Hausdorff dimension exceeds 4 at infrared fixed point

Scaling behavior affects cosmological constant screening

Implications for dark matter and large-scale structure

Abstract

We compute the intrinsic Hausdorff dimension of spacetime at the infrared fixed point of the quantum conformal factor in 4D gravity. The fractal dimension is defined by the appropriate covariant diffusion equation in four dimensions and is determined by the coefficient of the Gauss-Bonnet term in the trace anomaly to be generally greater than 4. In addition to being testable in simplicial simulations, this scaling behavior suggests a physical mechanism for the screening of the effective cosmological `constant' and inverse Newtonian coupling at very large distance scales, which has implications for the dark matter content and large scale structure of the universe.