Multiscale spacetimes from first principles

TL;DR

This paper derives the general characteristics of multiscale geometries, including quantum gravity models, showing how their dimensions change with scale and establishing the predictive power of multifractional theories with log oscillations.

Contribution

It provides a model-independent derivation of the multiscale measure and dimensions, demonstrating the predictivity and testability of multifractional geometry theories.

Findings

Hausdorff and spectral dimensions vary with scale in multiscale geometries

Unique multiscale measure with log oscillations is derived

Models are shown to be predictive and falsifiable

Abstract

Assuming only a smooth and slow change of spacetime dimensionality at large scales, we find, in a background- and model-independent way, the general profile of the Hausdorff and the spectral dimension of multiscale geometries such as those found in all known quantum gravities. Examples of various scenarios are given. In particular, we derive uniquely the multiscale measure with log oscillations of theories of multifractional geometry. Predictivity of this class of models and falsifiability of their abundant phenomenology are thus established.