English

Multiscale spacetimes from first principles

General Relativity and Quantum Cosmology 2017-03-31 v3 High Energy Physics - Theory Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.1609.02776,
  title  = {Multiscale spacetimes from first principles},
  author = {Gianluca Calcagni},
  journal= {arXiv preprint arXiv:1609.02776},
  year   = {2017}
}

Comments

7 pages; v2: abstract less technical, theorem split into two parts, text streamlined and simplified, some technical parts and some references removed; v3: proof of theorems expanded, results unchanged, typos corrected

R2 v1 2026-06-22T15:44:56.084Z