Probing the quantum nature of spacetime by diffusion

G. Calcagni, A. Eichhorn, F. Saueressig

Research output: Contribution to journalJournal articleResearchpeer-review


Many approaches to quantum gravity have resorted to diffusion processes to characterize the spectral properties of the resulting quantum spacetimes. We critically discuss these quantum-improved diffusion equations and point out that a crucial property, namely positivity of their solutions, is not preserved automatically. We then construct a novel set of diffusion equations with positive semidefinite probability densities, applicable to asymptotically safe gravity, Hořava-Lifshitz gravity and loop quantum gravity. These recover all previous results on the spectral dimension and shed further light on the structure of the quantum spacetimes by assessing the underlying stochastic processes. Pointing out that manifestly different diffusion processes lead to the same spectral dimension, we propose the probability distribution of the diffusion process as a refined probe of quantum spacetime.

Original languageEnglish
Article number124028
JournalPhysical Review D
Issue number12
Publication statusPublished - 2013
Externally publishedYes


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