The Spectral Geometry of de Sitter Space in Asymptotic Safety
Renata Ferrero, Martin Reuter

TL;DR
This paper investigates the nonperturbative geometry of de Sitter space in quantum gravity using a novel spectral flow method, revealing fewer effective degrees of freedom in the ultraviolet and a fragmented spatial structure with cosmological implications.
Contribution
It introduces a spectral flow approach to analyze quantum spacetime geometry, uncovering reduced degrees of freedom and spatial fragmentation in asymptotic safety.
Findings
Ultraviolet quantum gravity has fewer effective degrees of freedom than previously thought.
The spatial geometry fragments into coherent patches that cannot be described by a single effective action.
Analogies to cosmic microwave background properties suggest cosmological relevance.
Abstract
Within the functional renormalization group approach to Background Independent quantum gravity, we explore the scale dependent effective geometry of the de Sitter solution dS. The investigation employs a novel approach whose essential ingredient is a modified spectral flow of the metric dependent d'Alembertian, or of similar hyperbolic kinetic operators. The corresponding one-parameter family of spectra and eigenfunctions encodes information about the nonperturbative backreaction of the dynamically gravitating vacuum fluctuations on the mean field geometry of the quantum spacetime. Used as a diagnostic tool, the power of the spectral flow method resides in its ability to identify the scale dependent subsets of field modes that supply the degrees of freedom which participate in the effective field theory description of the respective scale. A central result is that the ultraviolet…
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