The spectral geometry of de Sitter space in asymptotic safety

A bstract Within the functional renormalization group approach to Background Independent quantum gravity, we explore scale dependent effective geometry of de Sitter solution dS 4 . The investigation employs a novel whose essential ingredient is modified spectral flow metric d’Alembertian, or similar hyperbolic kinetic operators. corresponding one-parameter family spectra and eigenfunctions encodes information about nonperturbative backreaction dynamically gravitating vacuum fluctuations on mean field spacetime. Used as diagnostic tool, power method resides in its ability identify subsets modes that supply degrees freedom which participate theory description respective scale. central result ultraviolet Quantum Einstein Gravity comprises far less than predicted (incorrectly) by background reasoning. Lorentzian signature taken into account selecting class trajectories are known apply both Euclidean version approach. Exploring spacetime’s spatial carried physical fields, find 3-dimensional space disintegrates collection coherent patches individually can, but their entirety cannot be described one average actions occurring along trajectory. natural concept an entropy introduced order quantify this fragmentation effect. Tentatively applied real Universe, surprising analogies properties observed cosmic microwave uncovered. Furthermore, set distinguished found which, principle, has transport asymptotic fixed point regime from ultraviolet, across almost entire “scale history”, cosmological distances Universe.