The R-Universe: A Renormalization-Group Origin of Dark Energy

The cosmological constant represents one of the most profound unresolved problems in modern physics. Observations of the cosmic microwave background, large-scale structure, and distant supernovae indicate that approximately 69 % of the energy content of the Universe is in the form of dark energy. Within the standard ΛCDM model this component is described by a cosmological constant, whose extremely small magnitude lacks a microscopic explanation and exhibits strong radiative instability under quantum corrections. In this work we introduce the R-Universe framework, in which dark energy arises as an infrared manifestation of ultraviolet gravitational criticality. The construction combines three structural ingredients: a global constraint on the effective action that removes additive vacuum energy contributions, dimensional flow of the spectral dimension of spacetime, and renormalization-group improvement of Friedmann dynamics in the vicinity of an asymptotically safe gravitational fixed point. Within this framework, cosmological evolution corresponds to a renormalization-group trajectory connecting two fixed points. The dark-energy fraction obeys the logistic equation: dΩΛ/dN = (3/2) θ ΩΛ (1 − ΩΛ), where N = ln a denotes the number of e-folds and θ is the relevant critical exponent of the gravitational fixed point. The dynamics leads to the universal scaling relation: ΩΛ = θ / (θ + 1) The observed value ΩΛ ≃ 0. 69 corresponds to θ ≃ 2. 2, in remarkable agreement with critical exponents obtained in functional renormalization-group calculations within the Einstein–Hilbert truncation. The framework further implies a global invariant of cosmological evolution: H ΩΛ^ (1/θ) = const, which constrains the trajectory of the Universe in the reduced cosmological phase space and indicates that cosmic expansion and dark-energy dominance are not independent processes but manifestations of a single renormalization-group flow. The R-Universe framework is sharply falsifiable: functional renormalization-group calculations on cosmological backgrounds must simultaneously yield a regulator-stable relevant exponent and admit a covariantly consistent late-time scaling solution. If confirmed, precision cosmology would provide a direct observational probe of microscopic quantum-gravitational fixed points.