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| Format: | Recurso digital |
| Langue: | anglais |
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2026
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| Accès en ligne: | https://doi.org/10.5281/zenodo.19145471 |
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| _version_ | 1866901221191712768 |
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| author | Petrásek, Martin |
| author_facet | Petrásek, Martin |
| contents | <p>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.</p> <p>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.</p> <p>Within this framework, cosmological evolution corresponds to a renormalization-group trajectory connecting two fixed points. The dark-energy fraction obeys the logistic equation:</p> <p>dΩΛ/dN = (3/2) θ ΩΛ(1 − ΩΛ),</p> <p>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:</p> <p>ΩΛ = θ / (θ + 1)</p> <p>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.</p> <p>The framework further implies a global invariant of cosmological evolution:</p> <p>H ΩΛ^(1/θ) = const,</p> <p>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.</p> <p>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.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19145471 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The R-Universe: A Renormalization-Group Origin of Dark Energy Petrásek, Martin Quantum Gravity Dark Energy Renormalization Group Asymptotic Safety Cosmology Cosmological Constant Fixed Points Spectral Dimension <p>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.</p> <p>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.</p> <p>Within this framework, cosmological evolution corresponds to a renormalization-group trajectory connecting two fixed points. The dark-energy fraction obeys the logistic equation:</p> <p>dΩΛ/dN = (3/2) θ ΩΛ(1 − ΩΛ),</p> <p>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:</p> <p>ΩΛ = θ / (θ + 1)</p> <p>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.</p> <p>The framework further implies a global invariant of cosmological evolution:</p> <p>H ΩΛ^(1/θ) = const,</p> <p>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.</p> <p>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.</p> |
| title | The R-Universe: A Renormalization-Group Origin of Dark Energy |
| topic | Quantum Gravity Dark Energy Renormalization Group Asymptotic Safety Cosmology Cosmological Constant Fixed Points Spectral Dimension |
| url | https://doi.org/10.5281/zenodo.19145471 |