Derivations and Structural Consequences of the R-Universe Framework

Derivations and Structural Consequences of the R-Universe Framework | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Derivations and Structural Consequences of the R-Universe Framework Martin Petrásek This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9097693/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Despite its remarkable phenomenological success, the ΛCDM model does not provide a microscopic explanation for the observed value of the cosmological constant. In particular, the origin of the present dark-energy fraction ΩΛ ≃ 0.69 remains unexplained within standard cosmology. Here we propose a framework in which the late-time cosmological evolution can be interpreted as an effective renormalization–group (RG) flow of the vacuum sector driven by the Hubble scale. Within this description the dimensionless dark-energy fraction obeys a closed evolution equation that takes the form of a logistic RG flow connecting the fixed points ΩΛ = 0 and ΩΛ = 1, corresponding to matter-dominated and vacuum-dominated cosmological regimes. Consistency between the RG scaling of the cosmological coupling and the Friedmann background dynamics implies a non-trivial stationary solution for the dark-energy fraction: ΩΛ = θ / (θ + 1) which relates the present cosmological composition directly to the relevant critical exponent θ of the underlying gravitational fixed point. Using the observed value ΩΛ ≃ 0.69 yields θ ≃ 2.2, numerically close to critical exponents obtained in functional renormalization–group studies of asymptotically safe gravity. Astrophysics and Cosmology cosmology dark energy cosmological constant renormalization group quantum gravity vacuum energy cosmic acceleration Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9097693","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":604657793,"identity":"1e706e1b-2a28-45c9-8adc-0dc3a8820ff0","order_by":0,"name":"Martin Petrásek","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEklEQVRIiWNgGAWjYLCCBCSmHBuQ/EBAA2MDWAsbRIsxkGacQVALA5KWxAZCWnTbzz5/8HAHQx6/fO/Djz8q0tL7pI8/bC5gsMmXd8CuxexMumFD4hmGYsk2dmNpnjM5uW18OYbNMxjSLDcewKHlQBpjQ2IbQ+KGY2wM0oxtFbltPDzsj3kYDhsYNuDQcv4ZRMv+Y2zMP3/+q0hn42F/2IxXyw2YLWxsbBK8DTkJbDwMhmAt8ji8b3bjGeOMxDaJYoljaWzWPMfSDIEOA/rFIM3AAJeW82kMH3+22eTxNx9jvvmjJllevgfosIIKGwN5HA6DAokEFC4zA9AKgwN4tSCnGbAWICBgyygYBaNgFIwcAADZ7lWFZCvHZQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0009-0007-4512-9528","institution":"Institute for Resonant Synthesis and Field Physics","correspondingAuthor":true,"prefix":"","firstName":"Martin","middleName":"","lastName":"Petrásek","suffix":""}],"badges":[],"createdAt":"2026-03-11 19:32:30","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9097693/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9097693/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104781402,"identity":"ac0d1cdd-b020-4622-a9b5-946969544ac7","added_by":"auto","created_at":"2026-03-17 07:55:37","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":432390,"visible":true,"origin":"","legend":"","description":"","filename":"Derivations.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9097693/v1_covered_fd65e0f0-24e7-4885-9770-d7a431be2c1e.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eDerivations and Structural Consequences of the R-Universe Framework\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Institute for Resonant Synthesis and Field Physics ","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"cosmology, dark energy, cosmological constant, renormalization group, quantum gravity, vacuum energy, cosmic acceleration","lastPublishedDoi":"10.21203/rs.3.rs-9097693/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9097693/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDespite its remarkable phenomenological success, the ΛCDM model does not provide a microscopic explanation for the observed value of the cosmological constant. In particular, the origin of the present dark-energy fraction ΩΛ ≃ 0.69 remains unexplained within standard cosmology.\u003c/p\u003e\n\u003cp\u003eHere we propose a framework in which the late-time cosmological evolution can be interpreted as an effective renormalization–group (RG) flow of the vacuum sector driven by the Hubble scale. Within this description the dimensionless dark-energy fraction obeys a closed evolution equation that takes the form of a logistic RG flow connecting the fixed points ΩΛ = 0 and ΩΛ = 1, corresponding to matter-dominated and vacuum-dominated cosmological regimes.\u003c/p\u003e\n\u003cp\u003eConsistency between the RG scaling of the cosmological coupling and the Friedmann background dynamics implies a non-trivial stationary solution for the dark-energy fraction:\u003c/p\u003e\n\u003cp\u003eΩΛ = θ / (θ + 1)\u003c/p\u003e\n\u003cp\u003ewhich relates the present cosmological composition directly to the relevant critical exponent θ of the underlying gravitational fixed point. 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