CDxM Cosmology: A Divergence-Based Reformulation of the Expanding Universe

CDxM Cosmology: A Divergence-Based Reformulation of the Expanding Universe | 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 CDxM Cosmology: A Divergence-Based Reformulation of the Expanding Universe Barry Brian Bolter This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6766481/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 This paper introduces a cosmological model in which the evolution of the universe is driven not by spatial expansion but by the divergence of temporal coherence. In the Coherence–Divergence Model (CDxM), gravitational structure defines the present, and time is reinterpreted as a local curvature away from this coherence. The entropy divergence field E(t) replaces the scale factor, and its derivative dE/dt replaces the Hubble parameter. We reformulate the Friedmann equations accordingly, derive redshift and luminosity distance relationships, and demonstrate alignment with supernova data and late-universe acceleration—without invoking dark energy. The CDxM framework preserves observational structure while replacing metric inflation with ontological divergence, and offers a new path for resolving the Hubble tension. Figures Figure 1 1. Introduction Conventional cosmology treats the universe's expansion as a geometric inflation of spacetime. In contrast, CDxM proposes that what is observed is not spatial expansion but coherence erosion—where gravitational structure, once immediate, becomes increasingly misaligned with observation over time. Time, in this model, is not a flow but a divergence vector originating from gravitational immediacy and curving outward through entropy. 2. The CDxM Friedmann Reformulation The CDxM model recasts the Friedmann equation as follows: (dE/dt)^2 = α·C(t) - κ / E(t)^2 + ∇_Λ Where: - E(t): entropy divergence field - dE/dt: divergence velocity (CDM Hubble parameter) - C(t): clarity stressor, analog to energy density - κ: topological constraint (curvature replacement) - ∇_Λ: entropy asymptotic limit 3. Epoch Modelling in CDxM - Early Universe: High C(t), zero ∇_Λ. Mimics inflation via rapid coherence loss. - Mid-Universe: C(t) declines, E(t) increases. Divergence continues in stable form. - Late Universe: Low C(t), dominant ∇_Λ. Coherence loss plateaus, entropy field asymptotes—mimicking dark energy without invoking it. 4. Redshift, Luminosity Distance, and Observation Redshift: 1 + z = E(t_0)/E(t) Hubble parameter in CDM: H_CDM(z) = dE/dt Luminosity distance: d_L(z) = (1 + z) ∫₀^z c / (dE/dt)(z') dz' 5. Simulation and Results Using a simulated divergence curve based on CDxM entropy logic, the model accurately reproduces the late-universe Hubble curve, matching supernovae data and offering a potential resolution to the Hubble tension. A synthetic entropy curve was also tested and shown to be mathematically elegant but structurally fragile under precision. 6. Structural Comparison: ΛCDM vs CDxM 7. Philosophical Implications We are not watching space inflate—we are watching coherence erode. Observation decouples from gravitational structure. Time doesn’t flow; it fractures outward from gravitational immediacy. This ontological inversion restores clarity to entropy and opens new ground for measurement, translation, and emergence. 8. Project Series Outline This manuscript forms the fourth paper in a four-part research sequence titled "The Divergence Paradigm: Reconstructing Time, Coherence, and the Universe from Within." The series includes: 1. Paper 1 – Event-Time: Redefining Time as Ordinal Divergence from Within Redefines time as local, entity-specific sequences of definable events. 2. Paper 2 – The Ontology of Coherence: Entropy, Divergence, and the Limits of Measurement Establishes coherence as structural integrity and divergence as the root of entropy and observability. 3. Paper 3 – Singularity + / Singularity – : Dual Origins of Coherence and Divergence Introduces a dual-singularity model to account for emergence, structure, and asymmetry. 4. Paper 4 (This Work) – CDxM Cosmology: A Divergence-Based Reformulation of the Expanding Universe Reformulates cosmological dynamics in terms of entropy divergence, reproducing observational curves and resolving late-universe tensions. The complete series is intended for eventual compilation as a monograph titled "The Divergence Paradigm." Declarations Author Contribution Barry Brian Bolter is the sole author of this work. He conceptualized the CDxM model, conducted all theoretical development, prepared the manuscript, and curated the supporting material, including the mathematical audit, provenance mapping, and methodological analysis. The author acknowledges the use of dialogical AI (ChatGPT) as a reflective and generative instrument throughout the process—serving not as a co-author but as a structured tool for refining coherence, challenging assumptions, and facilitating interdisciplinary synthesis. References and Observational Anchors Scolnic, D. M., et al. (2018). The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample . ApJ, 859(2), 101. Riess, A. G., et al. (2019). Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond ΛCDM . ApJ, 876(1), 85. Planck Collaboration. (2020). Planck 2018 results. VI. Cosmological parameters . A&A, 641, A6. Lelli, F., McGaugh, S. S., & Schombert, J. M. (2016). SPARC: Mass Models for 175 Disk Galaxies with Spitzer Photometry and Accurate Rotation Curves . AJ, 152(6), 157. Additional Declarations No competing interests reported. Supplementary Files CDxMMethodologyAppendix.docx CDxMMathematicalAudit.docx CDxMProvenanceMap.docx CDxMVisualReferences.docx AppendixA.docx 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. 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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-6766481","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":462984008,"identity":"832f7ba6-3165-4db0-81d5-8812c7c1ba78","order_by":0,"name":"Barry Brian Bolter","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0klEQVRIiWNgGAWjYBACAwkGxgNAul6evQHEtSBKC8MBoJ4Ew54DUC7RWhhuJID4RGgxl24+cPhDxb08xpnPr274USDBwN/enYBXi+WcYwkHDpwpLmaXzim72QO0VOLM2Q34HXYjx+DAwbYExsbZOWk3eIBaDCRyidHyL4Gx4eaZtJt/iNfSkJDYcIP92G2ibAH75cyxBGPDnhy22zIGEjwE/QIMsYMPKmoS5OTZjz+7+eaPjRx/ey9+LUiAxwBMEqscBNgfkKJ6FIyCUTAKRhAAAFi1URxd0wpRAAAAAElFTkSuQmCC","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Barry","middleName":"Brian","lastName":"Bolter","suffix":""}],"badges":[],"createdAt":"2025-05-28 09:23:33","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6766481/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6766481/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":83584107,"identity":"ca77f377-9ac6-4606-a070-1e349cc4d171","added_by":"auto","created_at":"2025-05-29 02:54:41","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":55644,"visible":true,"origin":"","legend":"\u003cp\u003eCDxM Hubble Curve from Entropy Divergence\u003c/p\u003e\n\u003cp\u003eCDxM-predicted luminosity distance as a function of redshift, derived from a simulated entropy divergence field E(t). The curve shows late-universe acceleration without invoking dark energy.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6766481/v1/50f902f45a5c1d2d5be7cacc.png"},{"id":84986762,"identity":"49ece11d-0d57-4ead-8fb2-72dabdd8b229","added_by":"auto","created_at":"2025-06-19 14:31:54","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":368280,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6766481/v1/8c088cd8-9ede-481b-b40e-c3ccd2e1406f.pdf"},{"id":83584219,"identity":"d1e5fb53-e872-4524-a854-4943f984a8b1","added_by":"auto","created_at":"2025-05-29 03:02:41","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":71740,"visible":true,"origin":"","legend":"","description":"","filename":"CDxMMethodologyAppendix.docx","url":"https://assets-eu.researchsquare.com/files/rs-6766481/v1/38c00c2e64da3e52415157e3.docx"},{"id":83584224,"identity":"44c6d112-72f6-46cd-8e01-56ca1af94035","added_by":"auto","created_at":"2025-05-29 03:02:41","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":131234,"visible":true,"origin":"","legend":"","description":"","filename":"CDxMMathematicalAudit.docx","url":"https://assets-eu.researchsquare.com/files/rs-6766481/v1/475ff9f14e702bc8c49bc52f.docx"},{"id":83584220,"identity":"46e19455-9b69-4ccd-9b85-fa3e3dc92610","added_by":"auto","created_at":"2025-05-29 03:02:41","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":24572,"visible":true,"origin":"","legend":"","description":"","filename":"CDxMProvenanceMap.docx","url":"https://assets-eu.researchsquare.com/files/rs-6766481/v1/e7c151f6139bb16d837753d2.docx"},{"id":83584116,"identity":"df576465-cf5e-4356-8361-8b88ef714d5f","added_by":"auto","created_at":"2025-05-29 02:54:41","extension":"docx","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":4178192,"visible":true,"origin":"","legend":"","description":"","filename":"CDxMVisualReferences.docx","url":"https://assets-eu.researchsquare.com/files/rs-6766481/v1/9e79ee243d170a590e8d1fbe.docx"},{"id":83584225,"identity":"676c61a2-ad04-4035-bae6-1654ac54278e","added_by":"auto","created_at":"2025-05-29 03:02:41","extension":"docx","order_by":5,"title":"","display":"","copyAsset":false,"role":"supplement","size":16881,"visible":true,"origin":"","legend":"","description":"","filename":"AppendixA.docx","url":"https://assets-eu.researchsquare.com/files/rs-6766481/v1/66ec82d0d3aa6b863ed8e8f5.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"CDxM Cosmology: A Divergence-Based Reformulation of the Expanding Universe","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eConventional cosmology treats the universe's expansion as a geometric inflation of spacetime. In contrast, CDxM proposes that what is observed is not spatial expansion but coherence erosion\u0026mdash;where gravitational structure, once immediate, becomes increasingly misaligned with observation over time. Time, in this model, is not a flow but a divergence vector originating from gravitational immediacy and curving outward through entropy.\u003c/p\u003e"},{"header":"2. The CDxM Friedmann Reformulation","content":"\u003cp\u003eThe CDxM model recasts the Friedmann equation as follows:\u003c/p\u003e\n\u003cp\u003e(dE/dt)^2 = \u0026alpha;\u0026middot;C(t) - \u0026kappa; / E(t)^2 + \u0026nabla;_\u0026Lambda;\u003c/p\u003e\n\u003cp\u003eWhere:\u003c/p\u003e\n\u003cp\u003e- E(t): entropy divergence field\u003c/p\u003e\n\u003cp\u003e- dE/dt: divergence velocity (CDM Hubble parameter)\u003c/p\u003e\n\u003cp\u003e- C(t): clarity stressor, analog to energy density\u003c/p\u003e\n\u003cp\u003e- \u0026kappa;: topological constraint (curvature replacement)\u003c/p\u003e\n\u003cp\u003e- \u0026nabla;_\u0026Lambda;: entropy asymptotic limit\u003c/p\u003e"},{"header":"3. Epoch Modelling in CDxM","content":"\u003cp\u003e- Early Universe: High C(t), zero \u0026nabla;_\u0026Lambda;. Mimics inflation via rapid coherence loss.\u003c/p\u003e\n\u003cp\u003e- Mid-Universe: C(t) declines, E(t) increases. Divergence continues in stable form.\u003c/p\u003e\n\u003cp\u003e- Late Universe: Low C(t), dominant \u0026nabla;_\u0026Lambda;. Coherence loss plateaus, entropy field asymptotes\u0026mdash;mimicking dark energy without invoking it.\u003c/p\u003e"},{"header":"4. Redshift, Luminosity Distance, and Observation","content":"\u003cp\u003eRedshift:\u003c/p\u003e\n\u003cp\u003e1 + z = E(t_0)/E(t)\u003c/p\u003e\n\u003cp\u003eHubble parameter in CDM:\u003c/p\u003e\n\u003cp\u003eH_CDM(z) = dE/dt\u003c/p\u003e\n\u003cp\u003eLuminosity distance:\u003c/p\u003e\n\u003cp\u003ed_L(z) = (1 + z) \u0026int;₀^z c / (dE/dt)(z\u0026apos;) dz\u0026apos;\u003c/p\u003e"},{"header":"5. Simulation and Results","content":"\u003cp\u003eUsing a simulated divergence curve based on CDxM entropy logic, the model accurately reproduces the late-universe Hubble curve, matching supernovae data and offering a potential resolution to the Hubble tension. A synthetic entropy curve was also tested and shown to be mathematically elegant but structurally fragile under precision.\u003c/p\u003e"},{"header":"6. Structural Comparison: ΛCDM vs CDxM","content":"\u003cp\u003e\u003cimg 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\" height=\"289\" width=\"584\"\u003e\u003c/p\u003e"},{"header":"7. Philosophical Implications","content":"\u003cp\u003eWe are not watching space inflate\u0026mdash;we are watching coherence erode. Observation decouples from gravitational structure. Time doesn\u0026rsquo;t flow; it fractures outward from gravitational immediacy. This ontological inversion restores clarity to entropy and opens new ground for measurement, translation, and emergence.\u003c/p\u003e"},{"header":"8. Project Series Outline","content":"\u003cp\u003eThis manuscript forms the fourth paper in a four-part research sequence titled \u0026quot;The Divergence Paradigm: Reconstructing Time, Coherence, and the Universe from Within.\u0026quot; The series includes:\u003c/p\u003e\n\u003cp\u003e1. Paper 1 \u0026ndash; Event-Time: Redefining Time as Ordinal Divergence from Within Redefines time as local, entity-specific sequences of definable events.\u003c/p\u003e\n\u003cp\u003e2. Paper 2 \u0026ndash; The Ontology of Coherence: Entropy, Divergence, and the Limits of Measurement Establishes coherence as structural integrity and divergence as the root of entropy and observability.\u003c/p\u003e\n\u003cp\u003e3. Paper 3 \u0026ndash; Singularity + / Singularity \u0026ndash; : Dual Origins of Coherence and Divergence \u0026nbsp;Introduces a dual-singularity model to account for emergence, structure, and asymmetry.\u003c/p\u003e\n\u003cp\u003e4. Paper 4 (This Work) \u0026ndash; CDxM Cosmology: A Divergence-Based Reformulation of the Expanding Universe \u0026nbsp;Reformulates cosmological dynamics in terms of entropy divergence, reproducing observational curves and resolving late-universe tensions.\u003c/p\u003e\n\u003cp\u003eThe complete series is intended for eventual compilation as a monograph titled \u0026quot;The Divergence Paradigm.\u0026quot;\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eBarry Brian Bolter is the sole author of this work. He conceptualized the CDxM model, conducted all theoretical development, prepared the manuscript, and curated the supporting material, including the mathematical audit, provenance mapping, and methodological analysis. The author acknowledges the use of dialogical AI (ChatGPT) as a reflective and generative instrument throughout the process\u0026mdash;serving not as a co-author but as a structured tool for refining coherence, challenging assumptions, and facilitating interdisciplinary synthesis.\u003c/p\u003e"},{"header":"References and Observational Anchors","content":"\u003col type=\"disc\"\u003e\n \u003cli\u003eScolnic, D. M., et al. (2018). \u003cem\u003eThe Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample\u003c/em\u003e. ApJ, 859(2), 101.\u003c/li\u003e\n \u003cli\u003eRiess, A. G., et al. (2019). \u003cem\u003eLarge Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond \u0026Lambda;CDM\u003c/em\u003e. ApJ, 876(1), 85.\u003c/li\u003e\n \u003cli\u003ePlanck Collaboration. (2020). \u003cem\u003ePlanck 2018 results. VI. Cosmological parameters\u003c/em\u003e. A\u0026amp;A, 641, A6.\u003c/li\u003e\n \u003cli\u003eLelli, F., McGaugh, S. S., \u0026amp; Schombert, J. M. (2016). \u003cem\u003eSPARC: Mass Models for 175 Disk Galaxies with Spitzer Photometry and Accurate Rotation Curves\u003c/em\u003e. AJ, 152(6), 157.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"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":"","lastPublishedDoi":"10.21203/rs.3.rs-6766481/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6766481/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper introduces a cosmological model in which the evolution of the universe is driven not by spatial expansion but by the divergence of temporal coherence. In the Coherence\u0026ndash;Divergence Model (CDxM), gravitational structure defines the present, and time is reinterpreted as a local curvature away from this coherence. The entropy divergence field E(t) replaces the scale factor, and its derivative dE/dt replaces the Hubble parameter. We reformulate the Friedmann equations accordingly, derive redshift and luminosity distance relationships, and demonstrate alignment with supernova data and late-universe acceleration\u0026mdash;without invoking dark energy. The CDxM framework preserves observational structure while replacing metric inflation with ontological divergence, and offers a new path for resolving the Hubble tension.\u003c/p\u003e","manuscriptTitle":"CDxM Cosmology: A Divergence-Based Reformulation of the Expanding Universe","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-29 02:54:34","doi":"10.21203/rs.3.rs-6766481/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"f1af614a-6588-44ae-b2f7-d0d3915dcb17","owner":[],"postedDate":"May 29th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-06-19T14:23:44+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-29 02:54:34","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6766481","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6766481","identity":"rs-6766481","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}