Retarded gravitational field of a Hubble sphere with radially varying density

Retarded gravitational field of a Hubble sphere with radially varying density | 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 Retarded gravitational field of a Hubble sphere with radially varying density Ahmed Rouini This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8398846/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 Birkhoff’s theorem in general relativity states that the metric outside a static,spherically symmetric mass distribution is necessarily the Schwarzschild metric. This work demonstrates that when the cosmological density evolves temporally and spatially due to relativistic contraction along the radial direction, differential propagation delays combined with an overdensity in peripheral regions induce anisotropy in the energy-momentum tensor perturbations. This anisotropy leads to the emergence of a positive, non-zero additional curvature inside the Hubble sphere, manifesting as an effective outward-oriented gravitational field. Numerical simulations reveal accelerations on the order of 10 −10 m/s 2 to 10 −8 m/s 2 in the local universe, sufficient to induce cumulative velocity changes on the order of 10 8 m/s over the Hubble time. This mechanism provides a natural geometric explanation for the acceleration of cosmic expansion without resorting to the dark energy hypothesis. The model’s predictions are in qualitative agreement with observations from the Cosmicflows-4 catalog (Tully et al. 2023), showing marked acceleration up to 300 Mpc followed by gradual weakening. Long-term extrapolation of this model predicts a reversal of the cosmological dynamics, culminating in an ultimate phase of global gravitational collapse. retarded gravity Hubble sphere emergent curvature metric perturbations cosmology Birkhoff theorem Full Text Additional Declarations No competing interests reported. Supplementary Files Shelldelayedenall.zip Shelldelayedenall.zip 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. 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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-8398846","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":563300301,"identity":"7e3585ab-d1a4-4e21-a008-ef2d5a4b204f","order_by":0,"name":"Ahmed Rouini","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA70lEQVRIiWNgGAWjYJCCAwwGDAlA2vhBQgWQYmZuIFqLmcGDMyAtjIS1gABIi4HkwzYQm4AW8/Yew8MFBXZ5uu3NGwwS59VG87cDtfyo2IZTi8yZMwaHZxgkF5udOVbwIHHb8dwZhxkbGHvO3MapRUIix+AwjwFz4rYbOQYGiduO5TYAtTAzthHUUp+47f4bA4nEOcdy5xOp5TDQFh6gloaa3A0EtfAcKwBqOZ647UxamUHCsQO5G4FaDuL1C3vz5s88f6qBHj+8+eGPmrrceecPH3zwowK3FnRwGEweIFo9ENSRongUjIJRMApGCAAAOAlhiarWVFkAAAAASUVORK5CYII=","orcid":"","institution":"National School of Built and Ground Works Engineering","correspondingAuthor":true,"prefix":"","firstName":"Ahmed","middleName":"","lastName":"Rouini","suffix":""}],"badges":[],"createdAt":"2025-12-18 21:08:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8398846/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8398846/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":99322368,"identity":"ef8aa933-91c7-4ca9-bcef-8bcebe4356be","added_by":"auto","created_at":"2025-12-31 16:43:30","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":8878830,"visible":true,"origin":"","legend":"","description":"","filename":"Shelldeleyedmnras.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8398846/v1_covered_27eb969f-fb54-4e94-b0bd-793ef59aac45.pdf"},{"id":98855675,"identity":"b5a1b535-04de-4ebe-b28b-f3bc919e3e9f","added_by":"auto","created_at":"2025-12-23 07:43:20","extension":"zip","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":2578966,"visible":true,"origin":"","legend":"","description":"","filename":"Shelldelayedenall.zip","url":"https://assets-eu.researchsquare.com/files/rs-8398846/v1/e6a9bdbf2514ddd43c3c398f.zip"},{"id":99308967,"identity":"012f27cf-92c5-45bf-9fa7-a439405c3616","added_by":"auto","created_at":"2025-12-31 16:09:35","extension":"zip","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":4825582,"visible":true,"origin":"","legend":"","description":"","filename":"Shelldelayedenall.zip","url":"https://assets-eu.researchsquare.com/files/rs-8398846/v1/ad5264f948795df0f38d2475.zip"}],"financialInterests":"No competing interests reported.","formattedTitle":"Retarded gravitational field of a Hubble sphere with radially varying density","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","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":"retarded gravity,Hubble sphere, emergent curvature, metric perturbations, cosmology, Birkhoff theorem","lastPublishedDoi":"10.21203/rs.3.rs-8398846/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8398846/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Birkhoff’s theorem in general relativity states that the metric outside a static,spherically symmetric mass distribution is necessarily the Schwarzschild metric. 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