Emergent Cosmological Dynamics from Stochastic Bidirectional Causality: A Unified Extension of ΛCDM

Emergent Cosmological Dynamics from Stochastic Bidirectional Causality: A Unified Extension of ΛCDM | 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 Emergent Cosmological Dynamics from Stochastic Bidirectional Causality: A Unified Extension of ΛCDM Carlos Hernan Quintero, Emili Quintero Castillo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7324968/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 We introduce the Stochastic Bidirectional Causality (SBC) model, a relational and memory-driven extension of ΛCDM in which cosmological observables emerge hierarchically from non-Markovian, temporally correlated dynamics. Unlike conventional models that assume immutable universal parameters, SBC posits that quantities such as the Hubble constant (H 0) and the structure growth parameter (S 8) arise as statistical expectations conditioned on the observer’s causal accessibility. The mathematical foundation of the model is built upon generalized stochastic Friedmann equations and norm-preserving evolution laws modulated by memory kernels. These encode both past fluctuations and ensemble-level statistical constraints without invoking retrocausal signaling. The resulting architecture generates a structured form of physical dispersion, in which observable variance is not experimental noise but a signature of stochastic causal depth. Empirical validation proceeds hierarchically: from highly constrained primor-dial spectra (C T T ℓ , C EE ℓ) to intermediate observables (H(z), f σ 8 (z)), and finally to context-sensitive parameters like H 0 and S 8. Applied to current cos-mological datasets (Planck, SH0ES, DESI, KiDS, Pantheon+), the SBC model yields emergent ensemble values of H 0 = 70.1 ± 1.1 km s −1 Mpc −1 and S 8 = 0.790±0.021, outperforming both ΛCDM and Early Dark Energy (EDE) in joint fits across all observables under equal or fewer degrees of freedom. All results are fully reproducible from open-source Jupyter notebooks. SBC thus offers not only a novel theoretical framework, but a transparent, falsifiable and epistemologically grounded approach to cosmic inference. Cosmology Stochastic Processes Hubble Tension Quantum Gravity Relational Physics Observer Dependence Causal Inference Full Text Additional Declarations No competing interests reported. Supplementary Files SBCModelRepository.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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-7324968","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":497661841,"identity":"7a47cedd-df80-4ebd-a143-617eedc3a6db","order_by":0,"name":"Carlos Hernan Quintero","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6ElEQVRIiWNgGAWjYNCCAgnGBobExgdAJg8fcVoMQFqSmw1AWtiI1MIA1JLeJgFiE9TC337G+MMPAwvZ/vbEtsqvOXYybAzMDx/dwKNF4kyOmWSPgYTxjDMP227LbksGOozN2DgHr5NyzBh4DCQSG24ktt2W3MYM1MLDJo1XC/8b449/gFrmA7UUS26rJ0KLRI6BNMiWDUAtjB+3HSasReLGszJpGaBfNp552CzNuO04DxszAb/w9ydv/vimok523vH0hx9/bqu252dvfvgYnxYUwMwDJolVDgKMP0hRPQpGwSgYBSMGAADYK0bP9Nlc2wAAAABJRU5ErkJggg==","orcid":"","institution":"SBC Research Group : Cali , Valle , CO","correspondingAuthor":true,"prefix":"","firstName":"Carlos","middleName":"Hernan","lastName":"Quintero","suffix":""},{"id":497661842,"identity":"3da9ba21-f497-4c07-aec2-d68f31a1d097","order_by":1,"name":"Emili Quintero Castillo","email":"","orcid":"","institution":"SBC Research Group : Cali , Valle , CO","correspondingAuthor":false,"prefix":"","firstName":"Emili","middleName":"Quintero","lastName":"Castillo","suffix":""}],"badges":[],"createdAt":"2025-08-08 08:08:36","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7324968/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7324968/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":89686725,"identity":"79277547-1cec-4a80-a220-f0dddac3cd1d","added_by":"auto","created_at":"2025-08-22 15:38:55","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1052204,"visible":true,"origin":"","legend":"","description":"","filename":"SBCManuscriptFoP.pdf.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7324968/v1_covered_8e70b92e-1f3a-42f5-bf2f-817f46a7621d.pdf"},{"id":88747132,"identity":"054baa7f-5ea8-4f93-972c-b4179e76171c","added_by":"auto","created_at":"2025-08-11 04:46:49","extension":"zip","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":14430300,"visible":true,"origin":"","legend":"","description":"","filename":"SBCModelRepository.zip","url":"https://assets-eu.researchsquare.com/files/rs-7324968/v1/bc0d4db0f7f6b141bdc96c5a.zip"}],"financialInterests":"No competing interests reported.","formattedTitle":"Emergent Cosmological Dynamics from Stochastic Bidirectional Causality: A Unified Extension of ΛCDM","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":"Cosmology, Stochastic Processes, Hubble Tension, Quantum Gravity, Relational Physics, Observer Dependence, Causal Inference","lastPublishedDoi":"10.21203/rs.3.rs-7324968/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7324968/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We introduce the Stochastic Bidirectional Causality (SBC) model, a relational and memory-driven extension of ΛCDM in which cosmological observables emerge hierarchically from non-Markovian, temporally correlated dynamics. Unlike conventional models that assume immutable universal parameters, SBC posits that quantities such as the Hubble constant (H 0) and the structure growth parameter (S 8) arise as statistical expectations conditioned on the observer’s causal accessibility. The mathematical foundation of the model is built upon generalized stochastic Friedmann equations and norm-preserving evolution laws modulated by memory kernels. These encode both past fluctuations and ensemble-level statistical constraints without invoking retrocausal signaling. The resulting architecture generates a structured form of physical dispersion, in which observable variance is not experimental noise but a signature of stochastic causal depth. Empirical validation proceeds hierarchically: from highly constrained primor-dial spectra (C T T ℓ , C EE ℓ) to intermediate observables (H(z), f σ 8 (z)), and finally to context-sensitive parameters like H 0 and S 8. Applied to current cos-mological datasets (Planck, SH0ES, DESI, KiDS, Pantheon+), the SBC model yields emergent ensemble values of H 0 = 70.1 ± 1.1 km s −1 Mpc −1 and S 8 = 0.790±0.021, outperforming both ΛCDM and Early Dark Energy (EDE) in joint fits across all observables under equal or fewer degrees of freedom. All results are fully reproducible from open-source Jupyter notebooks. SBC thus offers not only a novel theoretical framework, but a transparent, falsifiable and epistemologically grounded approach to cosmic inference.","manuscriptTitle":"Emergent Cosmological Dynamics from Stochastic Bidirectional Causality: A Unified Extension of ΛCDM","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-11 04:46:42","doi":"10.21203/rs.3.rs-7324968/v1","editorialEvents":[{"type":"communityComments","content":8}],"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":"fa3a27b5-6e41-4ae5-b81d-946704b40fb1","owner":[],"postedDate":"August 11th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-08-22T15:38:19+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-11 04:46:42","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7324968","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7324968","identity":"rs-7324968","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}