Geometric Scalar Invariants as Dynamical Vacuum Energy: Coherence, Reheating, and the Cosmological Constant

Geometric Scalar Invariants as Dynamical Vacuum Energy: Coherence, Reheating, and the Cosmological Constant | 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 Systematic Review Geometric Scalar Invariants as Dynamical Vacuum Energy: Coherence, Reheating, and the Cosmological Constant Gregory Howell This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6704049/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 investigate a geometric scalar invariant of the form \(\:{\dot{\varphi\:}}^{2}{\varphi\:}^{2}\) , motivated by energy–volume–frequency structures in relativistic particle systems. Embedded in a scalar field theory in FLRW spacetime, this term dynamically modulates energy density and coherence. We show that the invariant can support an inflationary phase, induce graceful exit without fine-tuned potentials, and decay as a power law, potentially explaining the current tiny dark energy scale. We then explore the field’s perturbation stability, reheating, quantum corrections, and radiative stability. Numerical simulations confirm that the invariant drives both inflationary behavior and a late-time vacuum-like energy component without requiring an unnaturally small cosmological constant. We discuss observational signatures, including the evolution of the expansion rate and growth of structure, and argue that upcoming surveys may constrain or detect this class of dynamical vacuum energy models. Full Text Additional Declarations No competing interests reported. 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-6704049","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Systematic Review","associatedPublications":[],"authors":[{"id":467945889,"identity":"eae5e7fc-5be0-42c4-af65-843ad8d17f84","order_by":0,"name":"Gregory Howell","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2klEQVRIiWNgGAWjYJACZsY/NTz8IFZCAdFaGo7JSTaAtBgQr4XZ2OAAiEmMFvnow4dfF+5gS9x8fnXihwcGDPL8YgfwazE8l5ZmPfOMTOK2G283SwAdZjhzdgIBLT08ZsY8bGxALWc3gLQkGNwmqIX/G1ALc+LmGWc3/yBKizwPD/Nj3jag9/l7txFniwEPmxkzz5ljchI3eLdZJBhIEPaLfA/z4888FcCo7D+7+eaPCht5fmlCthxgYJMAsyTAKiXwKwfb0sDA/AHM4j9AWPUoGAWjYBSMTAAAUxFDWppFHSoAAAAASUVORK5CYII=","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Gregory","middleName":"","lastName":"Howell","suffix":""}],"badges":[],"createdAt":"2025-05-20 05:53:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6704049/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6704049/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":84284087,"identity":"9ed88f5f-b6ef-4ea6-b40c-1453a054adaa","added_by":"auto","created_at":"2025-06-10 07:14:03","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":496860,"visible":true,"origin":"","legend":"","description":"","filename":"GeometricScalarInvariantsasDynamicalVacuumEnergy.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6704049/v1_covered_e3f8ee62-cdf6-44a9-9a21-c25ada5ffea8.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Geometric Scalar Invariants as Dynamical Vacuum Energy: Coherence, Reheating, and the Cosmological Constant","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":"","lastPublishedDoi":"10.21203/rs.3.rs-6704049/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6704049/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe investigate a geometric scalar invariant of the form \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\dot{\\varphi\\:}}^{2}{\\varphi\\:}^{2}\\)\u003c/span\u003e\u003c/span\u003e, motivated by energy\u0026ndash;volume\u0026ndash;frequency structures in relativistic particle systems. Embedded in a scalar field theory in FLRW spacetime, this term dynamically modulates energy density and coherence. We show that the invariant can support an inflationary phase, induce graceful exit without fine-tuned potentials, and decay as a power law, potentially explaining the current tiny dark energy scale. We then explore the field\u0026rsquo;s perturbation stability, reheating, quantum corrections, and radiative stability. Numerical simulations confirm that the invariant drives both inflationary behavior and a late-time vacuum-like energy component without requiring an unnaturally small cosmological constant. 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