{"paper_id":"36ff1dab-a99c-4ca9-81da-ca9da29cff88","body_text":"Non-singular Polynomial Redshift Parametrization of Dark Energy Equation of State: Hubble Tension and Machine Learning | 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 Article Non-singular Polynomial Redshift Parametrization of Dark Energy Equation of State: Hubble Tension and Machine Learning Prabir Rudra, Aritra Sanyal, Promila Biswas, Tuhina Ghorui, Ritabrata Biswas, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9552897/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract In this paper, we explore a new type of smooth and well-behaved polynomial redshift function that can avoid a future singularity. Using this function, we have proposed different redshift parametrizations of the dark energy equation of state, drawing motivation from different polynomial functions like conventional polynomial, Legendre polynomial, Laguerre polynomial, Chebyshev polynomial and Fibonacci polynomial. The main feature of these parametrizations is their well-behaved nature throughout the evolution of the universe, which was a matter of concern in most of the previous polynomial parametrizations of the dark energy equation of state (EoS). This form of parametrization may be considered as an extension of those forms with no divergence at any redshift value. A comprehensive observational data analysis is performed with the Hubble, BAO and DESI datasets to constrain the parameter space of the models. Confidence contours showing joint and marginalized posterior distribution with different combinations of datasets are generated using a Markov Chain Monte Carlo approach. We see that our improved parametrizations enable us to derive more stringent restrictions on the current dark energy EoS and its derivative, which improves performance. We have explored the Hubble tension in the proposed model frameworks and performed a comparative analysis. Finally, a machine learning analysis is performed using some suitable algorithms like ELR, PILR, ANN, SVR, ERFR and GBR to compare the models. Among all the tested polynomial bases, the Legendre basis demonstrated superior performance with the lowest test RMSE and reduced χ 2 value under the Modified Differential Evolution theoretical model, indicating exceptional physical accuracy and numerical stability. Physical sciences/Mathematics and computing Physical sciences/Physics dark energy polynomial redshift parametrization equation of state Hubble cosmic microwave background machine learning algorithm artificial neural network Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 24 May, 2026 Reviewers agreed at journal 13 May, 2026 Reviewers agreed at journal 09 May, 2026 Reviewers invited by journal 07 May, 2026 Editor invited by journal 07 May, 2026 Editor assigned by journal 02 May, 2026 Submission checks completed at journal 02 May, 2026 First submitted to journal 28 Apr, 2026 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-9552897\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":false,\"archivedVersions\":[],\"articleType\":\"Article\",\"associatedPublications\":[],\"authors\":[{\"id\":639421419,\"identity\":\"4789081b-422c-4e00-a231-e8486b0bd83c\",\"order_by\":0,\"name\":\"Prabir 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