{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T01:22:47Z","timestamp":1773883367914,"version":"3.50.1"},"reference-count":102,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,12]],"date-time":"2023-03-12T00:00:00Z","timestamp":1678579200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Macronix Research Corporation","award":["2020-23"],"award-info":[{"award-number":["2020-23"]}]},{"name":"Macronix Research Corporation","award":["309984\/2020-3"],"award-info":[{"award-number":["309984\/2020-3"]}]},{"DOI":"10.13039\/501100003593","name":"National Council for Scientific and Technological Development","doi-asserted-by":"publisher","award":["2020-23"],"award-info":[{"award-number":["2020-23"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"National Council for Scientific and Technological Development","doi-asserted-by":"publisher","award":["309984\/2020-3"],"award-info":[{"award-number":["309984\/2020-3"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A scalar\u2013tensor theory of gravity was considered, wherein the gravitational coupling G and the speed of light c were admitted as space\u2013time functions and combined to form the definition of the scalar field \u03d5. The varying c participates in the definition of the variation of the matter part of the action; it is related to the effective stress\u2013energy tensor, which is a result of the requirement of symmetry under general coordinate transformations in our gravity model. The effect of the cosmological coupling \u039b is accommodated within a possible behavior of \u03d5. We analyzed the dynamics of \u03d5 in the phase space, thereby showing the existence of an attractor point for reasonable hypotheses on the potential V(\u03d5) and no particular assumption on the Hubble function. The phase space analysis was performed both with the linear stability theory and via the more general Lyapunov method. Either method led to the conclusion that the condition G\u02d9\/G=\u03c3c\u02d9\/c, where \u03c3=3 must hold for the rest of cosmic evolution after the system arrives at the globally asymptotically stable fixed point and the dynamics of \u03d5 ceases. This result realized our main motivation: to provide a physical foundation for the phenomenological model admitting G\/G0=c\/c03, used recently to interpret cosmological and astrophysical data. The thus covarying couplings G and c impact the cosmic evolution after the dynamical system settles to equilibrium. The secondary goal of our work was to investigate how this impact occurs. This was performed by constructing the generalized continuity equation in our scalar\u2013tensor model and considering two possible regimes for the varying speed of light\u2014decreasing c and increasing c\u2014while solving our modified Friedmann equations. The solutions to the latter equations make room for radiation- and matter-dominated eras that progress to a dark-energy-type of accelerated expansion.<\/jats:p>","DOI":"10.3390\/sym15030709","type":"journal-article","created":{"date-parts":[[2023,3,13]],"date-time":"2023-03-13T06:09:56Z","timestamp":1678687796000},"page":"709","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Dynamical Analysis of the Covarying Coupling Constants in Scalar\u2013Tensor Gravity"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1189-0515","authenticated-orcid":false,"given":"Rodrigo","family":"Cuzinatto","sequence":"first","affiliation":[{"name":"Department of Physics, University of Ottawa, Ottawa, ON K1N 6N5, Canada"},{"name":"Instituto de Ci\u00eancia e Tecnologia, Universidade Federal de Alfenas, Rodovia Jos\u00e9 Aur\u00e9lio Vilela 11999, Po\u00e7os de Caldas CEP 37715-400, MG, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5423-2673","authenticated-orcid":false,"given":"Rajendra","family":"Gupta","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Ottawa, Ottawa, ON K1N 6N5, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0474-1362","authenticated-orcid":false,"given":"Pedro","family":"Pompeia","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Ottawa, Ottawa, ON K1N 6N5, Canada"},{"name":"Departamento de F\u00edsica, Instituto Tecnol\u00f3gico de Aeron\u00e1utica, Pra\u00e7a Mal. Eduardo Gomes 50, S\u00e3o Jos\u00e9 dos Campos CEP 12228-900, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1103\/RevModPhys.75.403","article-title":"The fundamental constants and their variation: Observational status and theoretical motivations","volume":"75","author":"Uzan","year":"2003","journal-title":"Rev. Mod. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2","DOI":"10.12942\/lrr-2011-2","article-title":"Varying constants, gravitation and Cosmology","volume":"14","author":"Uzan","year":"2011","journal-title":"Living Rev. Relativ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1119\/1.1819929","article-title":"\u2018c\u2019 is the speed of light, isn\u2019t it?","volume":"73","author":"Ellis","year":"2005","journal-title":"Am. J. 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