{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T01:58:26Z","timestamp":1773107906249,"version":"3.50.1"},"reference-count":24,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,11]],"date-time":"2025-03-11T00:00:00Z","timestamp":1741651200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Unimodular theory incorporating the Kaluza\u2013Klein construction in five dimensions leads, after reduction to four dimensions, to a new class of scalar\u2013tensor theory. The vacuum cosmological solutions display a bounce with non-singular behavior the effective lower dimension model: from the four-dimensional point of view, the solutions are completely regular. However, the propagation of gravitational waves in this geometry displays the presence of instabilities which reflect singular features of the original five-dimensional structure connected to a degenerate metric at the bounce. A four-dimensional quantum model with cosmological constant, which has a similar background behavior, is discussed and revealed to be stable.<\/jats:p>","DOI":"10.3390\/sym17030419","type":"journal-article","created":{"date-parts":[[2025,3,11]],"date-time":"2025-03-11T08:59:52Z","timestamp":1741683592000},"page":"419","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the Stability of Non-Singular Solutions in Effective Theory from Kaluza\u2013Klein Unimodular Gravity"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8880-107X","authenticated-orcid":false,"given":"J\u00falio C.","family":"Fabris","sequence":"first","affiliation":[{"name":"N\u00facleo Cosmo-ufes & Departamento de F\u00edsica, Universidade Federal do Esp\u00edrito Santo, Vit\u00f3ria CEP 29075-910, Brazil"}]},{"given":"Richard","family":"Kerner","sequence":"additional","affiliation":[{"name":"Laboratoire de Physique Th\u00e9orique de la Mati\u00e8re Condens\u00e9e (LPTMC), UMR 7600, Sorbonne Universit\u00e9, 75005 Paris, France"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,11]]},"reference":[{"key":"ref_1","first-page":"349","article-title":"Spielen Gravitationsfelder im Aufbau der materiellen Elementarteilchen eine wesentliche Rolle?","volume":"1919","author":"Einstein","year":"1919","journal-title":"Sitzungsber. Preuss. Akad. Wiss. Berlin Math. Phys."},{"key":"ref_2","first-page":"966","article-title":"Zum Unit\u00e4tsproblem der Physik","volume":"K1","author":"Kaluza","year":"1921","journal-title":"Sitzungsber. Preuss. Akad. Wiss."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1007\/BF01397481","article-title":"Quantentheorie und f\u00fcnfdimensionale Relativit\u00e4tstheorie","volume":"37","author":"Klein","year":"1926","journal-title":"Zeitschr. Phys."},{"key":"ref_4","unstructured":"Einstein, A. (1927). Zu Kaluza Theorie des Zusammenhanges von Gravitation und Elektrizit\u00e4t. Sitzungsber. Preuss. Akad. Wiss. Phys. Math., Kl23."},{"key":"ref_5","first-page":"193","article-title":"On a Generalization of Kaluza\u2019s Theory of Electricity","volume":"34","author":"Einstein","year":"1938","journal-title":"Ann. Math."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1103\/PhysRevLett.51.87","article-title":"Kaluza-Klein Monopole","volume":"51","author":"Sorkin","year":"1983","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/0550-3213(83)90462-5","article-title":"Magnetic monopoles in Kaluza-Klein theories","volume":"B226","author":"Gross","year":"1983","journal-title":"Nucl. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1103\/PhysRev.124.925","article-title":"Mach\u2019s Principle and a Relativistic Theory of Gravitation","volume":"124","author":"Brans","year":"1961","journal-title":"Phys. Rev."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"812","DOI":"10.2307\/1968467","article-title":"A Remarkable Property of the Riemann-Christoffel Tensor in Four Dimensions","volume":"39","author":"Lanczos","year":"1938","journal-title":"Ann. Math."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1063\/1.1665613","article-title":"The Einstein Tensor and Its Generalizations","volume":"12","author":"Lovelock","year":"1971","journal-title":"J. Math. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1016\/0550-3213(81)90021-3","article-title":"Search for a Realistic Kaluza-Klein theory","volume":"186","author":"Witten","year":"1981","journal-title":"Nucl. Phys. B"},{"key":"ref_12","first-page":"631","article-title":"Non-linear Electrodynamics derived from the Kaluza-Klein Theory","volume":"304","author":"Kerner","year":"1987","journal-title":"Comptes Rendus Acad. Sci. Paris"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1088\/0264-9381\/5\/2\/013","article-title":"Cosmology in Ten Dimensions with the Generalised Gravitational Lagrangian","volume":"5","author":"Giorgini","year":"1988","journal-title":"Class. Quant. Grav."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"085042","DOI":"10.1088\/1402-4896\/ad6351","article-title":"A Unimodular Kaluza-Klein Theory","volume":"99","author":"Fabris","year":"2024","journal-title":"Phys. Scr."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1016\/j.crhy.2012.04.008","article-title":"Everything You Always Wanted to Know About the Cosmological Constant Problem (but were afraid to ask)","volume":"13","author":"Martin","year":"2012","journal-title":"Comptes Rendus Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"021","DOI":"10.1088\/1475-7516\/2014\/09\/021","article-title":"Cosmological Perturbations in Unimodular Gravity","volume":"9","author":"Gao","year":"2014","journal-title":"JCAP"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"243001","DOI":"10.1088\/1361-6382\/aca386","article-title":"Unimodular gravity vs. general relativity: A status report","volume":"39","author":"Garay","year":"2022","journal-title":"Class. Quantum Grav."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1023\/A:1015986011295","article-title":"Quantum Cosmological Perfect Fluid Models","volume":"34","author":"Alvarenga","year":"2002","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_19","first-page":"2762","article-title":"Perfect Fluids in General Relativity: Velocity Potentials and a Variational Principle","volume":"D2","author":"Schutz","year":"1970","journal-title":"Phys. Rev."},{"key":"ref_20","first-page":"3559","article-title":"Hamiltonian Theory of a Relativistic Perfect Fluid","volume":"D4","author":"Schutz","year":"1971","journal-title":"Phys. Rev."},{"key":"ref_21","first-page":"063519","article-title":"Quantum cosmological perfect fluid model and its classical analogue","volume":"D65","author":"Batista","year":"2002","journal-title":"Phys. Rev."},{"key":"ref_22","unstructured":"Weinberg, S. (1972). Gravitation and Cosmology, Wiley."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/BF00647424","article-title":"On the Problem of the Initial State in the Isotropic Scalar-Tensor Cosmology of Brans-Dicke","volume":"22","author":"Gurevich","year":"1973","journal-title":"Astrophys. Spc. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"125002","DOI":"10.1088\/1361-6382\/ab8bb8","article-title":"Cosmological models with asymmetric quantum bounces","volume":"37","author":"Delgado","year":"2020","journal-title":"Class. Quantum Grav."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/419\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:50:26Z","timestamp":1760028626000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/419"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,11]]},"references-count":24,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["sym17030419"],"URL":"https:\/\/doi.org\/10.3390\/sym17030419","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,11]]}}}