{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,12]],"date-time":"2026-01-12T22:42:48Z","timestamp":1768257768031,"version":"3.49.0"},"reference-count":59,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,7,5]],"date-time":"2021-07-05T00:00:00Z","timestamp":1625443200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["PTDC\/FIS-OUT\/29048\/2017"],"award-info":[{"award-number":["PTDC\/FIS-OUT\/29048\/2017"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Universe"],"abstract":"<jats:p>We investigate the possibility of gravitationally generated particle production via the mechanism of nonminimal torsion\u2013matter coupling. An intriguing feature of this theory is that the divergence of the matter energy\u2013momentum tensor does not vanish identically. We explore the physical and cosmological implications of the nonconservation of the energy\u2013momentum tensor by using the formalism of irreversible thermodynamics of open systems in the presence of matter creation\/annihilation. The particle creation rates, pressure, and the expression of the comoving entropy are obtained in a covariant formulation and discussed in detail. Applied together with the gravitational field equations, the thermodynamics of open systems lead to a generalization of the standard \u039bCDM cosmological paradigm, in which the particle creation rates and pressures are effectively considered as components of the cosmological fluid energy\u2013momentum tensor. We consider specific models, and we show that cosmology with a torsion\u2013matter coupling can almost perfectly reproduce the \u039bCDM scenario, while it additionally gives rise to particle creation rates, creation pressures, and entropy generation through gravitational matter production in both low and high redshift limits.<\/jats:p>","DOI":"10.3390\/universe7070227","type":"journal-article","created":{"date-parts":[[2021,7,5]],"date-time":"2021-07-05T04:18:21Z","timestamp":1625458701000},"page":"227","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Gravitationally Induced Particle Production through a Nonminimal Torsion\u2013Matter Coupling"],"prefix":"10.3390","volume":"7","author":[{"given":"Tiberiu","family":"Harko","sequence":"first","affiliation":[{"name":"Astronomical Observatory, 19 Ciresilor Street, 400487 Cluj-Napoca, Romania"},{"name":"Department of Physics, Babes-Bolyai University, Kogalniceanu Street, 400084 Cluj-Napoca, Romania"},{"name":"School of Physics, Sun Yat-Sen University, Xingang Road, Guangzhou 510275, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9388-8373","authenticated-orcid":false,"given":"Francisco S. N.","family":"Lobo","sequence":"additional","affiliation":[{"name":"Instituto de Astrof\u00edsica e Ci\u00eancias do Espa\u00e7o, Faculdade de Ci\u00eancias da Universidade de Lisboa, Edif\u00edcio C8, Campo Grande, PT1749-016 Lisbon, Portugal"},{"name":"Departamento de F\u00edsica, Faculdade de Ci\u00eancias, Universidade de Lisboa, Edif\u00edcio C8, Campo Grande, PT1749-016 Lisbon, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1500-0874","authenticated-orcid":false,"given":"Emmanuel N.","family":"Saridakis","sequence":"additional","affiliation":[{"name":"National Observatory of Athens, Lofos Nymfon, 11852 Athens, Greece"},{"name":"CAS Key Laboratory for Researches in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of China, Hefei 230026, China"},{"name":"School of Astronomy, School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1142\/S0219887807001928","article-title":"Introduction to modified gravity and gravitational alternative for dark energy","volume":"4","author":"Nojiri","year":"2007","journal-title":"Int. J. Geom. Meth. Mod. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2012.01.001","article-title":"Modified Gravity and Cosmology","volume":"513","author":"Clifton","year":"2012","journal-title":"Phys. Rept."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.physrep.2011.09.003","article-title":"Extended Theories of Gravity","volume":"509","author":"Capozziello","year":"2011","journal-title":"Phys. Rept."},{"key":"ref_4","unstructured":"Valentino, E.D., Anchordoqui, L.A., Akarsu, O., Ali-Haimoud, Y., Amendola, L., Arendse, N., Asgari, M., Ballardini, M., Basilakos, S., and Battistelli, E. (2020). Cosmology Intertwined II: The Hubble Constant Tension. arXiv."},{"key":"ref_5","unstructured":"Valentino, E.D., Anchordoqui, L.A., Akarsu, O., Ali-Haimoud, Y., Amendola, L., Arendse, N., Asgari, M., Ballardini, M., Basilakos, S., and Battistelli, E. (2020). Cosmology Intertwined III: f\u03c38 and S8. arXiv."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1103\/PhysRevD.16.953","article-title":"Renormalization of Higher Derivative Quantum Gravity","volume":"16","author":"Stelle","year":"1977","journal-title":"Phys. Rev. D"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/0550-3213(87)90465-2","article-title":"The Quartic Effective Action for the Heterotic String","volume":"291","author":"Gross","year":"1987","journal-title":"Nucl. Phys. B"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"031101","DOI":"10.1103\/PhysRevLett.108.031101","article-title":"Towards singularity and ghost free theories of gravity","volume":"108","author":"Biswas","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Saridakis, E.N., Lazkoz, R., Salzano, V., Moniz, P.V., Capozziello, S., Jim\u00e9nez, J.B., Laurentis, M.D., Olmo, G.J., Akrami, Y., and Bahamonde, S. (2021). Modified Gravity and Cosmology: An Update by the CANTATA Network. arXiv.","DOI":"10.1007\/978-3-030-83715-0"},{"key":"ref_10","first-page":"10","article-title":"Conservation laws and absolute parallelism in general relativity","volume":"1","year":"1961","journal-title":"Mat. Fys. Skr. Dan. Vid. Selsk."},{"key":"ref_11","first-page":"4","article-title":"Tetrad fields and gravitational fields","volume":"2","author":"Pellegrini","year":"1963","journal-title":"Mat. Fys. Skr. Dan. Vid. Selsk."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3524","DOI":"10.1103\/PhysRevD.19.3524","article-title":"New general relativity","volume":"19","author":"Hayashi","year":"1979","journal-title":"Phys. Rev. D"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1002\/andp.201200272","article-title":"The teleparallel equivalent of general relativity","volume":"525","author":"Maluf","year":"2013","journal-title":"Ann. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"124019","DOI":"10.1103\/PhysRevD.79.124019","article-title":"Dark torsion as the cosmic speed-up","volume":"79","author":"Bengochea","year":"2009","journal-title":"Phys. Rev. D"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"106901","DOI":"10.1088\/0034-4885\/79\/10\/106901","article-title":"f(T) teleparallel gravity and cosmology","volume":"79","author":"Cai","year":"2016","journal-title":"Rept. Prog. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"084044","DOI":"10.1103\/PhysRevD.90.084044","article-title":"Teleparallel equivalent of Gauss-Bonnet gravity and its modifications","volume":"90","author":"Kofinas","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1016\/j.physletb.2011.09.082","article-title":"Teleparallel dark energy","volume":"704","author":"Geng","year":"2011","journal-title":"Phys. Lett. B"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"104042","DOI":"10.1103\/PhysRevD.92.104042","article-title":"Modified teleparallel theories of gravity","volume":"92","author":"Bahamonde","year":"2015","journal-title":"Phys. Rev. D"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"021","DOI":"10.1088\/1475-7516\/2014\/12\/021","article-title":"f(T,T) gravity and cosmology","volume":"12","author":"Harko","year":"2014","journal-title":"JCAP"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"124036","DOI":"10.1103\/PhysRevD.89.124036","article-title":"Nonminimal torsion-matter coupling extension of f(T) gravity","volume":"89","author":"Harko","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"704","DOI":"10.1140\/epjc\/s10052-016-4560-4","article-title":"Non-minimal coupling of torsion matter satisfying null energy condition for wormhole solutions","volume":"76","author":"Jawad","year":"2016","journal-title":"Eur. Phys. J. C"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1140\/epjc\/s10052-018-5793-1","article-title":"Generalised nonminimally gravity-matter coupled theory","volume":"78","author":"Bahamonde","year":"2018","journal-title":"Eur. Phys. J. C"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"124013","DOI":"10.1103\/PhysRevD.98.124013","article-title":"Growth of matter perturbations in nonminimal teleparallel dark energy","volume":"98","author":"Luongo","year":"2018","journal-title":"Phys. Rev. D"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1140\/epjc\/s10052-018-6286-y","article-title":"Growth of matter overdensities in non-minimal torsion-matter coupling theories","volume":"78","author":"Otalora","year":"2018","journal-title":"Eur. Phys. J. C"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"6245","DOI":"10.1073\/pnas.83.17.6245","article-title":"Entropy, matter, and cosmology","volume":"83","author":"Prigogine","year":"1986","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"7428","DOI":"10.1073\/pnas.85.20.7428","article-title":"Thermodynamics of cosmological matter creation","volume":"85","author":"Prigogine","year":"1988","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/0375-9601(92)90437-Q","article-title":"On the thermodynamics of matter creation in cosmology","volume":"162","author":"Lima","year":"1992","journal-title":"Phys. Lett. A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/0375-9601(92)90890-X","article-title":"On the Equivalence of matter creation in cosmology","volume":"170","author":"Lima","year":"1992","journal-title":"Phys. Lett. A"},{"key":"ref_29","first-page":"044018","article-title":"Irreversible thermodynamic description of interacting dark energy-dark matter cosmological models","volume":"D87","author":"Harko","year":"2013","journal-title":"Phys. Rev."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"100521","DOI":"10.1016\/j.dark.2020.100521","article-title":"Irreversible thermodynamical description of warm inflationary cosmological models","volume":"28","author":"Harko","year":"2020","journal-title":"Phys. Dark Universe"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"047302","DOI":"10.1103\/PhysRevD.87.047302","article-title":"Entropy evolution of universes with initial and final de Sitter eras","volume":"87","author":"Mimoso","year":"2013","journal-title":"Phys. Rev. D"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s10714-012-1457-x","article-title":"Does the entropy of the Universe tend to a maximum?","volume":"45","author":"Radicella","year":"2013","journal-title":"Gen. Rel. Grav."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"L83","DOI":"10.1088\/0264-9381\/17\/15\/101","article-title":"Cosmic holography","volume":"17","author":"Bak","year":"2000","journal-title":"Class. Quantum Gravity"},{"key":"ref_34","first-page":"307","article-title":"Particle Production in Cosmology","volume":"12","author":"Ya","year":"1970","journal-title":"Phys. JETP Lett."},{"key":"ref_35","first-page":"4231","article-title":"Big-bang model without singularities","volume":"D8","author":"Murphy","year":"1973","journal-title":"Phys. Rev."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/0375-9601(82)90635-1","article-title":"Vacuum viscosity description of quantum processes in the early universe","volume":"90","author":"Hu","year":"1982","journal-title":"Phys. Lett. A"},{"key":"ref_37","unstructured":"Weitzenb\u00f6ck, R. (1923). Invarianten Theorie, Nordhoff."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Aldrovandi, R., and Pereira, J.G. (2013). Teleparallel Gravity: An Introduction, Springer.","DOI":"10.1007\/978-94-007-5143-9"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1063\/1.530774","article-title":"Hamiltonian formulation of the teleparallel description of general relativity","volume":"35","author":"Maluf","year":"1994","journal-title":"J. Math. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Oeyvind Groen and Sigbjorn Hervik (2007). Einstein\u2019s General Theory of Relativity, Springer.","DOI":"10.1007\/978-0-387-69200-5"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"064036","DOI":"10.1103\/PhysRevD.78.064036","article-title":"Non-minimum coupling of perfect fluids to curvature","volume":"78","author":"Bertolami","year":"2008","journal-title":"Phys. Rev. D"},{"key":"ref_42","unstructured":"Bertolami, O., Paramos, J., Harko, T., and Lobo, F.S.N. (2008). Non-minimal curvature-matter couplings in modified gravity. arXiv."},{"key":"ref_43","first-page":"064018","article-title":"Perfect fluid Lagrangian and its cosmological implications in theories of gravity with nonminimally coupled matter fields","volume":"D97","author":"Avelino","year":"2018","journal-title":"Phys. Rev."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Landau, L.D., and Lifshitz, E.M. (1980). Statistical Physics, Part 1, Pergamon Press.","DOI":"10.1016\/B978-0-08-057046-4.50008-7"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Saridakis, E.N. (2021). Do we need soft cosmology?. arXiv.","DOI":"10.1016\/j.physletb.2021.136649"},{"key":"ref_46","unstructured":"Maartens, R. (1996). Causal thermodynamics in relativity. arXiv."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1937","DOI":"10.1103\/PhysRevD.55.1937","article-title":"Nonlinear bulk viscosity and inflation","volume":"55","author":"Maartens","year":"1997","journal-title":"Phys. Rev. D"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1016\/0003-4916(76)90064-6","article-title":"Nonstationary irreversible thermodynamics: A Causal relativistic theory","volume":"100","author":"Israel","year":"1976","journal-title":"Ann. Phys. (N. Y.)"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/0375-9601(76)90075-X","article-title":"Thermodynamics of nonstationary and transient effects in a relativistic gas","volume":"58","author":"Israel","year":"1976","journal-title":"Phys. Lett. A"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Jou, D., Casas-V\u00e1zquez, J., and Lebon, G. (2010). Extended Irreversible Thermodynamics, Springer.","DOI":"10.1007\/978-90-481-3074-0_2"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Harko, T., and Lobo, F.S.N. (2018). Extensions of f(R) Gravity: Curvature-Matter Couplings and Hybrid Metric Palatini Theory, Cambridge University Press.","DOI":"10.1017\/9781108645683"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"A6","DOI":"10.1051\/0004-6361\/201833910","article-title":"[Planck], Planck 2018 results. VI. Cosmological parameters","volume":"641","author":"Aghanim","year":"2020","journal-title":"Astron. Astrophys."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"044067","DOI":"10.1103\/PhysRevD.90.044067","article-title":"Thermodynamic interpretation of the generalized gravity models with geometry-matter coupling","volume":"90","author":"Harko","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1140\/epjc\/s10052-015-3620-5","article-title":"Gravitational induced particle production through a nonminimal curvature\u2013matter coupling","volume":"75","author":"Harko","year":"2015","journal-title":"Eur. Phys. J. C"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"562","DOI":"10.1103\/PhysRevLett.21.562","article-title":"Particle creation in expanding universes","volume":"21","author":"Parker","year":"1968","journal-title":"Phys. Rev. Lett."},{"key":"ref_56","first-page":"2546","article-title":"Quantized fields and particle creation in expanding universes. 2","volume":"D3","author":"Parker","year":"1971","journal-title":"Phys. Rev."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Fulling, S.A. (1989). Aspects of Quantum Field Theory in Curved Space-Time, Cambridge University Press.","DOI":"10.1017\/CBO9781139172073"},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Parker, L.E., and Toms, D.J. (2009). Quantum Field Theory in Curved Spacetime-Quantized Fields and Gravity, Cambridge University Press.","DOI":"10.1017\/CBO9780511813924"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1007\/s10701-007-9199-4","article-title":"Physics of dark energy particles","volume":"38","author":"Harko","year":"2008","journal-title":"Found. Phys."}],"container-title":["Universe"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-1997\/7\/7\/227\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:26:01Z","timestamp":1760163961000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-1997\/7\/7\/227"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,5]]},"references-count":59,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["universe7070227"],"URL":"https:\/\/doi.org\/10.3390\/universe7070227","relation":{},"ISSN":["2218-1997"],"issn-type":[{"value":"2218-1997","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,5]]}}}