{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,29]],"date-time":"2026-03-29T09:09:54Z","timestamp":1774775394188,"version":"3.50.1"},"reference-count":113,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,2]],"date-time":"2024-10-02T00:00:00Z","timestamp":1727827200000},"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>We perform observational confrontation and cosmographic analysis of f(T,TG) gravity and cosmology. This higher-order torsional gravity is based on both the torsion scalar, as well as on the teleparallel equivalent of the Gauss\u2013Bonnet combination, and gives rise to an effective dark-energy sector which depends on the extra torsion contributions. We employ observational data from the Hubble function and supernova Type Ia Pantheon datasets, applying a Markov chain Monte Carlo sampling technique, and we provide the iso-likelihood contours, as well as the best-fit values for the parameters of the power-law model, an ansatz which is expected to be a good approximation of most realistic deviations from general relativity. Additionally, we reconstruct the effective dark-energy equation-of-state parameter, which exhibits a quintessence-like behavior, while in the future the Universe enters into the phantom regime, before it tends asymptotically to the cosmological constant value. Furthermore, we perform a detailed cosmographic analysis, examining the deceleration, jerk, snap, and lerk parameters, showing that the transition to acceleration occurs in the redshift range 0.52\u2264ztr\u22640.89, as well as the preference of the scenario for quintessence-like behavior. Finally, we apply the Om diagnostic analysis to cross-verify the behavior of the obtained model.<\/jats:p>","DOI":"10.3390\/sym16101299","type":"journal-article","created":{"date-parts":[[2024,10,2]],"date-time":"2024-10-02T08:03:29Z","timestamp":1727856209000},"page":"1299","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Observational Constraints and Cosmographic Analysis of f(T,TG) Gravity and Cosmology"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4665-9903","authenticated-orcid":false,"given":"Harshna","family":"Balhara","sequence":"first","affiliation":[{"name":"Department of Mathematics, Netaji Subhas University of Technology, New Delhi 110078, India"}]},{"given":"Jainendra Kumar","family":"Singh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Netaji Subhas University of Technology, New Delhi 110078, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9598-5900","authenticated-orcid":false,"family":"Shaily","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Netaji Subhas University of Technology, New Delhi 110078, India"},{"name":"School of Computer Science Engineering and Technology, Bennett University, Greater Noida 201310, India"}]},{"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 Research in Galaxies and Cosmology, University of Science and Technology of China, Hefei 230026, China"},{"name":"Departamento de Matem\u00e1ticas, Universidad Cat\u00f3lica del Norte, Avda. Angamos 0610, Casilla 1280, Antofagasta 1270709, Chile"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1753","DOI":"10.1142\/S021827180600942X","article-title":"Dynamics of dark energy","volume":"15","author":"Copeland","year":"2006","journal-title":"Int. J. Mod. Phys. D"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2010.04.001","article-title":"Quintom Cosmology: Theoretical implications and observations","volume":"493","author":"Cai","year":"2010","journal-title":"Phys. Rept."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1103\/RevModPhys.78.537","article-title":"Inflation dynamics and reheating","volume":"78","author":"Bassett","year":"2006","journal-title":"Rev. Mod. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Saridakis, E.N., Lazkoz, R., Salzano, V., Moniz, P.V., Capozziello, S., Jim\u00e9nez, J.B., De Laurentis, M., and Olmo, G.J. (2021). [CANTATA]. Modified Gravity and Cosmology: An Update by the CANTATA Network, Springer.","DOI":"10.1007\/978-3-030-83715-0"},{"key":"ref_5","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. Rep."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.jheap.2022.04.002","article-title":"Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies","volume":"34","author":"Abdalla","year":"2022","journal-title":"J. High Energy Astrophys."},{"key":"ref_7","unstructured":"Batista, R.A., Amelino-Camelia, G., Boncioli, D., Carmona, J.M., di Matteo, A., Gubitosi, G., Lobo, I., Mavromatos, N.E., Pfeifer, C., and Rubiera-Garcia, D. (2023). White Paper and Roadmap for Quantum Gravity Phenomenology in the Multi-Messenger Era. arXiv."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/0370-2693(80)90670-X","article-title":"A New Type of Isotropic Cosmological Models Without Singularity","volume":"91","author":"Starobinsky","year":"1980","journal-title":"Phys. Lett. B"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3","DOI":"10.12942\/lrr-2010-3","article-title":"f(R) theories","volume":"13","author":"Tsujikawa","year":"2010","journal-title":"Living Rev. Relativ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physletb.2005.10.010","article-title":"Modified Gauss-Bonnet theory as gravitational alternative for dark energy","volume":"631","author":"Nojiri","year":"2005","journal-title":"Phys. Lett. B"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"063516","DOI":"10.1103\/PhysRevD.80.063516","article-title":"Solar system constraints on f(G) gravity models","volume":"80","author":"Tsujikawa","year":"2009","journal-title":"Phys. Rev. D"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"123527","DOI":"10.1103\/PhysRevD.99.123527","article-title":"Cosmology in cubic and f(P) gravity","volume":"99","author":"Erices","year":"2019","journal-title":"Phys. Rev. D"},{"key":"ref_13","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_14","doi-asserted-by":"crossref","unstructured":"Aldrovandi, R., and Pereira, J.G. (2013). Teleparallel Gravity, Springer Science + Business Media.","DOI":"10.1007\/978-94-007-5143-9"},{"key":"ref_15","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":"Annalen Phys."},{"key":"ref_16","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_17","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_18","doi-asserted-by":"crossref","first-page":"101513","DOI":"10.1016\/j.dark.2024.101513","article-title":"EDSFD parameterization in f(R,T) gravity with linear curvature terms","volume":"45","author":"Singh","year":"2024","journal-title":"Phys. Dark Univ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"100876","DOI":"10.1016\/j.ascom.2024.100876","article-title":"Late time phantom characteristic of the model in f(R,T) gravity with quadratic curvature term","volume":"49","author":"Shaily","year":"2024","journal-title":"Astron. Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"100795","DOI":"10.1016\/j.ascom.2024.100795","article-title":"The constrained accelerating universe in f(R,T) gravity","volume":"46","author":"Singh","year":"2024","journal-title":"Astron. Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"123536","DOI":"10.1103\/PhysRevD.97.123536","article-title":"Bouncing cosmology in f(R,T) gravity","volume":"97","author":"Singh","year":"2018","journal-title":"Phys. Rev. D"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"169781","DOI":"10.1016\/j.aop.2024.169781","article-title":"The consequence of higher-order curvature-based constraints on f(R,Lm) gravity","volume":"469","author":"Singh","year":"2024","journal-title":"Annals Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/j.cjph.2023.05.019","article-title":"Bouncing universe in modified Gauss\u2013Bonnet gravity","volume":"84","author":"Singh","year":"2023","journal-title":"Chin. J. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/JHEP03(2023)191","article-title":"Bouncing cosmology in modified gravity with higher-order curvature terms","volume":"3","author":"Singh","year":"2023","journal-title":"J. High Energ. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2300244","DOI":"10.1002\/prop.202300244","article-title":"Bouncing Cosmology in f(R,G) Gravity with Thermodynamic Analysis","volume":"72","author":"Shaily","year":"2024","journal-title":"Fortsch. Phys."},{"key":"ref_26","first-page":"113","article-title":"Symmetric teleparallel general relativity","volume":"37","author":"Nester","year":"1999","journal-title":"Chin. J. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.jheap.2024.06.011","article-title":"FLRW cosmology in Weyl type f(Q) gravity and observational constraints","volume":"43","author":"Goswami","year":"2024","journal-title":"J. High Energy Astrophys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"044048","DOI":"10.1103\/PhysRevD.98.044048","article-title":"Coincident General Relativity","volume":"98","author":"Heisenberg","year":"2018","journal-title":"Phys. Rev. D"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2024.02.001","article-title":"Review on f(Q) Gravity","volume":"1066","author":"Heisenberg","year":"2024","journal-title":"Phys. Rept."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/s10509-012-1181-8","article-title":"Dark energy cosmology: The equivalent description via different theoretical models and cosmography tests","volume":"342","author":"Bamba","year":"2012","journal-title":"Astrophys. Space Sci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.physrep.2011.04.001","article-title":"Unified cosmic history in modified gravity: From F(R) theory to Lorentz non-invariant models","volume":"505","author":"Nojiri","year":"2011","journal-title":"Phys. Rep."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"245014","DOI":"10.1088\/0264-9381\/29\/24\/245014","article-title":"On the stability of the cosmological solutions in f(R,G) gravity","volume":"29","year":"2012","journal-title":"Class. Quantum Gravity"},{"key":"ref_33","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. Rep."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1016\/j.physletb.2014.01.066","article-title":"Energy conditions in modified gravity","volume":"730","author":"Capozziello","year":"2014","journal-title":"Phys. Lett. B"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"044023","DOI":"10.1103\/PhysRevD.91.044023","article-title":"Dynamical features of scalar-torsion theories","volume":"91","author":"Skugoreva","year":"2015","journal-title":"Phys. Rev. D"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"018","DOI":"10.1088\/1475-7516\/2015\/02\/018","article-title":"Exploring gravitational theories beyond Horndeski","volume":"02","author":"Gleyzes","year":"2015","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"104038","DOI":"10.1103\/PhysRevD.97.104038","article-title":"Generalized framework for testing gravity with gravitational-wave propagation. II. Constraints on Horndeski theory","volume":"97","author":"Arai","year":"2018","journal-title":"Phys. Rev. D"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"024020","DOI":"10.1103\/PhysRevD.84.024020","article-title":"f(R,T) gravity","volume":"84","author":"Harko","year":"2011","journal-title":"Phys. Rev. D"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1140\/epjc\/s10052-020-7827-8","article-title":"FLRW cosmology with EDSFD parametrization","volume":"80","author":"Singh","year":"2020","journal-title":"Eur. Phys. J. C"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1140\/epjc\/s10052-024-12582-3","article-title":"Cosmology of f(Q) gravity in non-flat Universe","volume":"84","author":"Shabani","year":"2024","journal-title":"Eur. Phys. J. C"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"084007","DOI":"10.1103\/PhysRevD.73.084007","article-title":"Dark energy in modified Gauss-Bonnet gravity: Late-time acceleration and the hierarchy problem","volume":"73","author":"Cognola","year":"2006","journal-title":"Phys. Rev. D"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"084051","DOI":"10.1103\/PhysRevD.105.084051","article-title":"Scalarization of Chern-Simons-Kerr black hole solutions and wormholes","volume":"105","author":"Chatzifotis","year":"2022","journal-title":"Phys. Rev. D"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"102070","DOI":"10.1016\/j.newast.2023.102070","article-title":"A constrained cosmological model in f(R,Lm) gravity","volume":"104","author":"Singh","year":"2023","journal-title":"New Astron."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"169382","DOI":"10.1016\/j.aop.2023.169382","article-title":"A non-singular bouncing cosmology in f(R,T) gravity","volume":"455","author":"Singh","year":"2023","journal-title":"Ann. Phys."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"104027","DOI":"10.1103\/PhysRevD.100.104027","article-title":"Observational constraints of f(Q) gravity","volume":"100","author":"Lazkoz","year":"2019","journal-title":"Phys. Rev. D"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"121301","DOI":"10.1103\/PhysRevD.101.121301","article-title":"Interpreting cosmological tensions from the effective field theory of torsional gravity","volume":"101","author":"Yan","year":"2020","journal-title":"Phys. Rev. D"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"137229","DOI":"10.1016\/j.physletb.2022.137229","article-title":"Model-independent reconstruction of f(Q) non-metric gravity","volume":"832","author":"Capozziello","year":"2022","journal-title":"Phys. Lett. B"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"084053","DOI":"10.1103\/PhysRevD.107.084053","article-title":"Thermal stability of hairy black holes","volume":"107","author":"Chatzifotis","year":"2023","journal-title":"Phys. Rev. D"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"116158","DOI":"10.1016\/j.nuclphysb.2023.116158","article-title":"Constant sound speed and its thermodynamical interpretation in f(Q) gravity","volume":"990","author":"Koussour","year":"2023","journal-title":"Nucl. Phys. B"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"024001","DOI":"10.1103\/PhysRevD.108.024001","article-title":"Regular compact objects with scalar hair","volume":"108","author":"Karakasis","year":"2023","journal-title":"Phys. Rev. D"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"138507","DOI":"10.1016\/j.physletb.2024.138507","article-title":"Gravitational wave signatures of no-scale Supergravity in NANOGrav and beyond","volume":"850","author":"Basilakos","year":"2024","journal-title":"Phys. Lett. B"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"055","DOI":"10.1088\/1475-7516\/2023\/11\/055","article-title":"Stealth Ellis wormholes in Horndeski theories","volume":"11","author":"Bakopoulos","year":"2023","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Boehmer, C.G., Jensko, E., and Lazkoz, R. (2023). Dynamical Systems Analysis of f(Q) Gravity. Universe, 9.","DOI":"10.3390\/universe9040166"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"103507","DOI":"10.1103\/PhysRevD.101.103507","article-title":"Cosmology in f(Q) geometry","volume":"101","author":"Heisenberg","year":"2020","journal-title":"Phys. Rev. D"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"063505","DOI":"10.1103\/PhysRevD.103.063505","article-title":"Observational constraints on cosmological solutions of f(Q) theories","volume":"103","author":"Ayuso","year":"2021","journal-title":"Phys. Rev. D"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"084061","DOI":"10.1103\/PhysRevD.105.084061","article-title":"Reconstructing isotropic and anisotropic f(Q) cosmologies","volume":"105","author":"Esposito","year":"2022","journal-title":"Phys. Rev. D"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"024009","DOI":"10.1103\/PhysRevD.99.024009","article-title":"Propagation of gravitational waves in symmetric teleparallel gravity theories","volume":"99","author":"Hohmann","year":"2019","journal-title":"Phys. Rev. D"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"124077","DOI":"10.1103\/PhysRevD.104.124077","article-title":"General covariant symmetric teleparallel cosmology","volume":"104","author":"Hohmann","year":"2021","journal-title":"Phys. Rev. D"},{"key":"ref_59","first-page":"039","article-title":"Teleparallel Palatini theories","volume":"08","author":"Heisenberg","year":"2018","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1140\/epjc\/s10052-019-7038-3","article-title":"Cosmology in symmetric teleparallel gravity and its dynamical system","volume":"79","author":"Lu","year":"2019","journal-title":"Eur. Phys. J. C"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"025013","DOI":"10.1088\/1361-6382\/ac3f99","article-title":"Revisiting cosmologies in teleparallelism","volume":"39","author":"Heisenberg","year":"2022","journal-title":"Class. Quantum Gravity"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"064046","DOI":"10.1103\/PhysRevD.103.064046","article-title":"Thick brane in f(T,B) gravity","volume":"103","author":"Moreira","year":"2021","journal-title":"Phys. Rev. D"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"136634","DOI":"10.1016\/j.physletb.2021.136634","article-title":"First evidence that non-metricity f(Q) gravity could challenge \u039bCDM","volume":"822","author":"Anagnostopoulos","year":"2021","journal-title":"Phys. Lett. B"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1103\/PhysRevD.104.064052","article-title":"Can f(Q) gravity challenge \u039bCDM?","volume":"104","author":"Atayde","year":"2021","journal-title":"Phys. Rev. D"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"024042","DOI":"10.1103\/PhysRevD.105.024042","article-title":"Black holes in f(Q) gravity","volume":"105","author":"Fell","year":"2022","journal-title":"Phys. Rev. D"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1140\/epjc\/s10052-022-10266-4","article-title":"Covariant formulation of f(Q) theory","volume":"82","author":"Zhao","year":"2022","journal-title":"Eur. Phys. J. C"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"048501","DOI":"10.1103\/PhysRevD.106.048501","article-title":"Comment on \u201cEnergy conditions in f(Q) gravity\u201d","volume":"106","author":"De","year":"2022","journal-title":"Phys. Rev. D"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"124001","DOI":"10.1103\/PhysRevD.103.124001","article-title":"Spherically symmetric configuration in f(Q) gravity","volume":"103","author":"Lin","year":"2021","journal-title":"Phys. Rev. D"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"100616","DOI":"10.1016\/j.dark.2020.100616","article-title":"Testing F(Q) gravity with redshift space distortions","volume":"30","author":"Barros","year":"2020","journal-title":"Phys. Dark Univ."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"124003","DOI":"10.1103\/PhysRevD.101.124003","article-title":"Well-posed formulation of Lovelock and Horndeski theories","volume":"101","author":"Reall","year":"2020","journal-title":"Phys. Rev. D"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"640","DOI":"10.1140\/epjc\/s10052-020-8204-3","article-title":"Cosmological bouncing solutions in f(T,B) gravity","volume":"80","author":"Caruana","year":"2020","journal-title":"Eur. Phys. J. C"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"103521","DOI":"10.1103\/PhysRevD.103.103521","article-title":"Cosmological solutions and growth index of matter perturbations in f(Q) gravity","volume":"103","author":"Khyllep","year":"2021","journal-title":"Phys. Rev. D"},{"key":"ref_73","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_74","doi-asserted-by":"crossref","first-page":"050","DOI":"10.1088\/1475-7516\/2024\/03\/050","article-title":"Non-metricity with bounday terms: f(Q,C) gravity and cosmology","volume":"03","author":"De","year":"2024","journal-title":"JCAP"},{"key":"ref_75","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_76","doi-asserted-by":"crossref","first-page":"175011","DOI":"10.1088\/0264-9381\/31\/17\/175011","article-title":"Dynamical behavior in f(T,TG) cosmology","volume":"31","author":"Kofinas","year":"2014","journal-title":"Class. Quantum Gravity"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"084045","DOI":"10.1103\/PhysRevD.90.084045","article-title":"Cosmological applications of F(T,TG) gravity","volume":"90","author":"Kofinas","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"100724","DOI":"10.1016\/j.dark.2020.100724","article-title":"Generalized gravitational baryogenesis of well-known f(T,TG) and f(T,B) models","volume":"30","author":"Azhar","year":"2020","journal-title":"Phys. Dark Univ."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1140\/epjc\/s10052-016-4491-0","article-title":"Noether symmetries in Gauss\u2013Bonnet-teleparallel cosmology","volume":"76","author":"Capozziello","year":"2016","journal-title":"Eur. Phys. J. C"},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"104040","DOI":"10.1103\/PhysRevD.97.104040","article-title":"Cosmological bouncing solutions in extended teleparallel gravity theories","volume":"97","author":"Farrugia","year":"2018","journal-title":"Phys. Rev. D"},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/s10509-014-2029-1","article-title":"Pilgrim dark energy in f(T,TG) cosmology","volume":"353","author":"Chattopadhyay","year":"2014","journal-title":"Astrophys. Space Sci."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/s10509-015-2527-9","article-title":"Generalized Second Law of Thermodynamics in f(T,TG) gravity","volume":"360","author":"Zubair","year":"2015","journal-title":"Astrophys. Space Sci."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"1750083","DOI":"10.1142\/S0217732317500833","article-title":"Noncommutative wormhole solutions in F(T, TG) gravity","volume":"32","author":"Sharif","year":"2017","journal-title":"Mod. Phys. Lett. A"},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1016\/j.cjph.2019.05.025","article-title":"Wormhole solutions in F(T,TG) gravity under Gaussian and Lorentzian non-commutative distributions with conformal motions","volume":"60","author":"Mustafa","year":"2019","journal-title":"Chin. J. Phys."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"084010","DOI":"10.1103\/PhysRevD.105.084010","article-title":"Big bang nucleosynthesis constraints on higher-order modified gravities","volume":"105","author":"Asimakis","year":"2022","journal-title":"Phys. Rev. D"},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"235011","DOI":"10.1088\/1361-6382\/aa93c8","article-title":"Cosmological reconstructed solutions in extended teleparallel gravity theories with a teleparallel Gauss\u2013Bonnet term","volume":"34","author":"Farrugia","year":"2017","journal-title":"Class. Quantum Gravity"},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"101164","DOI":"10.1016\/j.dark.2022.101164","article-title":"Analyzing the geometrical and dynamical parameters of modified Teleparallel-Gauss\u2013Bonnet model","volume":"39","author":"Lohakare","year":"2023","journal-title":"Phys. Dark Univ."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"578","DOI":"10.1140\/epjc\/s10052-016-4419-8","article-title":"Modified teleparallel theories of gravity: Gauss\u2013Bonnet and trace extensions","volume":"76","author":"Bahamonde","year":"2016","journal-title":"Eur. Phys. J. C"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"045017","DOI":"10.1088\/1402-4896\/acc0ac","article-title":"Noether symmetries in f(T, T G) cosmology","volume":"98","author":"Kadam","year":"2023","journal-title":"Phys. Scr."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"2153","DOI":"10.1088\/0264-9381\/24\/8\/013","article-title":"Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach","volume":"24","author":"Capozziello","year":"2007","journal-title":"Class. Quantum Gravity"},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"104042","DOI":"10.1103\/PhysRevD.89.104042","article-title":"New Schwarzschild-like solutions in f(T) gravity through Noether symmetries","volume":"89","author":"Paliathanasis","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physletb.2009.03.060","article-title":"Construction of cosmologically viable f(G) dark energy models","volume":"675","author":"Tsujikawa","year":"2009","journal-title":"Phys. Lett. B"},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1140\/epjp\/i2013-13088-x","article-title":"Reconstruction of f(G) Gravity with New Agegraphic Dark Energy Model","volume":"128","author":"Jawad","year":"2013","journal-title":"Eur. Phys. J. Plus"},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"183001","DOI":"10.1088\/1361-6382\/ab2e1f","article-title":"Teleparallel theories of gravity: Illuminating a fully invariant approach","volume":"36","author":"Krssak","year":"2019","journal-title":"Class. Quantum Gravity"},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"026901","DOI":"10.1088\/1361-6633\/ac9cef","article-title":"Teleparallel gravity: From theory to cosmology","volume":"86","author":"Bahamonde","year":"2023","journal-title":"Rep. Prog. Phys."},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1086\/670067","article-title":"emcee: The MCMC Hammer","volume":"125","author":"Hogg","year":"2013","journal-title":"Publ. Astron. Soc. Pac."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"101","DOI":"10.3847\/1538-4357\/aab9bb","article-title":"[Pan-STARRS1]. The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample","volume":"859","author":"Scolnic","year":"2018","journal-title":"Astrophys. J."},{"key":"ref_98","first-page":"1","article-title":"How predictions of cosmological models depend on Hubble parameter data sets","volume":"6","author":"Sharov","year":"2018","journal-title":"Math. Model. Geom."},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.physletb.2008.07.064","article-title":"Unified model of baryonic matter and dark components","volume":"666","author":"Chimento","year":"2008","journal-title":"Phys. Lett. B"},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"2350040","DOI":"10.1142\/S0218271823500402","article-title":"The constrained cosmological model in Lyra geometry","volume":"32","author":"Singh","year":"2023","journal-title":"Int. J. Mod. Phys. D"},{"key":"ref_101","doi-asserted-by":"crossref","unstructured":"Singh, J.K., Singh, P., Saridakis, E.N., Myrzakul, S., and Balhara, H. (2024). New parametrization of the dark-energy equation of state with a single parameter. Universe, 10.","DOI":"10.3390\/universe10060246"},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"103502","DOI":"10.1103\/PhysRevD.78.103502","article-title":"Two new diagnostics of dark energy","volume":"78","author":"Sahni","year":"2008","journal-title":"Phys. Rev. D"},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"1541","DOI":"10.1007\/s10714-005-0134-8","article-title":"Cosmography: Cosmology without the Einstein equations","volume":"37","author":"Visser","year":"2005","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"1510","DOI":"10.1111\/j.1365-2966.2006.11419.x","article-title":"A kinematical approach to dark energy studies","volume":"375","author":"Rapetti","year":"2007","journal-title":"Mon. Not. Roy. Astron. Soc."},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1140\/epjc\/s10052-023-11545-4","article-title":"Revisiting cosmography via Gaussian process","volume":"83","author":"Liu","year":"2023","journal-title":"Eur. Phys. J. C"},{"key":"ref_106","doi-asserted-by":"crossref","first-page":"A96","DOI":"10.1051\/0004-6361\/201220724","article-title":"Baryon Acoustic Oscillations in the Ly-\u03b1 forest of BOSS quasars","volume":"552","author":"Busca","year":"2013","journal-title":"Astron. Astrophys."},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"L7","DOI":"10.1088\/2041-8205\/766\/1\/L7","article-title":"Hubble parameter measurement constraints on the cosmological deceleration-acceleration transition redshift","volume":"766","author":"Farooq","year":"2013","journal-title":"Astrophys. J. Lett."},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"044016","DOI":"10.1103\/PhysRevD.90.044016","article-title":"Cosmographic bounds on the cosmological deceleration-acceleration transition redshift in f(R) gravity","volume":"90","author":"Capozziello","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_109","doi-asserted-by":"crossref","first-page":"103506","DOI":"10.1103\/PhysRevD.89.103506","article-title":"Cosmographic analysis of the equation of state of the universe through Pad\u00e9 approximations","volume":"89","author":"Gruber","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"059","DOI":"10.1088\/1475-7516\/2020\/06\/059","article-title":"The evidence of cosmic acceleration and observational constraints","volume":"06","author":"Yang","year":"2020","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_111","doi-asserted-by":"crossref","first-page":"123516","DOI":"10.1103\/PhysRevD.86.123516","article-title":"Cosmography and constraints on the equation of state of the Universe in various parametrizations","volume":"86","author":"Aviles","year":"2012","journal-title":"Phys. Rev. D"},{"key":"ref_112","doi-asserted-by":"crossref","first-page":"043531","DOI":"10.1103\/PhysRevD.90.043531","article-title":"Precision cosmology with Pad\u00e9 rational approximations: Theoretical predictions versus observational limits","volume":"90","author":"Aviles","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_113","doi-asserted-by":"crossref","first-page":"124037","DOI":"10.1103\/PhysRevD.91.124037","article-title":"Transition redshift in f(T) cosmology and observational constraints","volume":"91","author":"Capozziello","year":"2015","journal-title":"Phys. Rev. D"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/10\/1299\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:09:24Z","timestamp":1760112564000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/10\/1299"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,2]]},"references-count":113,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2024,10]]}},"alternative-id":["sym16101299"],"URL":"https:\/\/doi.org\/10.3390\/sym16101299","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,2]]}}}