{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:49:11Z","timestamp":1760230151281,"version":"build-2065373602"},"reference-count":54,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,12]],"date-time":"2022-07-12T00:00:00Z","timestamp":1657584000000},"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 have considered the holographic dark energy and modified holographic Ricci dark energy models to analyze the time-dependent gravitational constant G(t) and cosmological constant \u039b(t) in the context of Chern\u2013Simons modified gravity theory. The FRW metric is used to examine the physical and kinematical properties of these models, which predicted the accelerated expansion phase of universe. Further, the \u039b(t) showed increasing trends while G(t) showed decreasing trends for both cases. Finally, the range \u22121.99\u00d710\u221210yr\u22121\u2264G\u02d9G\u22640 was estimated mathematically, which is similar to the results obtained from observational data.<\/jats:p>","DOI":"10.3390\/sym14071430","type":"journal-article","created":{"date-parts":[[2022,7,12]],"date-time":"2022-07-12T23:02:01Z","timestamp":1657666921000},"page":"1430","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Note on Varying G and \u039b in Chern\u2013Simons Modified Gravity"],"prefix":"10.3390","volume":"14","author":[{"given":"Sarfraz","family":"Ali","sequence":"first","affiliation":[{"name":"Department of Mathematics, Division of Science and Technology, University of Education, Lahore 38000, Pakistan"}]},{"given":"Maryam","family":"Saif","sequence":"additional","affiliation":[{"name":"Faisalabad Campus, Riphah International University, Islamabad 38000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3468-2295","authenticated-orcid":false,"given":"Khuram Ali","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan"}]},{"given":"Nehad Ali","family":"Shah","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9595-6096","authenticated-orcid":false,"given":"Wajaree","family":"Weera","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1086\/300499","article-title":"Observational evidence from supernovae for an accelerating universe and a cosmological constant","volume":"116","author":"Riess","year":"1998","journal-title":"Astron. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1086\/307221","article-title":"Measurements of \u03a9 and \u039b from 42 high-redshift supernovae","volume":"517","author":"Perlmutter","year":"1999","journal-title":"Astrophys. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"104012","DOI":"10.1103\/PhysRevD.68.104012","article-title":"Chern-Simons modification of general relativity","volume":"68","author":"Jackiw","year":"2003","journal-title":"Phys. Rev. D"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2009.07.002","article-title":"Chern-Simons modified general relativity","volume":"480","author":"Alexander","year":"2009","journal-title":"Phys. Rep."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"024015","DOI":"10.1103\/PhysRevD.77.024015","article-title":"Effects of Chern-Simons gravity on bodies orbiting the Earth","volume":"77","author":"Smith","year":"2008","journal-title":"Phys. Rev. D"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physletb.2004.10.014","article-title":"A model of holographic dark energy","volume":"603","author":"Li","year":"2004","journal-title":"Phys. Lett. B"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"107302","DOI":"10.1103\/PhysRevD.84.107302","article-title":"Holographic Scalar Fields Models of Dark Energy","volume":"84","author":"Sheykhi","year":"2011","journal-title":"Phys. Rev. D"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"123510","DOI":"10.1103\/PhysRevD.73.123510","article-title":"Interacting dark energy, holographic principle and coincidence problem","volume":"73","author":"Hu","year":"2006","journal-title":"Phys. Rev. D"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1140\/epjc\/s10052-009-0876-7","article-title":"Features of holographic dark energy under the combined cosmological constraints","volume":"60","author":"Ma","year":"2009","journal-title":"Eur. Phys. J. C"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.physletb.2004.05.020","article-title":"Entropy bounds and dark energy","volume":"594","author":"Hsu","year":"2004","journal-title":"Phys. Lett. B"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"063003","DOI":"10.1103\/PhysRevD.76.063003","article-title":"Age Problem in the Holographic Dark Energy Model","volume":"76","author":"Wei","year":"2007","journal-title":"Phys. Rev. D"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"043511","DOI":"10.1103\/PhysRevD.79.043511","article-title":"Holographic dark energy model from Ricci scalar curvature","volume":"79","author":"Gao","year":"2009","journal-title":"Phys. Rev. D"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/j.physletb.2008.10.017","article-title":"Infrared cut-off proposal for the holographic density","volume":"669","author":"Granda","year":"2008","journal-title":"Phys. Lett. B"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/j.physletb.2008.12.025","article-title":"New infrared cut-off for the holographic scalar fields models of dark energy","volume":"671","author":"Granda","year":"2009","journal-title":"Phys. Lett. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.physletb.2009.12.060","article-title":"New holographic scalar field models of dark energy in non-flat universe","volume":"684","author":"Karami","year":"2010","journal-title":"Phys. Lett. B"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2017.06.003","article-title":"Holographic Dark Energy","volume":"696","author":"Wang","year":"2017","journal-title":"Phys. Rep."},{"key":"ref_17","unstructured":"\u0165Hooft, G. (1993). Dimensional reduction in quantum gravity. arXiv."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1140\/epjc\/s10052-017-5097-x","article-title":"Covariant generalized holographic dark energy and accelerating universe","volume":"77","author":"Nojiri","year":"2017","journal-title":"Eur. Phys. J. C"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1140\/epjc\/s10052-019-6740-5","article-title":"Modified cosmology from extended entropy with varying exponent","volume":"79","author":"Nojiri","year":"2019","journal-title":"Eur. Phys. J. C"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"134829","DOI":"10.1016\/j.physletb.2019.134829","article-title":"Holographic inflation","volume":"797","author":"Nojiri","year":"2019","journal-title":"Phys. Lett. B"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"023450","DOI":"10.1103\/PhysRevD.102.023540","article-title":"Unifying holographic inflation with holographic dark energy","volume":"102","author":"Nojiri","year":"2020","journal-title":"Phys. Rev. D"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Nojiri, S., Odintsov, S.D., and Paul, T. (2021). Different faces of generalized holographic dark energy. Symmetry, 13.","DOI":"10.3390\/sym13060928"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"954","DOI":"10.1088\/0253-6102\/51\/5\/39","article-title":"Holography, UV\/IR relation, causal entropy bound, and dark energy","volume":"51","author":"Cai","year":"2009","journal-title":"Commun. Theor. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2500","DOI":"10.1140\/epjc\/s10052-013-2500-0","article-title":"Ricci dark energy in Chern\u2013Simons modified gravity","volume":"73","author":"Silva","year":"2013","journal-title":"Eur. Phys. J. C"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1362","DOI":"10.1007\/s10773-014-2334-z","article-title":"Ricci dark dnergy of Amended FRW universe in Chern-Simon modified gravity","volume":"54","author":"Amir","year":"2015","journal-title":"Int. J. Theor. Phys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3709472","DOI":"10.1155\/2019\/3709472","article-title":"Cosmological analysis of modified holographic Ricci dark energy in Chern-Simons modified gravity","volume":"2019","author":"Ali","year":"2019","journal-title":"Adv. High Energy Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5095","DOI":"10.1007\/s10773-016-3131-7","article-title":"A study of holographic dark energy models in Chern-Simon modified gravity","volume":"55","author":"Amir","year":"2016","journal-title":"Int. J. Theor. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1140\/epjc\/s10052-014-3256-x","article-title":"Holographic dark energy models and higher order generalizations in dynamical Chern-Simons modified gravity","volume":"75","author":"Pasqua","year":"2015","journal-title":"Eur. Phys. J. C"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1140\/epjc\/s10052-018-6309-8","article-title":"Thermodynamic approach to holographic dark energy and the R\u00e9nyi entropy","volume":"78","author":"Moradpour","year":"2018","journal-title":"Eur. Phys. J. C"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"104057","DOI":"10.1103\/PhysRevD.94.104057","article-title":"On the causality aspects of the dynamical Chern-Simons modified gravity","volume":"94","author":"Porfirio","year":"2016","journal-title":"Phys. Rev. D"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"024037","DOI":"10.1103\/PhysRevD.78.024037","article-title":"Flat rotation curves in Chern-Simons modified gravity","volume":"78","author":"Konno","year":"2008","journal-title":"Phys. Rev. D"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"044011","DOI":"10.1103\/PhysRevD.76.044011","article-title":"Papapetrou energy-momentum tensor for Chern-Simons modified gravity","volume":"76","author":"Guarrera","year":"2007","journal-title":"Phys. Rev. D"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"083006","DOI":"10.1103\/PhysRevD.79.083006","article-title":"Quantum phase shift in Chern-Simons modified gravity","volume":"79","author":"Nandi","year":"2009","journal-title":"Phys. Rev. D"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1791","DOI":"10.1142\/S0218271807011097","article-title":"Dark energy models with a time-dependent gravitational constant","volume":"16","author":"Ray","year":"2007","journal-title":"Int. J. Mod. Phys. D"},{"key":"ref_35","first-page":"3","article-title":"Time Dependent Gravitational Constant in Chern Simons Modified Gravity","volume":"21","author":"Sarfraz","year":"2021","journal-title":"Iran. J. Phys. Res."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Alfedeel, A.H.A., Abebe, A., and Gubara, H.M. (2018). A generalized solution of Bianchi type-V models with time-dependent G and \u039b. Universe, 4.","DOI":"10.3390\/universe4080083"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2050076","DOI":"10.1142\/S0219887820500760","article-title":"Bianchi type-V solutions with varying and: The general case","volume":"17","author":"Alfedeel","year":"2020","journal-title":"Int. J. Geom. Methods Mod. Phys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"4971","DOI":"10.1103\/PhysRevLett.82.4971","article-title":"Effective field theory, black holes, and the cosmological constant","volume":"82","author":"Cohen","year":"1999","journal-title":"Phys. Rev. Lett."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"233001","DOI":"10.1088\/0264-9381\/27\/23\/233001","article-title":"Gravitational lensing","volume":"27","author":"Bartelmann","year":"2010","journal-title":"Class. Quantum Grav."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1086\/340230","article-title":"Prospects for determining the equation of state of the dark energy: What can be learned from multiple observables?","volume":"572","author":"Kujat","year":"2002","journal-title":"Astrophys. J."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1086\/378560","article-title":"New constraints on \u03a9M, \u03a9\u039b, and \u03c9 from an independent set of 11 high-redshift supernovae observed with the Hubble Space Telescope","volume":"598","author":"Knop","year":"2003","journal-title":"Astrophys. J."},{"key":"ref_42","first-page":"70","article-title":"The 3D power spectrum of galaxies from the SDSS","volume":"606","author":"Tegmark","year":"2004","journal-title":"Astrophys. J."},{"key":"ref_43","unstructured":"Addazi, A. (2020). Holographic naturalness and cosmological relaxation. arXiv."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1007\/BF00755985","article-title":"A critical density cosmological model with varying gravitational and cosmological \u201cConstants\u201d","volume":"22","author":"Rahaman","year":"1990","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_45","first-page":"9","article-title":"Nonlinear density response and higher order correlation","volume":"595","year":"2004","journal-title":"Phys. Lett. B"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1086\/305567","article-title":"The age of globular clusters in light of hipparcos: Resolving the age problem?","volume":"2","author":"Guenther","year":"1998","journal-title":"Astrophys. J."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1007\/s00159-006-0004-8","article-title":"Astronomical measurements and constraints on the variability of fundamental constants","volume":"14","author":"Isern","year":"2007","journal-title":"Astron. Astrophys. Rev."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.1103\/PhysRevLett.61.1151","article-title":"Equation of state and the maximum mass of neutron stars","volume":"61","author":"Damour","year":"1988","journal-title":"Phys. Rev. Lett."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1111\/j.1365-2966.2004.07677.x","article-title":"A new white dwarf constraints on the rate of chage of gravitational constant","volume":"350","author":"Biesiada","year":"2004","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1140\/epjc\/s2004-01970-6","article-title":"Phantom appearance of non-phantom matter","volume":"36","year":"2004","journal-title":"Eur. Phys. J. C"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"043524","DOI":"10.1103\/PhysRevD.72.043524","article-title":"Constraints on holographic dark energy from type Ia supernova observations","volume":"72","author":"Zhang","year":"2005","journal-title":"Phys. Rev. D"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"023506","DOI":"10.1103\/PhysRevD.65.023506","article-title":"Bounds on the possible evolution of the gravitational constant from cosmological type-Ia supernovae","volume":"65","author":"Gaztanaga","year":"2001","journal-title":"Phys. Rev. D"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1007\/s10773-010-0639-0","article-title":"Phenomenology of Lambda-CDM model: A possibility of accelerating Universe with positive pressure","volume":"50","author":"Ray","year":"2011","journal-title":"Int. J. Theor. Phys."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1023\/A:1016390025190","article-title":"Cosmological models with \u2018some\u2019 variable constants","volume":"281","year":"2002","journal-title":"Astrophys. Space Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/7\/1430\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:48:42Z","timestamp":1760140122000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/7\/1430"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,12]]},"references-count":54,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["sym14071430"],"URL":"https:\/\/doi.org\/10.3390\/sym14071430","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,7,12]]}}}