{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T02:38:43Z","timestamp":1761964723978,"version":"build-2065373602"},"reference-count":94,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2016,2,22]],"date-time":"2016-02-22T00:00:00Z","timestamp":1456099200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Polish National Science Center","award":["DEC-2012\/06\/A\/ST2\/00395"],"award-info":[{"award-number":["DEC-2012\/06\/A\/ST2\/00395"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We formulate the basic framework of thermodynamical entropic force cosmology which allows variation of the gravitational constant G and the speed of light c. Three different approaches to the formulation of the field equations are presented. Some cosmological solutions for each framework are given and one of them is tested against combined observational data (supernovae, BAO, and CMB). From the fit of the data, it is found that the Hawking temperature numerical coefficient \u03b3 is two to four orders of magnitude less than usually assumed on the geometrical ground theoretical value of  O(1)                                  and that it is also compatible with zero. In addition, in the entropic scenario, we observationally test that the fit of the data is allowed for the speed of light c growing and the gravitational constant G diminishing during the evolution of the universe. We also obtain a bound on the variation of c to be                                        \u0394c \/               c \u221d                                10-5 &gt;               0                                 , which is at least one order of magnitude weaker than the quasar spectra observational bound.<\/jats:p>","DOI":"10.3390\/e18020060","type":"journal-article","created":{"date-parts":[[2016,2,22]],"date-time":"2016-02-22T10:24:17Z","timestamp":1456136657000},"page":"60","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Varying Constants Entropic-\u039bCDM Cosmology"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8722-9470","authenticated-orcid":false,"given":"Mariusz","family":"Da\u0327browski","sequence":"first","affiliation":[{"name":"Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland"},{"name":"National Centre for Nuclear Research, Andrzeja So\u0142tana 7, 05-400 Otwock, Poland"},{"name":"Copernicus Center for Interdisciplinary Studies, S\u0142awkowska 17, 31-016 Krak\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6862-0869","authenticated-orcid":false,"given":"Hussain","family":"Gohar","sequence":"additional","affiliation":[{"name":"Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vincenzo","family":"Salzano","sequence":"additional","affiliation":[{"name":"Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,2,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ellis, G.F.R., Maartens, R., and MacCallum, M.A.H. (2012). Relativistic Cosmology, Cambridge University Press.","DOI":"10.1017\/CBO9781139014403"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1086\/307221","article-title":"Measurements of Omega and Lambda from 42 high redshift supernovae","volume":"517","author":"Perlmutter","year":"1999","journal-title":"Astrophys. J."},{"key":"ref_3","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_4","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1086\/162425","article-title":"Tests of cosmological models constrained by inflation","volume":"284","author":"Peebles","year":"1984","journal-title":"Astrophys. J."},{"key":"ref_5","first-page":"271","article-title":"Effect of the cosmological constant on large-scale anisotropies in the microwave background","volume":"11","author":"Kofman","year":"1985","journal-title":"Sov. Astron. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1016\/0003-4916(86)90145-4","article-title":"Analytic Solutions of Friedman Equation for Spatially Opened Universes with Cosmological, Constant and Radiation Pressure","volume":"166","author":"Stelmach","year":"1986","journal-title":"J. Ann. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Weinberg, S. (1989). The cosmological constant problem. Rev. Mod. Phys., 61.","DOI":"10.1103\/RevModPhys.61.1"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1088\/0253-6102\/56\/3\/24","article-title":"Dark Energy","volume":"56","author":"Miao","year":"2011","journal-title":"Commun. Theor. Phys."},{"key":"ref_9","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_10","doi-asserted-by":"crossref","first-page":"2333","DOI":"10.1103\/PhysRevD.7.2333","article-title":"Black holes and entropy","volume":"7","author":"Bekenstein","year":"1973","journal-title":"Phys. Rev. D"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3292","DOI":"10.1103\/PhysRevD.9.3292","article-title":"Generalized second law of thermodynamics in black hole physics","volume":"9","author":"Bekenstein","year":"1974","journal-title":"Phys. Rev. D"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3077","DOI":"10.1103\/PhysRevD.12.3077","article-title":"Statistical Black Hole Thermodynamics","volume":"12","author":"Bekenstein","year":"1975","journal-title":"Phys. Rev. D"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1038\/248030a0","article-title":"Black hole explosions","volume":"248","author":"Hawking","year":"1974","journal-title":"Nature"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1260","DOI":"10.1103\/PhysRevLett.75.1260","article-title":"Thermodynamics of space-time: The Einstein equation of state","volume":"75","author":"Jacobson","year":"1995","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/JHEP04(2011)029","article-title":"On the Origin of Gravity and the Laws of Newton","volume":"2011","author":"Verlinde","year":"2011","journal-title":"J. High Energy Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4485","DOI":"10.1088\/0264-9381\/21\/18\/013","article-title":"Gravitational entropy of static space-times and microscopic density of states","volume":"21","author":"Padmanabhan","year":"2004","journal-title":"Class. Quant. Grav."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"046901","DOI":"10.1088\/0034-4885\/73\/4\/046901","article-title":"Thermodynamical Aspects of Gravity: New Insights","volume":"73","author":"Padmanabhan","year":"2010","journal-title":"Rep. Prog. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1129","DOI":"10.1142\/S021773231003313X","article-title":"Equipartition of energy in the horizon degrees of freedom and the emergence of gravity","volume":"25","author":"Padmanabhan","year":"2010","journal-title":"Mod. Phys. Lett. A"},{"key":"ref_19","unstructured":"Hooft, G.\u2019t (1993). Dimensional reduction in quantum gravity."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"021502","DOI":"10.1103\/PhysRevD.83.021502","article-title":"Gravity is not an entropic force","volume":"83","author":"Kobakhidze","year":"2011","journal-title":"Phys. Rev. D"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"043531","DOI":"10.1103\/PhysRevD.87.043531","article-title":"Non-adiabatic-like accelerated expansion of the late universe in entropic cosmology","volume":"87","author":"Komatsu","year":"2013","journal-title":"Phys. Rev. D"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"083534","DOI":"10.1103\/PhysRevD.88.083534","article-title":"Entropic cosmology for a generalized black-hole entropy","volume":"88","author":"Komatsu","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"123501","DOI":"10.1103\/PhysRevD.89.123501","article-title":"Evolution of the universe in entropic cosmologies via different formulations","volume":"89","author":"Komatsu","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Komatsu, N. (2013, January 14\u201319). Entropic cosmology from a thermodynamics viewpoint. Proceedings of the 12th Asia Pacific Physics Conference (APPC12), Kanazawa, Japan.","DOI":"10.7566\/JPSCP.1.013112"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.physletb.2010.05.033","article-title":"Entropic cosmology: A unified model of inflation and late-time acceleration","volume":"690","author":"Cai","year":"2010","journal-title":"Phys. Lett. B"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1016\/j.physletb.2011.02.020","article-title":"Inflation in Entropic Cosmology: Primordial Perturbations and non-Gaussianities","volume":"697","author":"Cai","year":"2011","journal-title":"Phys. Lett. B"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"043504","DOI":"10.1103\/PhysRevD.85.043504","article-title":"Entropic Force Scenarios and Eternal Inflation","volume":"85","author":"Qiu","year":"2012","journal-title":"Phys. Rev. D"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/j.physletb.2010.12.025","article-title":"Entropic Accelerating Universe","volume":"696","author":"Easson","year":"2011","journal-title":"Phys. Lett. B"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"125066","DOI":"10.1142\/S0217751X12500662","article-title":"Entropic Inflation","volume":"27","author":"Easson","year":"2012","journal-title":"Int. J. Mod. Phys. A"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1088\/1475-7516\/2011\/02\/027","article-title":"Constraining entropic cosmology","volume":"2011","author":"Koivisto","year":"2011","journal-title":"J. Cosmol. Astrop. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"043010","DOI":"10.1103\/PhysRevD.86.043010","article-title":"Generalizing the running vacuum energy model and comparing with the entropic-force models","volume":"86","author":"Basilakos","year":"2012","journal-title":"Phys. Rev. D"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"023008","DOI":"10.1103\/PhysRevD.90.023008","article-title":"Entropic-force dark energy reconsidered","volume":"90","author":"Basilakos","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2810","DOI":"10.1093\/mnras\/stv209","article-title":"Vacuum models with a linear and a quadratic term in H: Structure formation and number counts analysis","volume":"448","year":"2015","journal-title":"Mon. Not. Roy. Astron. Soc."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Cai, R.G., and Kim, S.P. (2005). First law of thermodynamics and Friedmann equations of Friedmann-Robertson-Walker universe. J. High Energy Phys.","DOI":"10.1088\/1126-6708\/2005\/02\/050"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"064008","DOI":"10.1103\/PhysRevD.75.064008","article-title":"Unified first law and thermodynamics of apparent horizon in FRW universe","volume":"75","author":"Cai","year":"2007","journal-title":"Phys. Rev. D"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Cai, R.G., Cao, L.M., and Hu, Y.P. (2008). Corrected Entropy-Area Relation and Modified Friedmann Equations. J. High Energy Phys., 2008.","DOI":"10.1088\/1126-6708\/2008\/08\/090"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.physletb.2006.02.035","article-title":"Friedmann equations of FRW universe in scalar-tensor gravity, f(R) gravity and first law of thermodynamics","volume":"635","author":"Akbar","year":"2006","journal-title":"Phys. Lett. B"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"81003","DOI":"10.1103\/PhysRevD.75.084003","article-title":"Thermodynamic Behavior of Friedmann Equations at Apparent Horizon of FRW Universe","volume":"75","author":"Akbar","year":"2007","journal-title":"Phys. Rev. D"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.physletb.2007.03.005","article-title":"Thermodynamic Behavior of Field Equations for f(R) Gravity","volume":"648","author":"Akbar","year":"2007","journal-title":"Phys. Lett. B"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"121301","DOI":"10.1103\/PhysRevLett.96.121301","article-title":"Non-equilibrium thermodynamics of spacetime","volume":"96","author":"Eling","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/S0375-9601(99)00225-X","article-title":"Dynamic black hole entropy","volume":"256","author":"Hayward","year":"1999","journal-title":"Phys. Lett. A"},{"key":"ref_42","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 Grav."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"023516","DOI":"10.1103\/PhysRevD.71.023516","article-title":"Transplanckian energy production and slow roll inflation","volume":"71","author":"Danielsson","year":"2005","journal-title":"Phys. Rev. D"},{"key":"ref_44","unstructured":"Wang, Y. (2010). Towards a Holographic Description of Inflation and Generation of Fluctuations from Thermodynamics."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Visser, M. (2011). Conservative entropic forces. J. High Energy Phys., 2011.","DOI":"10.1007\/JHEP10(2011)140"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"083511","DOI":"10.1103\/PhysRevD.80.083511","article-title":"Hubble expansion and Structure Formation in Time Varying Vacuum Models","volume":"80","author":"Basilakos","year":"2009","journal-title":"Phys. Rev. D"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"105004","DOI":"10.1088\/0264-9381\/27\/10\/105004","article-title":"Cosmic perturbations with running G and Lambda","volume":"27","author":"Grande","year":"2010","journal-title":"Class. Quantum Grav."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Grande, J., Sol\u00e1, J., Basilakos, S., and Plionis, M. (2011). Hubble expansion and structure formation in the \u201drunning FLRW model\u201d of the cosmic evolution. J. Cosmol. Astrop. Phys.","DOI":"10.1088\/1475-7516\/2011\/08\/007"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"G\u00f3mez-Valent, A., Sol\u00e1, J., and Basilakos, S. (2015). Dynamical vacuum energy in the expanding Universe confronted with observations: A dedicated study. J. Cosmol. Astrop. Phys., 2015.","DOI":"10.1088\/1475-7516\/2015\/01\/004"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"L14","DOI":"10.1088\/2041-8205\/811\/1\/L14","article-title":"Hints of dynamical vacuum energy in the expanding Universe","volume":"811","year":"2015","journal-title":"Astrophys. J. Lett."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"043515","DOI":"10.1103\/PhysRevD.59.043515","article-title":"Cosmologies with varying light speed","volume":"59","author":"Barrow","year":"1999","journal-title":"Phys. Rev. D"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1142\/S0217732301004042","article-title":"Solutions to cosmological problems with energy conservation and varying c, G and Lambda","volume":"16","author":"Gopakumar","year":"2001","journal-title":"Mod. Phys. Lett. A"},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Leszczy\u0144ska, K., Da\u0327browski, M.P., and Balcerzak, A. (2015). Varying constants quantum cosmology. J. Cosmol. Astropart. Phys.","DOI":"10.1088\/1475-7516\/2015\/02\/012"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1142\/S0218271893000246","article-title":"Superluminary universe: A Possible solution to the initial value problem in cosmology","volume":"2","author":"Moffat","year":"1993","journal-title":"Int. J. Mod. Phys. D"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"043516","DOI":"10.1103\/PhysRevD.59.043516","article-title":"A Time varying speed of light as a solution to cosmological puzzles","volume":"59","author":"Albrecht","year":"1999","journal-title":"Phys. Rev. D"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/S0370-2693(99)00008-8","article-title":"Solutions to the quasi-flatness and quasilambda problems","volume":"447","author":"Barrow","year":"1999","journal-title":"Phys. Lett. B"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"043502","DOI":"10.1103\/PhysRevD.63.043502","article-title":"Stars and black holes in varying speed of light theories","volume":"63","author":"Magueijo","year":"2001","journal-title":"Phys. Rev. D"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1119\/1.1819929","article-title":"c is the speed of light, isn\u2019t it?","volume":"73","author":"Ellis","year":"2005","journal-title":"Am. J. Phys."},{"key":"ref_59","unstructured":"Moffat, J.W. (2014). Variable speed of light cosmology, primordial fluctuations and gravitational waves."},{"key":"ref_60","unstructured":"Moffat, J.W. (2015). Nonlinear perturbations in a variable speed of light cosmology."},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Balcerzak, A. (2015). Non-minimally coupled varying constants quantum cosmologies. J. Cosmol. Astropart. Phys.","DOI":"10.1088\/1475-7516\/2015\/04\/019"},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Gibbons, G.W., and Hawking, S.W. (1977). Cosmological Event Horizons, Thermodynamics, and Particle Creation. Phys. Rev. D, 15.","DOI":"10.1103\/PhysRevD.15.2738"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.physletb.2013.11.029","article-title":"Redshift drift in varying speed of light cosmology","volume":"728","author":"Balcerzak","year":"2014","journal-title":"Phys. Lett. B"},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Amendola, L., and Tsujikawa, S. (2010). Dark Energy, Cambridge University Press.","DOI":"10.1017\/CBO9780511750823"},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Okun, L.B. (1991). The fundamental constants of physics. Sov. Phys. Usp., 34.","DOI":"10.1070\/PU1991v034n09ABEH002475"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"1891","DOI":"10.1023\/A:1022370717626","article-title":"The maximum tension principle in general relativity","volume":"32","author":"Gibbons","year":"2002","journal-title":"Found. Phys."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"1629","DOI":"10.1007\/s10773-005-4835-2","article-title":"General relativity and cosmology derived from principle of maximum power or force","volume":"44","author":"Schiller","year":"2005","journal-title":"Int. J. Theor. Phys."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"3874","DOI":"10.1093\/mnras\/stu2378","article-title":"Maximum tension: With and without a cosmological constant","volume":"446","author":"Barrow","year":"2014","journal-title":"Mon. Not. Royal Astron. Soc."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1016\/j.physletb.2015.07.047","article-title":"Abolishing the maximum tension principle","volume":"748","author":"Gohar","year":"2015","journal-title":"Phys. Lett. B"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"43506","DOI":"10.1103\/PhysRevD.66.043506","article-title":"Variable speed of light cosmology and second law of thermodynamics","volume":"66","author":"Youm","year":"2002","journal-title":"Phys. Rev. D"},{"key":"ref_71","unstructured":"Buchalter, A. (2004). On the time variation of c, G, and h and the dynamics of the cosmic expansion."},{"key":"ref_72","doi-asserted-by":"crossref","unstructured":"Betoule, M., Kessler, R., Guy, J., Mosher, J., Hardin, D., Biswas, R., Astier, P., El-Hage, P., Konig, M., and Kuhlmann, S. (2014). Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples. Astron. Astrophys.","DOI":"10.1051\/0004-6361\/201423413"},{"key":"ref_73","doi-asserted-by":"crossref","unstructured":"Balcerzak, A., and Da\u0327browski, M.P. (2014). A statefinder luminosity distance formula in varying speed of light cosmology. J. Cosmol. Astrop. Phys.","DOI":"10.1088\/1475-7516\/2014\/06\/035"},{"key":"ref_74","unstructured":"WiggleZ Dark Energy Survey. Available online: http:\/\/wigglez.swin.edu.au\/site\/."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1111\/j.1365-2966.2012.21473.x","article-title":"The WiggleZ Dark Energy Survey: Joint measurements of the expansion and growth history at z < 1","volume":"425","author":"Blake","year":"2012","journal-title":"Mon. Not. Royal Astron. Soc."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"2222","DOI":"10.1093\/mnras\/stu371","article-title":"The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Galaxy clustering measurements in the low-redshift sample of Data Release 11","volume":"440","author":"Tojeiro","year":"2014","journal-title":"Mon. Not. Royal Astron. Soc."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1093\/mnras\/stu523","article-title":"The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Baryon acoustic oscillations in the Data Releases 10 and 11 Galaxy samples","volume":"441","author":"Anderson","year":"2014","journal-title":"Mon. Not. Royal Astron. Soc."},{"key":"ref_78","doi-asserted-by":"crossref","unstructured":"Eisenstein, D., and Hu, W. (1998). Baryonic Features in the Matter Transfer Function. Astrophys. J., 496.","DOI":"10.1086\/305424"},{"key":"ref_79","doi-asserted-by":"crossref","unstructured":"Font-Ribera, A., Kirkby, D., Busca, N., Miralda-Escud\u00e9, J., Ross, N.P., Slosar, A., Rich, J., Aubourg, E., Bailey, S., and Bhardwaj, V. (2014). Quasar-Lyman \u03b1 forest cross-correlation from BOSS DR11: Baryon Acoustic Oscillations. J. Cosmol. Astropart. Phys., 2014.","DOI":"10.1088\/1475-7516\/2014\/05\/027"},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"043522","DOI":"10.1103\/PhysRevD.88.043522","article-title":"Distance priors from Planck and dark energy constraints from current data","volume":"88","author":"Wang","year":"2013","journal-title":"Phys. Rev. D"},{"key":"ref_81","doi-asserted-by":"crossref","unstructured":"Wang, Y., and Mukherjee, P. (2007). Observational constraints on dark energy and cosmic curvature. Phys. Rev. D, 76.","DOI":"10.1103\/PhysRevD.76.103533"},{"key":"ref_82","doi-asserted-by":"crossref","unstructured":"Hu, W., and Sugiyama, N. (1996). Small-Scale Cosmological Perturbations: An Analytic Approach. Astrophys. J., 471.","DOI":"10.1086\/177989"},{"key":"ref_83","doi-asserted-by":"crossref","unstructured":"Bennett, C.L., Larson, D., Weiland, J.L., and Hinshaw, G. (2014). The 1% Concordance Hubble Constant. Astrophys. J., 794.","DOI":"10.1088\/0004-637X\/794\/2\/135"},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1088\/0067-0049\/180\/2\/330","article-title":"Five-Year Wilkinson Microwave Anisotropy Probe Observations: Cosmological Interpretation","volume":"180","author":"Komatsu","year":"2009","journal-title":"Astrophys. J. Suppl. Ser."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"123512","DOI":"10.1103\/PhysRevD.89.123512","article-title":"Variations of the fine-structure constant \u03b1 in exotic singularity models","volume":"89","author":"Denkiewicz","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_86","doi-asserted-by":"crossref","unstructured":"Molaro, P., Centurion, M., Whitmore, J.B., Evans, T.M., Murphy, M.T., Agafonova, I.I., Bonifacio, P., D\u2019Odorico, S., Levshakov, S.A., and Lopez, S. (2013). The UVES Large Program for Testing Fundamental Physics: I Bounds on a change in \u03b1 towards quasar HE 2217\u20132818. Astron. Astrophys.","DOI":"10.1051\/0004-6361\/201321351"},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1140\/epjst\/e2008-00818-4","article-title":"Bounds on the fine structure constant variability from Fe II absorption lines in QSO spectra","volume":"163","author":"Molaro","year":"2008","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1051\/0004-6361:20054584","article-title":"On the variation of the fine-structure constant: Very high resolution spectrum of QSO HE 0515-4414","volume":"451","author":"Chand","year":"2006","journal-title":"Astron. Astrophys."},{"key":"ref_89","doi-asserted-by":"crossref","unstructured":"Agafonova, I.I., Molaro, P., and Levshakov, S.A. (2011). First measurement of Mg isotope abundances at high redshifts and accurate estimate of \u0394\u03b1\/\u03b1. Astron. Astrophys.","DOI":"10.1051\/0004-6361\/201016194"},{"key":"ref_90","doi-asserted-by":"crossref","unstructured":"O\u2019Brian, J., Smidt, J., de Bernardis, F., and Cooray, A. (2015). Constraints on Spatial Variations in the Fine-Structure constant from Planck. Astrophys. J.","DOI":"10.1088\/0004-637X\/798\/1\/18"},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"191101","DOI":"10.1103\/PhysRevLett.107.191101","article-title":"Indications of a spatial variation of the fine structure constant","volume":"107","author":"Webb","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_92","doi-asserted-by":"crossref","unstructured":"Hellings, R.W., Adams, P.J., Anderson, J.D., Keesey, M.S., Lau, E.L., Standish, E.M., Canuto, V.M., and Goldman, I. (1983). Experimental Test of the Variability of G Using Viking Lander Ranging Data. Phys. Rev. Lett., 51.","DOI":"10.1103\/PhysRevLett.51.1609"},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"26101","DOI":"10.1103\/PhysRevLett.93.261101","article-title":"Progress in lunar laser ranging tests of relativistic gravity","volume":"93","author":"Williams","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"ref_94","doi-asserted-by":"crossref","unstructured":"Uzan, J.-P. (2011). Varying constants, gravitation, and cosmology. Liv. Rev. Rel., 14.","DOI":"10.12942\/lrr-2011-2"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/2\/60\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:19:29Z","timestamp":1760210369000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/2\/60"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,22]]},"references-count":94,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,2]]}},"alternative-id":["e18020060"],"URL":"https:\/\/doi.org\/10.3390\/e18020060","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2016,2,22]]}}}