{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:30:45Z","timestamp":1772253045996,"version":"3.50.1"},"reference-count":22,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2017,9,25]],"date-time":"2017-09-25T00:00:00Z","timestamp":1506297600000},"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>One application of the Cosmological Gravitational Lensing in General Relativity is the measurement of the Hubble constant     H 0     using the time delay     \u0394 t     between multiple images of lensed quasars. This method has already been applied, obtaining a value of     H 0     compatible with that obtained from the SNe 1A, but non-compatible with that obtained studying the anisotropies of the CMB. This difference could be a statistical fluctuation or an indication of new physics beyond the Standard Model of Cosmology, so it desirable to improve the precision of the measurements. At the current technological capabilities it is possible to obtain     H 0     to a percent level uncertainty, so a more accurate theoretical model could be necessary in order to increase the precision about the determination of     H 0    . The actual formula which relates     \u0394 t     with     H 0     is approximated; in this paper we expose a proposal to go beyond the previous analysis and, within the context of a new model, we obtain a more precise formula than that present in the literature.<\/jats:p>","DOI":"10.3390\/sym9100202","type":"journal-article","created":{"date-parts":[[2017,9,26]],"date-time":"2017-09-26T04:28:01Z","timestamp":1506400081000},"page":"202","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Towards a New Proposal for the Time Delay in Gravitational Lensing"],"prefix":"10.3390","volume":"9","author":[{"given":"Nicola","family":"Alchera","sequence":"first","affiliation":[{"name":"Dipartimento di Fisica, Universit\u00e0 di Genova, via Dodecaneso 33, I-16146 Genova, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Bonici","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica, Universit\u00e0 di Genova, via Dodecaneso 33, I-16146 Genova, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicola","family":"Maggiore","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica, Universit\u00e0 di Genova, via Dodecaneso 33, I-16146 Genova, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,9,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"015005","DOI":"10.1088\/1361-6382\/34\/1\/015005","article-title":"Massive deformations of rank-2 symmetric tensor theory (a.k.a. BRS characterization of Fierz\u2013Pauli massive gravity)","volume":"34","author":"Blasi","year":"2017","journal-title":"Class. Quantum Gravity"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1140\/epjc\/s10052-017-5205-y","article-title":"Massive gravity and Fierz\u2014Pauli theory","volume":"77","author":"Blasi","year":"2017","journal-title":"Eur. Phys. J. C"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"013060","DOI":"10.1088\/1367-2630\/14\/1\/013060","article-title":"Non-Abelian BF theory for 2+1 dimensional topological states of matter","volume":"14","author":"Blasi","year":"2012","journal-title":"New J. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1002\/andp.20085201106","article-title":"Symanzik\u2019s method applied to the fractional quantum hall edge states","volume":"17","author":"Blasi","year":"2008","journal-title":"Ann. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2461","DOI":"10.1140\/epjc\/s10052-013-2461-3","article-title":"Duality and dimensional reduction of 5D BF theory","volume":"73","author":"Amoretti","year":"2013","journal-title":"Eur. Phys. J. C"},{"key":"ref_6","first-page":"409","article-title":"Thermo-electric transport in gauge\/gravity models","volume":"2","author":"Amoretti","year":"2017","journal-title":"Adv. Phys. X"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1007\/JHEP04(2014)142","article-title":"Holography in flat spacetime: 4D theories and electromagnetic duality on the border","volume":"1404","author":"Amoretti","year":"2014","journal-title":"JHEP"},{"key":"ref_8","unstructured":"Carroll, S.M. (2004). Spacetime and Geometry: An Introduction to General Relativity, Addison-Wesley."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1046\/j.1365-8711.1999.02274.x","article-title":"Cosmic confusion: Degeneracies among cosmological parameters derived from measurements of microwave background anisotropies","volume":"304","author":"Efstathiou","year":"1999","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"A13","DOI":"10.1051\/0004-6361\/201525830","article-title":"Planck 2015 results. XIII. Cosmological parameters","volume":"594","author":"Ade","year":"2016","journal-title":"Astron. Astrophys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2590","DOI":"10.1093\/mnras\/stx483","article-title":"H0LiCOW\u2014I. H0 Lenses in COSMOGRAIL\u2019s Wellspring: Program overview","volume":"468","author":"Suyu","year":"2017","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4838","DOI":"10.1093\/mnras\/stx1484","article-title":"H0LiCOW\u2014II. Spectroscopic survey and galaxy-group identification of the strong gravitational lens system HE0435-1223","volume":"470","author":"Sluse","year":"2017","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Rusu, C.E., Fassnacht, C.D., Sluse, D., Hilbert, S., Wong, K.C., Huang, K.H., Suyu, S.H., Collett, T.E., Marshall, P.J., and Treu, T. (2017). H0LiCOW\u2014III. Quantifying the effect of mass along the line of sight to the gravitational lens HE 0435-1223 through weighted galaxy counts. Mon. Not. R. Astron. Soc., 467.","DOI":"10.1093\/mnras\/stx285"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4895","DOI":"10.1093\/mnras\/stw3077","article-title":"H0LiCOW\u2014IV. Lens mass model of HE 0435-1223 and blind measurement of its time-delay distance for cosmology","volume":"465","author":"Wong","year":"2017","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4914","DOI":"10.1093\/mnras\/stw3006","article-title":"H0LiCOW\u2014V. New COSMOGRAIL time delays of HE 0435-1223: H0 to 3.8 per cent precision from strong lensing in a flat \u039bCDM model","volume":"465","author":"Bonvin","year":"2017","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1093\/mnras\/128.4.307","article-title":"On the possibility of determining Hubble\u2019s parameter and the masses of galaxies from the gravitational lens effect","volume":"128","author":"Refsdal","year":"1964","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"56","DOI":"10.3847\/0004-637X\/826\/1\/56","article-title":"A 2.4% Determination of the Local Value of the Hubble Constant","volume":"826","author":"Riess","year":"2016","journal-title":"Astrophys. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"043503","DOI":"10.1103\/PhysRevD.96.043503","article-title":"Can interacting dark energy solve the H0 tension?","volume":"96","author":"Melchiorri","year":"2017","journal-title":"Phys. Rev. D"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Schneider, P., Ehlers, J., and Falco, E.E. (1992). Gravitational Lenses, Springer.","DOI":"10.1007\/978-3-662-03758-4"},{"key":"ref_20","unstructured":"(2017, September 24). CASTLES Catalogue. Available online: https:\/\/www.cfa.harvard.edu\/castles."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Weinberg, S. (2008). Cosmology, Oxford University Press.","DOI":"10.1093\/oso\/9780198526827.001.0001"},{"key":"ref_22","unstructured":"Alchera, N., Bonici, M., Maggiore, N., and Panizzi, L. (2017). In progress."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/10\/202\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:45:51Z","timestamp":1760208351000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/10\/202"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,25]]},"references-count":22,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2017,10]]}},"alternative-id":["sym9100202"],"URL":"https:\/\/doi.org\/10.3390\/sym9100202","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints201709.0049.v1","asserted-by":"object"}]},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,25]]}}}