{"id":"https://openalex.org/W3185178224","doi":"https://doi.org/10.3390/sym13081345","title":"First-Order Formalism and Thick Branes in Mimetic Gravity","display_name":"First-Order Formalism and Thick Branes in Mimetic Gravity","publication_year":2021,"publication_date":"2021-07-26","ids":{"openalex":"https://openalex.org/W3185178224","doi":"https://doi.org/10.3390/sym13081345","mag":"3185178224"},"language":"en","primary_location":{"id":"doi:10.3390/sym13081345","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13081345","pdf_url":"https://www.mdpi.com/2073-8994/13/8/1345/pdf?version=1627282626","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/8/1345/pdf?version=1627282626","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026792000","display_name":"Qun-Ying Xie","orcid":null},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qun-Ying Xie","raw_affiliation_strings":["Lanzhou Center for Theoretical Physics & Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China","School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lanzhou Center for Theoretical Physics & Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China","institution_ids":["https://openalex.org/I76214153"]},{"raw_affiliation_string":"School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076489137","display_name":"Qi-Ming Fu","orcid":null},"institutions":[{"id":"https://openalex.org/I187175081","display_name":"Shaanxi University of Technology","ror":"https://ror.org/056m91h77","country_code":"CN","type":"education","lineage":["https://openalex.org/I187175081"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qi-Ming Fu","raw_affiliation_strings":["Institute of Physics, Shaanxi University of Technology, Hanzhong 723000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Physics, Shaanxi University of Technology, Hanzhong 723000, China","institution_ids":["https://openalex.org/I187175081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028547049","display_name":"Tao-Tao Sui","orcid":null},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao-Tao Sui","raw_affiliation_strings":["Lanzhou Center for Theoretical Physics & Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lanzhou Center for Theoretical Physics & Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101445780","display_name":"Li Zhao","orcid":"https://orcid.org/0000-0003-1078-6900"},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Zhao","raw_affiliation_strings":["Lanzhou Center for Theoretical Physics & Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lanzhou Center for Theoretical Physics & Research Center of Gravitation, Lanzhou University, Lanzhou 730000, China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109275496","display_name":"Yi Zhong","orcid":"https://orcid.org/0009-0001-9979-8790"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yi Zhong","raw_affiliation_strings":["Hunan Provincial Key Laboratory of High-Energy Scale Physics and Applications, Hunan University, Changsha 410082, China","School of Physics and Electronics, Hunan University, Changsha 410082, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hunan Provincial Key Laboratory of High-Energy Scale Physics and Applications, Hunan University, Changsha 410082, China","institution_ids":["https://openalex.org/I16609230"]},{"raw_affiliation_string":"School of Physics and Electronics, Hunan University, Changsha 410082, China","institution_ids":["https://openalex.org/I16609230"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5109275496"],"corresponding_institution_ids":["https://openalex.org/I16609230"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":2.3488,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.93600213,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":98},"biblio":{"volume":"13","issue":"8","first_page":"1345","last_page":"1345"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10026","display_name":"Galaxies: Formation, Evolution, Phenomena","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/conformal-map","display_name":"Conformal map","score":0.7070605158805847},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6795480251312256},{"id":"https://openalex.org/keywords/brane-cosmology","display_name":"Brane cosmology","score":0.6628433465957642},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.6107659339904785},{"id":"https://openalex.org/keywords/brane","display_name":"Brane","score":0.5554603934288025},{"id":"https://openalex.org/keywords/scalar-field","display_name":"Scalar field","score":0.5394587516784668},{"id":"https://openalex.org/keywords/conformal-symmetry","display_name":"Conformal symmetry","score":0.5051794648170471},{"id":"https://openalex.org/keywords/tensor-field","display_name":"Tensor field","score":0.500133752822876},{"id":"https://openalex.org/keywords/zero-mode","display_name":"Zero mode","score":0.4766298532485962},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.44410115480422974},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.44110819697380066},{"id":"https://openalex.org/keywords/newtonian-potential","display_name":"Newtonian potential","score":0.42247089743614197},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.38388827443122864},{"id":"https://openalex.org/keywords/gravitation","display_name":"Gravitation","score":0.37271881103515625},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.3644247353076935},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.21205604076385498},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.17921793460845947},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.16452041268348694},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16449368000030518}],"concepts":[{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.7070605158805847},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6795480251312256},{"id":"https://openalex.org/C57979875","wikidata":"https://www.wikidata.org/wiki/Q15091423","display_name":"Brane cosmology","level":2,"score":0.6628433465957642},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.6107659339904785},{"id":"https://openalex.org/C68249636","wikidata":"https://www.wikidata.org/wiki/Q385601","display_name":"Brane","level":2,"score":0.5554603934288025},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.5394587516784668},{"id":"https://openalex.org/C173848574","wikidata":"https://www.wikidata.org/wiki/Q3507963","display_name":"Conformal symmetry","level":3,"score":0.5051794648170471},{"id":"https://openalex.org/C166077713","wikidata":"https://www.wikidata.org/wiki/Q1758924","display_name":"Tensor field","level":3,"score":0.500133752822876},{"id":"https://openalex.org/C2780658932","wikidata":"https://www.wikidata.org/wiki/Q8069598","display_name":"Zero mode","level":2,"score":0.4766298532485962},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.44410115480422974},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.44110819697380066},{"id":"https://openalex.org/C70920666","wikidata":"https://www.wikidata.org/wiki/Q4328383","display_name":"Newtonian potential","level":3,"score":0.42247089743614197},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.38388827443122864},{"id":"https://openalex.org/C124017977","wikidata":"https://www.wikidata.org/wiki/Q11412","display_name":"Gravitation","level":2,"score":0.37271881103515625},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3644247353076935},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.21205604076385498},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.17921793460845947},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.16452041268348694},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16449368000030518},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym13081345","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13081345","pdf_url":"https://www.mdpi.com/2073-8994/13/8/1345/pdf?version=1627282626","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:ir.lzu.edu.cn/:262010/470537","is_oa":false,"landing_page_url":"http://ir.lzu.edu.cn/handle/262010/470325","pdf_url":null,"source":{"id":"https://openalex.org/S4406923049","display_name":"Lanzhou University Institutional Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"\u671f\u520a\u8bba\u6587"},{"id":"pmh:oai:doaj.org/article:518b33aaa5c64b7a991c09b574e70994","is_oa":true,"landing_page_url":"https://doaj.org/article/518b33aaa5c64b7a991c09b574e70994","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 8, p 1345 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/8/1345/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13081345","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry; Volume 13; Issue 8; Pages: 1345","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13081345","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13081345","pdf_url":"https://www.mdpi.com/2073-8994/13/8/1345/pdf?version=1627282626","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3185178224.pdf"},"referenced_works_count":90,"referenced_works":["https://openalex.org/W1749857245","https://openalex.org/W1796050503","https://openalex.org/W1963895195","https://openalex.org/W1976212189","https://openalex.org/W1990715309","https://openalex.org/W2015410749","https://openalex.org/W2016101535","https://openalex.org/W2023710666","https://openalex.org/W2041786764","https://openalex.org/W2062538222","https://openalex.org/W2064777467","https://openalex.org/W2069750773","https://openalex.org/W2076366537","https://openalex.org/W2078147560","https://openalex.org/W2081549207","https://openalex.org/W2081823902","https://openalex.org/W2095721433","https://openalex.org/W2116393936","https://openalex.org/W2120954321","https://openalex.org/W2134992822","https://openalex.org/W2158236748","https://openalex.org/W2202893734","https://openalex.org/W2205401419","https://openalex.org/W2212283619","https://openalex.org/W2228582482","https://openalex.org/W2291427481","https://openalex.org/W2323029274","https://openalex.org/W2337330888","https://openalex.org/W2394857727","https://openalex.org/W2509603410","https://openalex.org/W2527938812","https://openalex.org/W2562383181","https://openalex.org/W2570352522","https://openalex.org/W2593040725","https://openalex.org/W2594851385","https://openalex.org/W2603089078","https://openalex.org/W2612864215","https://openalex.org/W2738323568","https://openalex.org/W2743071381","https://openalex.org/W2761444032","https://openalex.org/W2768208069","https://openalex.org/W2770050306","https://openalex.org/W2792039743","https://openalex.org/W2792311770","https://openalex.org/W2903613084","https://openalex.org/W2909405680","https://openalex.org/W2950204282","https://openalex.org/W2952701956","https://openalex.org/W2963369954","https://openalex.org/W3003638120","https://openalex.org/W3037156011","https://openalex.org/W3037564844","https://openalex.org/W3042635787","https://openalex.org/W3083961145","https://openalex.org/W3093609984","https://openalex.org/W3094040793","https://openalex.org/W3098513801","https://openalex.org/W3098635170","https://openalex.org/W3099324098","https://openalex.org/W3099325627","https://openalex.org/W3099471289","https://openalex.org/W3100053982","https://openalex.org/W3100474509","https://openalex.org/W3101602560","https://openalex.org/W3101811086","https://openalex.org/W3102000926","https://openalex.org/W3102060154","https://openalex.org/W3102301084","https://openalex.org/W3102334582","https://openalex.org/W3102508101","https://openalex.org/W3102635008","https://openalex.org/W3104265355","https://openalex.org/W3104303094","https://openalex.org/W3104703904","https://openalex.org/W3105132102","https://openalex.org/W3106077045","https://openalex.org/W3106110610","https://openalex.org/W3116801141","https://openalex.org/W3120447313","https://openalex.org/W3122271791","https://openalex.org/W3123585062","https://openalex.org/W3125678162","https://openalex.org/W6667610315","https://openalex.org/W6670960053","https://openalex.org/W6671253348","https://openalex.org/W6687710447","https://openalex.org/W6688145489","https://openalex.org/W6700650238","https://openalex.org/W6726033343","https://openalex.org/W7000119408"],"related_works":["https://openalex.org/W3104706344","https://openalex.org/W2991197318","https://openalex.org/W2055799562","https://openalex.org/W2076719484","https://openalex.org/W45313028","https://openalex.org/W2088466563","https://openalex.org/W2243655051","https://openalex.org/W1990171414","https://openalex.org/W2063512529","https://openalex.org/W2033669382"],"abstract_inverted_index":{"In":[0],"this":[1,53],"paper,":[2],"we":[3,37],"investigate":[4],"thick":[5,60],"branes":[6],"generated":[7],"by":[8,19],"a":[9,47],"scalar":[10,68,88,107],"field":[11,41],"in":[12],"mimetic":[13],"gravity":[14],"theory,":[15],"which":[16],"is":[17],"inspired":[18],"considering":[20],"the":[21,25,39,44,85,103,106,112,120],"conformal":[22,26],"symmetry":[23],"under":[24],"transformation":[27],"of":[28,43,49,58,77],"an":[29],"auxiliary":[30,35],"metric.":[31],"By":[32],"introducing":[33],"two":[34],"super-potentials,":[36],"transform":[38],"second-order":[40],"equations":[42],"system":[45],"into":[46],"set":[48],"first-order":[50,54],"equations.":[51],"With":[52],"formalism,":[55],"several":[56],"types":[57],"analytical":[59],"brane":[61,104],"solutions":[62],"are":[63,70,79,90],"obtained.":[64],"Then,":[65],"tensor":[66,86,96],"and":[67,87],"perturbations":[69,78,89],"analyzed.":[71],"We":[72],"find":[73],"that":[74],"both":[75],"kinds":[76],"stable.":[80],"The":[81,95],"effective":[82],"potentials":[83],"for":[84],"dual":[91],"to":[92],"each":[93],"other.":[94],"zero":[97,108],"mode":[98,109],"can":[99,116],"be":[100,117],"localized":[101],"on":[102,119],"while":[105],"cannot.":[110],"Thus,":[111],"four-dimensional":[113],"Newtonian":[114],"potential":[115],"recovered":[118],"brane.":[121]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2021-08-02T00:00:00"}