{"id":"https://openalex.org/W1981306382","doi":"https://doi.org/10.1103/physrevd.85.023010","title":"Odd-parity bipolar spherical harmonics","display_name":"Odd-parity bipolar spherical harmonics","publication_year":2012,"publication_date":"2012-01-25","ids":{"openalex":"https://openalex.org/W1981306382","doi":"https://doi.org/10.1103/physrevd.85.023010","mag":"1981306382"},"language":"en","primary_location":{"id":"doi:10.1103/physrevd.85.023010","doi":"https://doi.org/10.1103/physrevd.85.023010","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevd.85.023010","pdf_url":null,"source":{"id":"https://openalex.org/S4210190737","display_name":"Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields","issn_l":"0556-2821","issn":["0556-2821","1089-4918","1538-4500","1550-2368","1550-7998"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review D","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1109.2910","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079727707","display_name":"Laura G. Book","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Laura G. Book","raw_affiliation_strings":["California Institute of Technology, Mail Code 350-17, Pasadena, California 91125, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"California Institute of Technology, Mail Code 350-17, Pasadena, California 91125, USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011447076","display_name":"Marc Kamionkowski","orcid":"https://orcid.org/0000-0001-7018-2055","observed_orcids":["https://orcid.org/0000-0001-7018-2055"]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]},{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Marc Kamionkowski","raw_affiliation_strings":["California Institute of Technology, Mail Code 350-17, Pasadena, California 91125, USA","Johns Hopkins University, Department of Physics and Astronomy, Bloomberg 439, 3400 N. Charles St., Baltimore, Maryland 21218, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"California Institute of Technology, Mail Code 350-17, Pasadena, California 91125, USA","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Johns Hopkins University, Department of Physics and Astronomy, Bloomberg 439, 3400 N. Charles St., Baltimore, Maryland 21218, USA","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103129535","display_name":"Tarun Souradeep","orcid":"https://orcid.org/0000-0003-3764-8102","observed_orcids":["https://orcid.org/0000-0003-3764-8102"]},"institutions":[{"id":"https://openalex.org/I59781447","display_name":"Inter-University Centre for Astronomy and Astrophysics","ror":"https://ror.org/04etcj997","country_code":"IN","type":"facility","lineage":["https://openalex.org/I59781447"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Tarun Souradeep","raw_affiliation_strings":["Inter-University Center for Astronomy and Astrophysics, Pune 411007, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inter-University Center for Astronomy and Astrophysics, Pune 411007, India","institution_ids":["https://openalex.org/I59781447"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7134,"has_fulltext":true,"cited_by_count":51,"citation_normalized_percentile":{"value":0.88367143,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":99},"biblio":{"volume":"85","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9980000257492065,"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"}},"topics":[{"id":"https://openalex.org/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9980000257492065,"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/T11090","display_name":"Dark Matter and Cosmic Phenomena","score":0.00019999999494757503,"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/T11415","display_name":"Noncommutative and Quantum Gravity Theories","score":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/cosmic-microwave-background","display_name":"cosmic microwave background","score":0.9549999833106995},{"id":"https://openalex.org/keywords/statistical-isotropy","display_name":"statistical isotropy","score":0.7269999980926514},{"id":"https://openalex.org/keywords/gaussianity","display_name":"Gaussianity","score":0.6579999923706055},{"id":"https://openalex.org/keywords/parity-violation","display_name":"parity violation","score":0.7519999742507935},{"id":"https://openalex.org/keywords/chiral-gravitational-waves","display_name":"chiral gravitational waves","score":0.8519999980926514},{"id":"https://openalex.org/keywords/gravitational-wave-lensing","display_name":"gravitational wave lensing","score":0.7960000038146973},{"id":"https://openalex.org/keywords/weak-gravitational-lensing","display_name":"weak gravitational lensing","score":0.7080000042915344},{"id":"https://openalex.org/keywords/cmb-polarization","display_name":"CMB polarization","score":0.7170000076293945},{"id":"https://openalex.org/keywords/tensor-perturbations","display_name":"tensor perturbations","score":0.7049999833106995}],"concepts":[{"id":"https://openalex.org/C207297109","wikidata":"https://www.wikidata.org/wiki/Q15605","display_name":"Cosmic microwave background","level":3,"score":0.8747879266738892},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.8492616415023804},{"id":"https://openalex.org/C52765159","wikidata":"https://www.wikidata.org/wiki/Q1027847","display_name":"Multipole expansion","level":2,"score":0.8179707527160645},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.729905366897583},{"id":"https://openalex.org/C190330329","wikidata":"https://www.wikidata.org/wiki/Q190035","display_name":"Gravitational wave","level":2,"score":0.6835544109344482},{"id":"https://openalex.org/C62796785","wikidata":"https://www.wikidata.org/wiki/Q12902765","display_name":"Cosmic background radiation","level":4,"score":0.5836066603660583},{"id":"https://openalex.org/C152321242","wikidata":"https://www.wikidata.org/wiki/Q7048759","display_name":"Non-Gaussianity","level":4,"score":0.4811038374900818},{"id":"https://openalex.org/C68498078","wikidata":"https://www.wikidata.org/wiki/Q185243","display_name":"Gravitational lens","level":4,"score":0.47186964750289917},{"id":"https://openalex.org/C188414643","wikidata":"https://www.wikidata.org/wiki/Q3001183","display_name":"Harmonics","level":3,"score":0.46456706523895264},{"id":"https://openalex.org/C3768446","wikidata":"https://www.wikidata.org/wiki/Q877100","display_name":"Spherical harmonics","level":2,"score":0.43256962299346924},{"id":"https://openalex.org/C205049153","wikidata":"https://www.wikidata.org/wiki/Q2698605","display_name":"Polarization (electrochemistry)","level":2,"score":0.4196532964706421},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.40857839584350586},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.36684978008270264},{"id":"https://openalex.org/C33024259","wikidata":"https://www.wikidata.org/wiki/Q76250","display_name":"Redshift","level":3,"score":0.3480374813079834},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2864561080932617},{"id":"https://openalex.org/C98444146","wikidata":"https://www.wikidata.org/wiki/Q318","display_name":"Galaxy","level":2,"score":0.12619590759277344},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1103/physrevd.85.023010","doi":"https://doi.org/10.1103/physrevd.85.023010","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevd.85.023010","pdf_url":null,"source":{"id":"https://openalex.org/S4210190737","display_name":"Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields","issn_l":"0556-2821","issn":["0556-2821","1089-4918","1538-4500","1550-2368","1550-7998"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review D","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1109.2910","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1109.2910","pdf_url":"https://arxiv.org/pdf/1109.2910","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:authors.library.caltech.edu:34840","doi":null,"is_oa":false,"landing_page_url":"https://authors.library.caltech.edu/34840/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:osti.gov:1099032","doi":null,"is_oa":false,"landing_page_url":"https://www.osti.gov/biblio/1099032","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},{"id":"doi:10.48550/arxiv.1109.2910","doi":"https://doi.org/10.48550/arxiv.1109.2910","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1109.2910","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1109.2910","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1109.2910","pdf_url":"https://arxiv.org/pdf/1109.2910","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6531812122","display_name":"THE COSMIC MICROWAVE BACKGROUND (CMB) HAS PROVIDED PRECISE CONSTRAINTS TO COSMOLOGICAL PARAMETERS AN","funder_award_id":"NNX10AD04G","funder_id":"https://openalex.org/F4320306101","funder_display_name":"National Aeronautics and Space Administration"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320306101","display_name":"National Aeronautics and Space Administration","ror":"https://ror.org/027ka1x80"},{"id":"https://openalex.org/F4320306202","display_name":"Gordon and Betty Moore Foundation","ror":"https://ror.org/006wxqw41"},{"id":"https://openalex.org/F4320309398","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055"},{"id":"https://openalex.org/F4320309634","display_name":"Adolph C. and Mary Sprague Miller Institute for Basic Research in Science, University of California Berkeley","ror":null},{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1981306382.pdf","grobid_xml":"https://content.openalex.org/works/W1981306382.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W1482812467","https://openalex.org/W1488453776","https://openalex.org/W1494738860","https://openalex.org/W1529804202","https://openalex.org/W1545796813","https://openalex.org/W1599376543","https://openalex.org/W1618492500","https://openalex.org/W1661084937","https://openalex.org/W1743244066","https://openalex.org/W1970053916","https://openalex.org/W1970571200","https://openalex.org/W1973018404","https://openalex.org/W1975129296","https://openalex.org/W1976942507","https://openalex.org/W1978556707","https://openalex.org/W2000539178","https://openalex.org/W2003411842","https://openalex.org/W2009441000","https://openalex.org/W2011706635","https://openalex.org/W2016888141","https://openalex.org/W2020298599","https://openalex.org/W2020400627","https://openalex.org/W2034910318","https://openalex.org/W2037232212","https://openalex.org/W2045003658","https://openalex.org/W2047553553","https://openalex.org/W2051694884","https://openalex.org/W2051730987","https://openalex.org/W2054899182","https://openalex.org/W2060902142","https://openalex.org/W2061233827","https://openalex.org/W2065593146","https://openalex.org/W2069171865","https://openalex.org/W2073479818","https://openalex.org/W2078223319","https://openalex.org/W2082286321","https://openalex.org/W2085068386","https://openalex.org/W2092150352","https://openalex.org/W2092870297","https://openalex.org/W2106411700","https://openalex.org/W2113023620","https://openalex.org/W2115937249","https://openalex.org/W2118413445","https://openalex.org/W2119297924","https://openalex.org/W2120760706","https://openalex.org/W2147875900","https://openalex.org/W2148545031","https://openalex.org/W2148659656","https://openalex.org/W2167835957","https://openalex.org/W2170470847","https://openalex.org/W2594268536","https://openalex.org/W3123796127"],"related_works":["https://openalex.org/W1494738860","https://openalex.org/W2123755476","https://openalex.org/W7223248691","https://openalex.org/W1969687948","https://openalex.org/W828560456","https://openalex.org/W4252272566","https://openalex.org/W3138766981","https://openalex.org/W4251816251","https://openalex.org/W2079140088","https://openalex.org/W2473728470"],"abstract_inverted_index":{"Bipolar":[0],"spherical":[1],"harmonics":[2],"(BiPoSHs)":[3],"provide":[4],"a":[5,58,140],"general":[6],"formalism":[7],"for":[8,92],"quantifying":[9],"departures":[10],"in":[11,57],"the":[12,93,98,110,129,135],"cosmic":[13],"microwave":[14],"background":[15],"(CMB)":[16],"from":[17,21],"statistical":[18],"isotropy":[19],"and":[20,47,104],"Gaussianity.":[22],"However,":[23],"prior":[24],"work":[25],"has":[26],"focused":[27],"only":[28],"on":[29],"BiPoSHs":[30,43],"with":[31,44,125],"even":[32],"parity.":[33],"Here":[34],"we":[35,48],"show":[36],"that":[37,61,134],"there":[38],"is":[39,142],"another":[40],"set":[41],"of":[42,67,101,112,128,138],"odd":[45],"parity,":[46],"explore":[49],"their":[50],"cosmological":[51],"applications.":[52],"We":[53,89,107,132],"describe":[54],"systematic":[55],"artifacts":[56],"CMB":[59,130],"map":[60],"could":[62],"be":[63,77],"sought":[64],"by":[65,82,97,120],"measurement":[66],"these":[68],"odd-parity":[69],"BiPoSH":[70,73,94,123],"modes.":[71],"These":[72],"modes":[74,95,124],"may":[75],"also":[76],"produced":[78],"cosmologically":[79],"through":[80],"lensing":[81,100],"gravitational":[83],"waves":[84],"(GWs),":[85],"among":[86],"other":[87],"sources.":[88],"derive":[90],"expressions":[91],"induced":[96],"weak":[99],"both":[102],"scalar":[103],"tensor":[105],"perturbations.":[106],"then":[108],"investigate":[109],"possibility":[111],"detecting":[113],"parity-breaking":[114],"physics,":[115],"such":[116,139],"as":[117],"chiral":[118],"GWs,":[119],"cross-correlating":[121],"opposite-parity":[122],"multipole":[126],"moments":[127],"polarization.":[131],"find":[133],"expected":[136],"signal-to-noise":[137],"detection":[141],"modest.":[143]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":7}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2016-06-24T00:00:00"}
