{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T10:55:46Z","timestamp":1777632946395,"version":"3.51.4"},"reference-count":28,"publisher":"AIP Publishing","issue":"3","license":[{"start":{"date-parts":[[2023,3,27]],"date-time":"2023-03-27T00:00:00Z","timestamp":1679875200000},"content-version":"vor","delay-in-days":26,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2023,3,27]],"date-time":"2023-03-27T00:00:00Z","timestamp":1679875200000},"content-version":"tdm","delay-in-days":26,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/04459\/202"],"award-info":[{"award-number":["UIDB\/04459\/202"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["UIDP\/04459\/202"],"award-info":[{"award-number":["UIDP\/04459\/202"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["UI\/BD\/152068\/202"],"award-info":[{"award-number":["UI\/BD\/152068\/202"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2023,3,1]]},"abstract":"<jats:p>We obtain explicit formulas for the solution of the wave equation in certain Friedmann\u2013Lema\u00eetre\u2013Robertson\u2013Walker (FLRW) spacetimes. Our method, pioneered by Klainerman and Sarnak, consists in finding differential operators that map solutions of the wave equation in these FLRW spacetimes to solutions of the conformally invariant wave equation in simpler, ultra-static spacetimes, for which spherical mean formulas are available. In addition to recovering the formulas for the dust-filled flat and hyperbolic FLRW spacetimes originally derived by Klainerman and Sarnak and generalizing them to the spherical case, we obtain new formulas for the radiation-filled FLRW spacetimes and also for the de Sitter, anti-de Sitter, and Milne universes. We use these formulas to study the solutions with respect to the Huygens principle and the decay rates and to formulate conjectures about the general decay rates in flat and hyperbolic FLRW spacetimes. The positive resolution of the conjecture in the flat case is seen to follow from known results in the literature.<\/jats:p>","DOI":"10.1063\/5.0135092","type":"journal-article","created":{"date-parts":[[2023,3,27]],"date-time":"2023-03-27T10:06:15Z","timestamp":1679911575000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":6,"title":["Explicit formulas and decay rates for the solution of the wave equation in cosmological spacetimes"],"prefix":"10.1063","volume":"64","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0885-9867","authenticated-orcid":false,"given":"Jos\u00e9","family":"Nat\u00e1rio","sequence":"first","affiliation":[{"name":"CAMGSD, Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Universidade de Lisboa 1 , Lisbon, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5500-2458","authenticated-orcid":false,"given":"Flavio","family":"Rossetti","sequence":"additional","affiliation":[{"name":"CAMGSD, Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Universidade de Lisboa 1 , Lisbon, Portugal"},{"name":"Department of Physics, LMU Munich 2 , Munich, Germany"}]}],"member":"317","published-online":{"date-parts":[[2023,3,27]]},"reference":[{"key":"2023080315455324500_c1","doi-asserted-by":"publisher","first-page":"20140361","DOI":"10.1098\/rspa.2014.0361","article-title":"On the initial value problem for the wave equation in Friedmann-Robertson-Walker spacetimes","volume":"470","year":"2014","journal-title":"Proc. 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