{"title":"椭圆函数中的弗里德曼宇宙论","authors":"A. E. Pavlov","doi":"10.1134/S0202289321040113","DOIUrl":null,"url":null,"abstract":"<p>We present exact solutions to the Friedmann equation in standard <span>\\(\\Lambda\\)</span>CDM cosmology in Weierstrass and Jacobi functions. The right-hand side of the Friedmann equation, describing various contributions of matter sources, is considered in a generic form. It is proved that the problem of integration of the Friedmann equation for simple equations of state of a medium is reduced to solving Abel integrals for algebraic functions.</p>","PeriodicalId":583,"journal":{"name":"Gravitation and Cosmology","volume":"27 4","pages":"403 - 408"},"PeriodicalIF":1.2000,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Friedmann Cosmology in Elliptic Functions\",\"authors\":\"A. E. Pavlov\",\"doi\":\"10.1134/S0202289321040113\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We present exact solutions to the Friedmann equation in standard <span>\\\\(\\\\Lambda\\\\)</span>CDM cosmology in Weierstrass and Jacobi functions. The right-hand side of the Friedmann equation, describing various contributions of matter sources, is considered in a generic form. It is proved that the problem of integration of the Friedmann equation for simple equations of state of a medium is reduced to solving Abel integrals for algebraic functions.</p>\",\"PeriodicalId\":583,\"journal\":{\"name\":\"Gravitation and Cosmology\",\"volume\":\"27 4\",\"pages\":\"403 - 408\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2021-12-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Gravitation and Cosmology\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S0202289321040113\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ASTRONOMY & ASTROPHYSICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Gravitation and Cosmology","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S0202289321040113","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
We present exact solutions to the Friedmann equation in standard \(\Lambda\)CDM cosmology in Weierstrass and Jacobi functions. The right-hand side of the Friedmann equation, describing various contributions of matter sources, is considered in a generic form. It is proved that the problem of integration of the Friedmann equation for simple equations of state of a medium is reduced to solving Abel integrals for algebraic functions.
期刊介绍：
Gravitation and Cosmology is a peer-reviewed periodical, dealing with the full range of topics of gravitational physics and relativistic cosmology and published under the auspices of the Russian Gravitation Society and Peoples’ Friendship University of Russia. The journal publishes research papers, review articles and brief communications on the following fields: theoretical (classical and quantum) gravitation; relativistic astrophysics and cosmology, exact solutions and modern mathematical methods in gravitation and cosmology, including Lie groups, geometry and topology; unification theories including gravitation; fundamental physical constants and their possible variations; fundamental gravity experiments on Earth and in space; related topics. It also publishes selected old papers which have not lost their topicality but were previously published only in Russian and were not available to the worldwide research community
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