Correspondence of gravity singularities in Jordan and Einstein frames

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• 作者：Sebastian Bahamonde^a ; ^{sebastian.beltran.14@ucl.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; S.D. Odintsov^b ; ^c ; ^d ; ^{odintsov@ieec.uab.es" class="auth_mail" title="E-mail the corresponding author} ; V.K. Oikonomou^e ; ^f ; ^{v.k.oikonomou1979@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; ^{voiko@sch.gr" class="auth_mail" title="E-mail the corresponding author} ; Matthew Wright^a ; ^{matthew.wright.13@ucl.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Modified gravity ; Finite time singularities ; Singular cosmology ; Einstein&ndash ; Jordan frame correspondence
• 刊名：Annals of Physics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：373
• 期：Complete
• 页码：96-114
• 全文大小：520 K

文摘

We study the finite time singularity correspondence between the Jordan and Einstein frames for various F(R)$F\left(R\right)$ gravity theories. Particularly we investigate the ordinary pure F(R)$F\left(R\right)$ gravity case and the unimodular F(R)$F\left(R\right)$ gravity cases, in the absence of any matter fluids. In the ordinary F(R)$F\left(R\right)$ gravity cases, by using specific illustrative examples, we show that it is possible to have various correspondences of finite time singularities, and in some cases it is possible a singular cosmology in one frame might be non-singular in the other frame. In the unimodular F(R)$F\left(R\right)$ gravity case, the unimodular constraint is affected by the conformal transformation, so this has an effect on the metric we choose. Moreover, we study the Einstein frame counterpart theory of the unimodular F(R)$F\left(R\right)$ gravity case, and we investigate the correspondences of the singularities in the two theories by considering specific illustrative examples. Finally, a brief dynamical system analysis is performed for the vacuum unimodular F(R)$F\left(R\right)$ gravity and we demonstrate how the dynamical system behaves near the future Big Rip singularity.