arXiv 2108.009922021-08gr-qcastro-ph.COhep-th

我们能绕过Ricci逆引力的不通过定理吗？

Can we bypass no-go theorem for Ricci-inverse Gravity?

Indranil Das, Joseph P Johnson, S. Shankaranarayanan

备注：: V2: Version accepted in EPJ-Plus, 35 pages, 13 figures, 2 tables
DOI：: 10.1140/epjp/s13360-022-03472-2

摘要：

最近，Amendola等人提出了一个包含高阶导数项的引力几何理论。引入反曲率标量$(A)$，它是Ricci张量的逆（$A^{μν} = R_{μν}^{-1}$）的迹.在这项工作中，我们考虑两类Ricci逆-I类和II类-模型。I类模型的形式为$f(R, A)$，其中$f$是Ricci和反曲率标量的函数。II类模型的形式为${\cal F}(R, A^{μν}A_{μν})$，其中${\cal F}$是Ricci标量和反曲率张量平方的函数。对于这两类模型，我们在红移范围$1500 < z < 0$数值求解了修正的Friedmann方程。我们表明，宇宙的晚期演化，即，从物质主导时代到加速膨胀时代的演化，\emph{can not}可以用这两类模型来解释。利用约化作用量方法，我们证明了\emph{can not bypass} Ricci逆重力模型的不可行定理。最后，我们讨论了我们的分析对早期宇宙宇宙学的影响。

英文摘要：

Recently, Amendola et al. proposed a geometrical theory of gravity containing higher-order derivative terms. The authors introduced anticurvature scalar $(A)$, which is the trace of the inverse of the Ricci tensor ($A^{μν} = R_{μν}^{-1}$). In this work, we consider two classes of Ricci-inverse -- Class I and Class II -- models. Class I models are of the form $f(R, A)$ where $f$ is a function of Ricci and anticurvature scalars. Class II models are of the form ${\cal F}(R, A^{μν}A_{μν})$ where ${\cal F}$ is a function of Ricci scalar and square of anticurvature tensor. For both these classes of models, we numerically solve the modified Friedmann equations in the redshift range $1500 < z < 0$. We show that the late-time evolution of the Universe, i.e., evolution from matter-dominated epoch to accelerated expansion epoch, \emph{can not} be explained by these two classes of models. Using the reduced action approach, we show that we \emph{can not bypass} the no-go theorem for Ricci-inverse gravity models. Finally, we discuss the implications of our analysis for the early-Universe cosmology.

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