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arXiv 2008.13326gr-qc
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$f(R, T)$引力中拉格朗日模糊性的一般方法

General approach to the Lagrangian ambiguity in $f(R, T)$ gravity

G. A. Carvalho, F. Rocha, H. O. Oliveira, R. V. Lobato

备注：
New section added with application to Cosmology. Matches the published version
发表信息：
Eur. Phys. J. C (2021) 81:134
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摘要：

$f(R,T)$引力理论的引力作用量任意依赖于里奇标量$R$和应力-能量张量的迹$T$ ;它的场方程也依赖于物质拉格朗日量$\mathcal{L}_{m}$。在修正的引力理论中，场方程依赖于拉格朗日，拉格朗日定义没有唯一性，引力场和物质场的动力学可以根据所执行的选择而不同。在这项工作中，我们消除了$\mathcal{L}_{m}$依赖$f(R,T)$重力场方程的推广Moraes [Eur. J. C 79（8），674（2019）]。我们还提出了一个一般的方法，我们认为，跟踪的能量动量张量必须被认为是一个“未知”变量的场方程。迹线只能依赖于基本常数和来自标准模型的少量输入。我们的建议解决了两个局限性：第一，能量动量张量的$f(R,T)$引力是不是完美的流体之一，第二，拉格朗日是不是很好地定义。作为对我们方法的测试，我们将其应用于宇宙学中物质时代的研究，该理论可以成功地描述减速宇宙到加速宇宙之间的过渡，而不需要暗能量。

英文摘要：

The $f(R,T)$ gravity is a theory whose gravitational action depends arbitrarily on the Ricci scalar, $R$, and the trace of the stress-energy tensor, $T$; its field equations also depend on matter Lagrangian, $\mathcal{L}_{m}$. In the modified theories of gravity where field equations depend on Lagrangian, there is no uniqueness on the Lagrangian definition and the dynamics of the gravitational and matter fields can be different depending on the choice performed. In this work, we have eliminated the $\mathcal{L}_{m}$ dependence from $f(R,T)$ gravity field equations by generalizing the approach of Moraes [Eur. Phys. J. C 79(8), 674 (2019)]. We also propose a general approach where we argue that the trace of the energy-momentum tensor must be considered an "unknown" variable of the field equations. The trace can only depend on fundamental constants and few inputs from the standard model. Our proposal resolves two limitations: first the energy-momentum tensor of the $f(R,T)$ gravity is not the perfect fluid one; second, the Lagrangian is not well-defined. As a test of our approach we applied it to the study of the matter era in cosmology, and the theory can successfully describe a transition between a decelerated Universe to an accelerated one without the need for dark energy.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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