论文标题
$ f（r，t）$重力的拉格朗日歧义的一般方法
General approach to the Lagrangian ambiguity in $f(R, T)$ gravity
论文作者
论文摘要
$ f（r，t）$重力是一种理论，其重力动作任意取决于ricci标量，$ r $，以及压力 - 能量张量的痕迹，$ t $;它的字段方程也取决于物质拉格朗日，$ \ nathcal {l} _ {m} $。在经过修改的重力理论中，场方程依赖于拉格朗日，拉格朗日定义没有独特性，而重力和物质场的动态可能会根据所执行的选择而有所不同。在这项工作中，我们通过概括了moraes [eur的方法，从$ f（r，t）$重力场方程中消除了$ \ mathcal {l} _ {m} $依赖性。物理。 J. C 79（8），674（2019）]。我们还提出了一种通用方法，我们认为必须将能量量张量的痕迹视为场方程的“未知”变量。该迹线只能取决于基本常数和标准模型中的很少的输入。我们的提案解决了两个局限性：首先，$ f（r，t）$重力的能量弹药张量不是完美的流体。其次，Lagrangian的定义不明确。作为对我们的方法的测试，我们将其应用于宇宙学的问题时代的研究，该理论可以成功地描述一个减速的宇宙到加速的宇宙之间的过渡，而无需黑能。
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.
