避免f（R，T）形式中的非continuity equation
Evading the non-continuity equation in the f(R, T) formalism
摘要：
我们提出了一种新的方法$f(R,T)$形式主义，通过探索其有效能量动量张量$T_{μν}^{eff}$，即$\tilde{T}_{μν}$额外的条款。这些结果来自于对量子效应的考虑，而量子效应在广义相对论和$f(R)$理论中通常被忽略，它们被加到通常的物质能量-动量张量中，得到$T_{μν}^{eff}=T_{μν}+\tilde{T}_{μν}$。从Bianchi恒等式出发，得到了有效能量动量张量的两部分守恒，而不是原来在$f(R,T)$理论中所讨论的物质不守恒.通过这种方式，物质创造的有趣场景，仍然缺乏观测证据，被回避了。这样一来，剩下两组宇宙学方程需要求解：类弗里德曼方程、$T_{μν}$守恒和$\tilde{T}_{μν}$守恒。我们提出了一个物理解释的有效能量动量张量，这是有关在宇宙中的刚性物质的存在的额外条款的守恒。这种方法的宇宙学特征，以及避免物质能量动量张量不守恒的好处。
英文摘要：
We present a new approach for the $f(R,T)$ formalism, by exploring the extra terms of its effective energy-momentum tensor $T_{μν}^{eff}$, namely $\tilde{T}_{μν}$. Those arise from the consideration of quantum effects, which are usually neglected in general relativity and $f(R)$ theories, and are summed to the usual matter energy-momentum tensor, yielding $T_{μν}^{eff}=T_{μν}+\tilde{T}_{μν}$. Purely from the Bianchi identities, the conservation of both parts of the effective energy-momentum tensor is obtained, rather than the non-conservation of the matter one, originally approached in the $f(R,T)$ theories. In this way, the intriguing scenario of matter-creation, which still lacks observational evidences, is evaded. One is left, then, with two sets of cosmological equations to be solved: the Friedmann-like equations along with the conservation of $T_{μν}$ and along with the conservation of $\tilde{T}_{μν}$. We present a physical interpretation for the conservation of the extra terms of the effective energy-momentum tensor, which is related to the presence of stiff matter in the universe. The cosmological features of this approach are presented and discussed as well as the benefits of evading the matter energy-momentum tensor non-conservation.
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