In today's scenario, going beyond Einstein's theory of gravity leads us to some more complete and modified gravity theories. One of them is the f(R, T) gravity in which R is the Ricci scalar, and T is the trace of the energy‐momentum tensor. Using a well‐motivated linear f(R, T) gravity model with a single parameter, we studied the strong energy condition (SEC), the weak energy condition (WEC), the null energy condition (NEC), and the dominant energy condition (DEC) under the simplest non‐minimal matter geometry coupling with a perfect fluid distribution. The model parameter is constrained by energy conditions and a single‐parameter proposed equation of state (EoS), resulting in the compatibility of the f(R, T) models with the accelerated expansion of the universe. It is seen that the EoS parameter illustrates the quintessence phase in a dominated accelerated phase, pinpoint to the cosmological constant yields as a prediction the phantom era. Also, the present values of the cosmological constant and the acceleration of the universe are used to check the viability of our linear f(R, T) model of gravity. It is observed that the positive behavior of DEC and WEC indicates the validation of the model. In contrast, SEC is violating the condition resulting in the accelerated expansion of the universe.

中文翻译：

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非最小耦合f（R，T）重力下的能量条件

在今天的情况下，超越爱因斯坦的引力理论会使我们得到一些更完整和经过修改的引力理论。其中之一是f（R，T）重力，其中R是Ricci标量，T是能量动量张量的迹线。使用动机良好的线性f（R，T）具有单个参数的重力模型，我们研究了最简单的非最小物质几何耦合下的强能条件（SEC），弱能条件（WEC），零能条件（NEC）和优势能条件（DEC）具有完美的流体分布。模型参数受能量条件和建议的单参数状态方程（EoS）约束，从而导致f（R，T）的兼容性宇宙加速膨胀的模型。可以看出，EoS参数说明了处于主导加速阶段的精粹阶段，指出了宇宙学常数产量作为对幻影时代的预测。同样，宇宙常数的当前值和宇宙的加速度也被用来检查我们的线性f（R，  T）引力模型的可行性。观察到DEC和WEC的积极行为表明了该模型的有效性。相反，SEC违反了导致宇宙加速膨胀的条件。