Emergent universe (EU) cosmological models with viscosity in a modified gravity which contains a general function [Formula: see text], where [Formula: see text] and [Formula: see text] denote the curvature scalar and the trace of the energy–momentum tensor, respectively, are studied in a flat Friedmann–Robertson–Walker metric. Cosmological solutions are obtained in [Formula: see text] theory of gravity, which represented as [Formula: see text] with bulk viscosity that described by Eckart theory, truncated Israel Stewart theory and full Israel Stewart Theory. The physical and geometrical features of the EU models in [Formula: see text] gravity, where [Formula: see text] and [Formula: see text] are coupling parameters, with bulk viscosity are studied in details. Constraints of the EU models parameters in [Formula: see text] gravity with bulk viscosity are estimated from observational data set. The stability analysis of the equilibrium points admitting cosmological solutions of the dynamical system associated with the evolution in the modified gravity is studied in Eckart theory, truncated Israel Stewart theory and full Israel Stewart theory.

中文翻译：

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具有体积粘度的 f(R,T) 重力中涌现宇宙的观测约束

新兴宇宙 (EU) 宇宙学模型在修正重力中具有粘性，其中包含一般函数 [公式：见文本]，其中 [公式：见文本] 和 [公式：见文本] 表示曲率标量和能量的轨迹——动量张量分别在平坦的 Friedmann-Robertson-Walker 度量中进行研究。宇宙学解是在[公式：见文本]重力理论中获得的，它表示为[公式：见文本]，具有由 Eckart 理论、截断的 Israel Stewart 理论和完整的 Israel Stewart 理论描述的体积粘度。EU模型在[公式：见文]重力中的物理和几何特征，其中[公式：见文]和[公式：见文]为耦合参数，对体积粘度进行了详细研究。[公式中的欧盟模型参数的约束：见正文] 具有体积粘度的重力是根据观测数据集估算的。在Eckart理论、截断Israel Stewart理论和完整Israel Stewart理论中研究了平衡点的稳定性分析，该平衡点承认与修正重力演化相关的动力系统的宇宙学解。