In the framework of the gravitational theory based on Lyra geometry and the general theory of relativity, we study Bianchi type I cosmological model in the presence of viscous fluid. A discussion about the suitability of the Sen equations as field equations in Lyra geometry is given. A clear physical meaning for the time component of the displacement vector, introduced in the Sen field equations used in the framework of Lyra geometry, is given by identifying it as a part of the energy momentum tensor (viscosity term). Exact solution of the Einstein field equations is given by assuming the model has a constant deceleration parameter. Moreover, we study the effect of the viscosity term on the entropy of the universe. A formula for calculating the entropy in the presence of viscosity is given by a combination between the second law of thermodynamics and the energy momentum tensor in a conservative manner. We calculate and study the thermodynamic functions (Enthalpy, Gibbs energy and Helmholtz energy) of the universe in the presence of viscosity in Lyra geometry and in the general theory of relativity. The physical and geometrical properties of the obtained models are discussed.

中文翻译：

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Lyra 几何学和广义相对论中的体积粘性 Bianchi I 型宇宙学模型

在基于天琴座几何的引力理论和广义相对论的框架下，我们研究了粘性流体存在下的比安奇I型宇宙学模型。讨论了 Sen 方程作为 Lyra 几何中的场方程的适用性。在 Lyra 几何框架中使用的 Sen 场方程中引入的位移矢量的时间分量的明确物理意义是通过将其识别为能量动量张量（粘度项）的一部分来给出的。假设模型具有恒定的减速参数，可以给出爱因斯坦场方程的精确解。此外，我们研究了粘度项对宇宙熵的影响。在存在粘度的情况下计算熵的公式是由热力学第二定律和能量动量张量以保守的方式组合给出的。我们在 Lyra 几何和广义相对论中计算和研究了在存在粘性的情况下宇宙的热力学函数（焓、吉布斯能量和亥姆霍兹能量）。讨论了所获得模型的物理和几何特性。