广义相对论与膨胀宇宙学中的约束与变形理论：广义相对论中的应力场和应变场理论与宇宙膨胀
Théorie des champs des contraintes et déformations en relativité générale et expansion cosmologique: Theory of stress and strain fields in general relativity and cosmological expansion
摘要：
本文提出在爱因斯坦方程中加入应力-能量张量，假定物质能量和度规时空都是具有弹性性质的连续介质。首先给出了应力张量的一般表达式，它与应变张量成线性关系。然后，我们给出了空间均匀各向同性宇宙介质应力张量的特殊表达式。在此基础上，我们推导出了修正的Friedmann方程。在第一近似中，我们最终得到通常的项$Λg_{μν}$，其中宇宙学常数$Λ=K\varepsilon$与体积模量K和体积的相对变化（膨胀）有关。然后，我们推导出在二次近似下对标准模型的修正，它依赖于这两个新的参数。
英文摘要：
In this article we propose to add stress-energy tensor to the Einstein equations, assuming that the matter-energy and the metric space-time is nothing but a continuous medium with some elastic properties. We first give a general expression of the stress tensor which is linearly related to the strain tensor. Then, we give the particular expression of the stress tensor for a spatially homnogeneous and isotropic cosmological medium. After that we derive the modified Friedmann equations. In first approximation, we end up with the usual term $Λg_{μν}$ , where the cosmological constant $Λ=K\varepsilon$ is related with the bulk modulus K and the relative variation of volume (dilatation). Then we derive corrections to the standard model in second approximation, which depend on these two new parameters.
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