标题： 相对宇宙学与物质的内禀自旋：爱因斯坦-卡特理论中的结果与定理 显示英文标题

标题： Relativistic cosmology and intrinsic spin of matter: Results and theorems in Einstein-Cartan theory

摘要： 我们首先呈现四维时空中的1+3分解的一般结构方程组，这些方程适用于基于度量相容仿射联络的任何引力理论。 然后我们将这些方程应用于爱因斯坦-卡特理论中宇宙解的研究，其中物质由具有固有自旋的完美流体建模。 结果显示度量张量可以由一个广义的FLRW解描述。 然而，由于存在挠率，Weyl张量可能不会消失。 挠率与Weyl张量之间的耦合导致结论，在这个宇宙学模型中，宇宙要么是平坦的，要么是开放的，排除了闭合宇宙的可能性。 在开放情况下，我们推导出Weyl张量磁部分无迹部分的波动方程，并展示了动态宇宙中物质的固有自旋如何导致引力波的产生和辐射。 最后，在这个宇宙学模型中发现，具有固有自旋作为其源的挠率张量有助于正加速膨胀的宇宙。 将该模型的理论预测与当前实验数据进行比较后，我们得出结论，挠率不能完全取代宇宙常数的作用。 显示英文摘要

摘要： We start by presenting the general set of structure equations for the 1+3 threading spacetime decomposition in 4 spacetime dimensions, valid for any theory of gravitation based on a metric compatible affine connection. We then apply these equations to the study of cosmological solutions of the Einstein-Cartan theory in which the matter is modeled by a perfect fluid with intrinsic spin. It is shown that the metric tensor can be described by a generic FLRW solution. However, due to the presence of torsion the Weyl tensors might not vanish. The coupling between the torsion and Weyl tensors leads to the conclusion that, in this cosmological model, the universe must either be flat or open, excluding definitely the possibility of a closed universe. In the open case, we derive a wave equation for the traceless part of the magnetic part of the Weyl tensor and show how the intrinsic spin of matter in a dynamic universe leads to the generation and emission of gravitational waves. Lastly, in this cosmological model, it is found that the torsion tensor, which has an intrinsic spin as its source, contributes to a positive accelerated expansion of the universe. Comparing the theoretical predictions of the model with the current experimental data, we conclude that torsion cannot completely replace the role of a cosmological constant.