All classes of spatially homogeneous space-time models are found that allow the integration of the equations of motion of test particles and the eikonal equation by the method of complete separation of variables according to type (2.1). Four classes of model data are obtained. The resulting models can be applied in any modified metric theories of gravity. Two of the above models allow solutions of the Einstein equations with a cosmological constant and radiation. For the models of a spatially homogeneous Universe with a cosmological constant and radiation obtained in Einstein's theory of gravity, the Hamilton-Jacobi equations of motion of the test particles and the eikonal equation for radiation are integrated by the method of separation of variables.

中文翻译：

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空间齐次模型 Stäckel 空间类型 (2.1)

找到了所有类别的空间均匀时空模型，它们允许通过根据类型 (2.1) 完全分离变量的方法整合测试粒子的运动方程和 eikonal 方程。获得四类模型数据。由此产生的模型可以应用于任何修正的引力度量理论。上述模型中的两个允许使用宇宙常数和辐射来求解爱因斯坦方程。对于爱因斯坦引力理论得到的具有宇宙常数和辐射的空间均质宇宙模型，通过变量分离的方法对测试粒子运动的Hamilton-Jacobi方程和辐射的ekonal方程进行积分。