We consider the Einstein static and the de Sitter universe solutions and examine their instabilities in a subclass of quadratic modified theories for gravity. This modification proposed by Nash is an attempt to generalize general relativity. Interestingly, we discover that the Einstein static universe is unstable in the context of the modified gravity. In contrast to Einstein static universe, the de Sitter universe remains stable under metric perturbation up to the second order.

中文翻译：

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修正引力二次理论中爱因斯坦和德西特宇宙的线性稳定性

我们考虑爱因斯坦静态和德西特宇宙解，并在引力二次修正理论的一个子类中检查它们的不稳定性。纳什提出的这种修改是对广义相对论的推广尝试。有趣的是，我们发现爱因斯坦静态宇宙在修正引力的背景下是不稳定的。与爱因斯坦静态宇宙相反，德西特宇宙在度量扰动下保持稳定，直到二阶。