An effective Lagrangian approach, partly inspired by Quantum Loop Cosmology (QLC), is presented and formulated in a non flat FLRW space–times, making use of modified gravitational models. The models considered are non generic, and their choice is dictated by the necessity to have at least second order differential equations of motion in a non flat FLRW space–time. This is accomplished by a class of Lagrangian which are not analytic in the curvature invariants, or making use of a mimetic gravitational scalar field. In this paper we want to show that, for some effective models, although the associated generalized Friedmann equation may admit non singular metrics as solutions, the de Sitter space–time is present only for a restricted class, which includes General Relativity and Lovelock gravity. The other models admit pseudo de Sitter solutions, namely FLRW metrics, such that for vanishing spatial curvature looks like flat de Sitter patch, but for non vanishing spatial curvature are regular bounce metrics or, when the spatial curvature is negative, Big-Bang singular metrics.

一种有效的拉格朗日方法，部分受量子环宇宙学（QLC）的启发，并利用修正的引力模型，在非平坦的FLRW时空中提出和提出。所考虑的模型是非通用的，其选择取决于在非平坦的FLRW时空中至少具有二阶运动微分方程的必要性。这是通过一类拉格朗日函数来完成的，该类不对曲率不变量进行解析，也不利用模拟引力标量场。在本文中，我们希望证明，对于某些有效的模型，尽管相关联的广义Friedmann方程可以接受非奇异度量作为解决方案，但de Sitter时空仅针对受限类（包括广义相对论和Lovelock引力）存在。其他模型接受伪de Sitter解决方案，