Inflationary models with a non-zero background curvature require additional hypothesis or parameters compared to flat inflation and the procedure to construct them cannot be as simple as in the flat case. For this reason, there is no consensus on the primordial power spectrum that should be considered at large scales in a curved Universe. In this letter, we propose a model of curved inflation in which the usual canonical quantization and Bunch–Davies vacuum choice of the flat case can be considered. The framework is a recently proposed modification of general relativity (GR) in which a non-dynamical topological term is added to the Einstein equation. The model is universal as it is the same for any background curvature, and no additional parameters or hypothesis on the initial spatial curvature are introduced. This gives a natural and simple solution to the problem of constructing curved inflation, and at the same time provides an additional argument for this topological modification of general relativity.

中文翻译：

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弯曲膨胀的自然模型


与平坦膨胀相比，具有非零背景曲率的膨胀模型需要额外的假设或参数，并且构建它们的过程不能像在平坦情况下那样简单。出于这个原因，对于在弯曲宇宙中应该在大尺度上考虑的原始功率谱没有达成共识。在这封信中，我们提出了一个弯曲膨胀模型，其中可以考虑通常的规范量化和平坦情况的 Bunch-Davies 真空选择。该框架是最近提出的广义相对论 （GR） 的修改，其中在爱因斯坦方程中添加了一个非动力学拓扑项。该模型是通用的，因为它对于任何背景曲率都是相同的，并且不会引入有关初始空间曲率的其他参数或假设。这为构建弯曲膨胀的问题提供了一个自然而简单的解决方案，同时为广义相对论的这种拓扑修改提供了额外的论据。