标题： 从$F(R)$引力的奇异暴胀宇宙 显示英文标题

标题： Singular Inflationary Universe from $F(R)$ Gravity

摘要： 与破碎奇点不同，所谓的第四类有限时间奇点提供了宇宙在不产生任何灾难性效应的情况下平滑通过它的可能性。 然后问题是，在宇宙演化过程中是否可以检测到第四类奇点的影响。 在本文中，我们在$F(R)$引力的背景下探讨这个问题。 正如我们所展示的，第四类奇点的影响出现在哈勃流参数中，这些参数决定了宇宙系统的动力学演化。 因此，我们研究了各种包含第四类奇点的暴胀模型，其中奇点发生在暴胀结束时。 特别是我们研究了一个玩具模型和一个奇异版本的$R^2$引力哈勃率。 正如我们证明的那样，一些哈勃流参数在奇点处变得奇异，这一效应表明在该点发生了动力学不稳定。 这种动力学不稳定性最终表明暴胀的优雅退出。 我们证明该玩具模型在奇点处有一个不稳定的德西特点，因此确实可以触发优雅退出。 在奇异暴胀模型的情况下，优雅退出以标准方式进行。 在奇异暴胀模型的情况下，我们发现了奇异演化的各种情景，其中大多数与观测结果相容，只有一种会导致严重的不稳定性。 我们还将普通的Starobinsky模型与奇异暴胀模型进行了比较，并指出了定性和定量的差异。 最后，我们研究了玩具模型和奇异暴胀模型的晚期动力学，并证明了早期和晚期加速的统一是可以实现的。 我们还表明，可以实现类似于$\Lambda$-冷暗物质模型的晚期加速。 显示英文摘要

摘要： Unlike crushing singularities, the so-called Type IV finite-time singularity offers the possibility that the Universe passes smoothly through it, without any catastrophic effects. Then the question is if the effects of a Type IV singularity can be detected in the process of cosmic evolution. In this paper we address this question in the context of $F(R)$ gravity. As we demonstrate, the effects of a Type IV singularity appear in the Hubble flow parameters, which determine the dynamical evolution of the cosmological system. So we study various inflation models incorporating a Type IV singularity, with the singularity occurring at the end of inflation. Particularly we study a toy model and a singular version of the $R^2$ gravity Hubble rate. As we evince, some of the Hubble flow parameters become singular at the singularity, an effect which indicates that at that point a dynamical instability occurs. This dynamical instability eventually indicates the graceful exit from inflation. We demonstrate that the toy model has an unstable de Sitter point at the singularity, so indeed graceful exit could be triggered. In the case of the singular inflation model, graceful exit proceeds in the standard way. In the case of the singular inflation model, we found various scenarios for singular evolution, most of which are compatible with observations, and only one leads to severe instabilities. We also compare the ordinary Starobinsky with the singular inflation model, and we point out the qualitative and quantitative differences. Finally, we study the late-time dynamics of the toy model and of the singular inflation model and we demonstrate that the unification of early and late-time acceleration can be achieved. We also show that it is possible to achieve late-time acceleration similar to the $\Lambda$-Cold Dark Matter model.