一般f（R）理论中极平坦性的含义
Implications of extreme flatness in a general f(R) theory
摘要：
本文讨论了由$f(R) = \sum_{n}^{l} α_n M^{2(1-n)} R^n$定义的一个修正的引力理论。我们考虑有限和无限数量的条款在该系列中，而要求的爱因斯坦框架潜力的理论有一个平坦的区域周围的任何一个固定点。我们证明了极大平坦驻点的要求导致偶（奇）$l$的鞍点（局部极大值）的存在。对于$l\to\infty$，在这两种情况下，都可以得到具有小的指数抑制修正的Starobinsky模型。除了GR极小值外，爱因斯坦框架势还有一个反德西特真空.然而，我们认为，GR真空是绝对稳定的，既不能通过经典演化，也不能通过量子隧穿AdS。我们的结果表明，类似Starobinsky的模型是爱因斯坦框架势中具有极其平坦区域的$f(R)$理论的唯一可能实现。
英文摘要：
We discuss a modified gravity theory defined by $f(R) = \sum_{n}^{l} α_n M^{2(1-n)} R^n$. We consider both finite and infinite number of terms in the series while requiring that the Einstein frame potential of the theory has a flat area around any of its stationary points. We show that the requirement of maximally flat stationary point leads to the existence of the saddle point (local maximum) for even (odd) $l$. In both cases for $l\to\infty$ one obtains the Starobinsky model with small, exponentially suppressed corrections. Besides the GR minimum the Einstein frame potential has an anti de Sitter vacuum. However we argue that the GR vacuum is absolutely stable and AdS cannot be reached neither via classical evolution nor via quantum tunnelling. Our results show that a Starobinsky-like model is the only possible realisation of $f(R)$ theory with an extremely flat area in the Einstein frame potential.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
