We discuss the Swampland Distance Conjecture in the framework of black hole thermodynamics. In particular, we consider black holes in de Sitter space and we show that the Swampland Distance Conjecture is a consequence of the fact that apparent horizons are always inside cosmic event horizons whenever they exist in the case of fast‐roll inflation. In addition, we show that the Bekenstein and the Hubble entropy bounds for the entropy in a region of spacetime lead similarly to the same conjecture.

中文翻译：

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关于沼泽距离猜想的一个注记

我们在黑洞热力学的框架内讨论了Swampland距离猜想。特别是，我们考虑了de Sitter空间中的黑洞，并且证明了Swampland距离猜想是以下事实的结果：在快速滚动式通货膨胀的情况下，视地平线始终存在于宇宙事件地平线之内。此外，我们证明了在时空区域中熵的Bekenstein熵和Hubble熵界类似地导致相同的猜想。