A Note on the Swampland Distance Conjecture

Abstract: 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.