Implication of the swampland distance conjecture on the Cohen–Kaplan–Nelson bound in de Sitter space

The Cohen–Kaplan–Nelson (CKN) bound formulates the condition that black hole is not produced by the low energy effective field theory dynamics. In de Sitter space it also constrains the maximal size of the matter distribution to be smaller than the cosmological horizon determined by black hole. On the other hand, the swampland distance conjecture (SDC) predicts that de Sitter space becomes unstable by the descent of the low energy degrees of freedom from UV. This results in the rapid increase in the energy inside the cosmological horizon, the distribution of which can be constrained by the CKN bound. We study the CKN bound in de Sitter space in detail and point out that when compared with the slow-roll in the inflation, the bound on the slow-roll parameter which forbids the eternal inflation is obtained.