  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.

High Energy Physics - Theory;Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology