Abstract
In this paper we generalize the black hole bound of arXiv:0706.2050 to de Sitter spaces, and apply it to various vacua in the landscape, with a special emphasis on slow-roll inflationary vacua. Non-trivial constraints on the lifetime and the Hubble expansion rate emerge. For example, the general tendency is, that for the fixed number and the increasing mass of the species, vacua must become more curved and more unstable, either classically or quantum mechanically. We also discuss the constraints on the lifetime of vacua in the landscape, due to decay into the neighboring states.
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