Eternal Inflation and the Refined Swampland Conjecture

I apply recently proposed "swampland" conjectures to eternal inflation in single-scalar field theories. Eternal inflation is a phase of infinite self-reproduction of a quasi-de Sitter universe which has been argued to be a generic consequence of cosmological inflation. The originally proposed de Sitter swampland conjectures were shown by Matsui and Takahashi, and by Dimopoulos, to be generically incompatible with eternal inflation. However, the more recently proposed "refined" swampland conjecture imposes a slightly weaker criterion on the scalar field potential in inflation, and is consistent with the existence of a tachyonic instability. In this Letter, I show that eternal inflation is marginally consistent with the refined de Sitter swampland conjecture. Thus, if the refined conjecture is correct, the existence of a landscape-based "multiverse" in string theory is not incompatible with a self-consistent ultraviolet completion, with significant consequences for model building in string theory.