Eternal Inflation and Swampland Conjectures

Abstract

We study if eternal inflation is realized while satisfying the recently proposed string Swampland criteria concerning the range of scalar field excursion, $|\Delta \varphi |<\mathcal{D}\cdot M_{\mathrm{P}}$, and the potential gradient, $|\nabla V|>c\cdot V/M_{\mathrm{P}}$, where $\mathcal{D}$ and $c$ are constants of order unity, and $M_{\mathrm{P}}$ is the reduced Planck mass. We find that only the eternal inflation of chaotic type is possible for $c\sim \mathcal{O}(0.01)$ and $1/\mathcal{D}\sim \mathcal{O}(0.01)$, and that the Hubble parameter during the eternal inflation is parametrically close to the Planck scale, and is in the range of $2\pi c\lesssim H_{\inf }/M_{\mathrm{P}}<1/\sqrt{3}$.

Comments: 6 pages; references added, version to appear in PRD