Eternal Inflation and Swampland Conjectures

TL;DR

The work investigates whether eternal inflation can coexist with the swampland constraints $|\Delta\phi| < \mathcal{D} M_{\rm P}$ and $|\nabla V| > c V/M_{\rm P}$. It shows that only eternal chaotic inflation can satisfy these bounds, and only if the parameters satisfy $c \lesssim {\cal O}(0.01)$ and $1/\mathcal{D} \lesssim {\cal O}(0.01)$, with the Hubble scale during eternal inflation approaching the Planck scale $H_{ m inf}/M_{\rm P}$ in the range $2\pi c \lesssim H_{ m inf}/M_{\rm P} < 1/\sqrt{3}$. This implies a tightly constrained, near-Planckian inflationary regime where quantum gravity effects become relevant, and it has potential implications for the tensor-to-scalar ratio and dark-energy phenomenology under swampland assumptions.

Abstract

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