Eternal Inflation and Swampland Conjectures

TL;DR

This paper investigates whether eternal inflation can occur under recent string Swampland criteria, finding that only chaotic eternal inflation near the Planck scale is compatible with these conjectures.

Contribution

It demonstrates that eternal inflation of the chaotic type can occur within the bounds of the Swampland criteria, specifying the conditions on parameters c and D.

Findings

Eternal inflation of chaotic type is possible for specific parameter ranges.

Hubble parameter during inflation is close to the Planck scale.

Only certain types of eternal inflation satisfy the Swampland constraints.

Abstract

We study if eternal inflation is realized while satisfying the recently proposed string Swampland criteria concerning the range of scalar field excursion, $|\Delta \phi| < \mathcal{D} \cdot M_{\rm P}$, 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 $2 \pi c \lesssim H_{\rm inf}/M_{\rm P} < 1/\sqrt{3}$.