Exponentially Large Extra Dimensions

TL;DR

This paper demonstrates how a light scalar in six dimensions can naturally stabilize extra dimensions at exponentially large sizes, resulting in a very light radion that affects early universe physics but remains consistent with current observations.

Contribution

It introduces a mechanism where a light scalar with cubic self-interaction stabilizes extra dimensions at exponentially large radii, producing a light radion with stable mass.

Findings

Extra dimensions stabilized at exponentially large radii.

Radion mass remains stable under radiative corrections.

Radion couplings lead to early universe deviations from General Relativity.

Abstract

We show how the presence of a very light scalar with a cubic self-interaction in six dimensions can stabilize the extra dimensions at radii which are naturally exponentially large, $r \sim \ell \exp [(4\pi)^3/g^2]$, where $\ell$ is a microscopic physics scale and $g$ is the (dimensionless) cubic coupling constant. The resulting radion mode of the metric becomes a very light degree of freedom whose mass, $m \sim 1/(M_p r^2)$ is stable under radiative corrections. For $1/r \sim 10^{-3}$ eV the radion is extremely light, $m \sim 10^{-33}$ eV. Its couplings cause important deviations from General Relativity in the very early universe, but naturally evolve to phenomenologically acceptable values at present.