Nonlinear dynamics of flux compactification

TL;DR

This paper investigates the nonlinear evolution of unstable flux compactifications using numerical relativity, revealing their potential to form warped geometries, undergo inflation-like expansion, or evolve towards singularities.

Contribution

It introduces a numerical relativity approach to study the nonlinear dynamics of flux compactifications, highlighting their instability and possible evolution pathways.

Findings

Homogeneous flux compactifications are unstable to warping.

Warping can mimic slow-roll inflation in certain cases.

Lower-dimensional vacua with slower expansion are favored dynamically.

Abstract

We study the nonlinear evolution of unstable flux compactifications, applying numerical relativity techniques to solve the Einstein equations in $D$ dimensions coupled to a $q$-form field and positive cosmological constant. We show that initially homogeneous flux compactifications are unstable to dynamically forming warped compactifications. In some cases, we find that the warping process can serve as a toy-model of slow-roll inflation, while in other instances, we find solutions that eventually evolve to a singular state. Analogous to dynamical black hole horizons, we use the geometric properties of marginally trapped surfaces to characterize the lower dimensional vacua in the inhomogeneous and dynamical settings we consider. We find that lower-dimensional vacua with a lower expansion rate are dynamically favoured, and in some cases find spacetimes that undergo a period of accelerated expansion followed by contraction.