Flux Compactifications: Stability and Implications for Cosmology

TL;DR

This paper analyzes flux compactifications, demonstrating conditions for stabilization, the relation between curvature and stability, and deriving an upper bound on inflation scale based on radion dynamics.

Contribution

It provides a detailed analysis of radion stabilization conditions and establishes a maximum inflation scale in flux compactification models.

Findings

Stable compactifications on hyperbolic manifolds require negative cosmological constant.

Radion mass is of order the compactification scale with Planck-suppressed couplings.

An upper bound on inflation scale is derived as V_max ~ M_c^2 M_P^2.

Abstract

We study the dynamics of the size of an extra-dimensional manifold stabilised by fluxes. Inspecting the potential for the 4D field associated with this size (the radion), we obtain the conditions under which it can be stabilised and show that stable compactifications on hyperbolic manifolds necessarily have a negative four-dimensional cosmological constant, in contradiction with experimental observations. Assuming compactification on a positively curved (spherical) manifold we find that the radion has a mass of the order of the compactification scale, M_c, and Planck suppressed couplings. We also show that the model becomes unstable and the extra dimensions decompactify when the four-dimensional curvature is higher than a maximum value. This in particular sets an upper bound on the scale of inflation in these models: V_max \sim M_c^2 M_P^2, independently of whether the radion or other field is responsible for inflation. We comment on other possible contributions to the radion potential as well as finite temperature effects and their impact on the bounds obtained.