D-brane Gases and Stabilization of Extra Dimensions in Dilaton Gravity

TL;DR

This paper models a 10-dimensional universe with wrapped Dp-branes, showing that a balance of pressures stabilizes extra dimensions and the dilaton, especially when p=6, leading to a stable 3D observed space.

Contribution

It generalizes low energy effective equations with brane sources in dilaton gravity and demonstrates dynamical stabilization of extra dimensions.

Findings

Extra dimensions are stabilized by brane pressure balance.

Dilaton becomes constant when p=6, stabilizing in Einstein frame.

Stabilization occurs in a string frame due to brane dynamics.

Abstract

We consider a toy cosmological model with a gas of wrapped Dp-branes in 10-dimensional dilaton gravity compactified on a p-dimensional Ricci flat internal manifold. A consistent generalization of the low energy effective field equations in the presence of a conserved brane source coupled to dilaton is obtained. It is then shown that the compact dimensions are dynamically stabilized in string frame as a result of a balance between negative winding and positive momentum pressures. Curiously, when p=6, i.e. when the observed space is three dimensional, the dilaton becomes a constant and stabilization in Einstein frame is also realized.