Linear Perturbations in Brane Gas Cosmology

TL;DR

The paper studies linear perturbations of the dilaton-gravity background in Brane Gas Cosmology with string matter sources, focusing on long-wavelength fluctuations. By deriving and solving the perturbation equations in the generalized longitudinal gauge, the authors show that string inhomogeneities and dilaton perturbations do not induce instabilities; the internal six dimensions remain stabilized at the self-dual radius while the three large spatial dimensions expand with a power-law, and perturbations decay or stay constant at late times. The key finding is that long-wavelength perturbations are sub-leading to purely gravitational and dilaton terms, ensuring the robustness of BGC predictions. This supports the viability of moduli stabilization within BGC against linear inhomogeneities, while also highlighting the limitations of linear analysis and the need to explore non-linear effects and flux dynamics.

Abstract

We consider the effect of string inhomogeneities on the time dependent background of Brane Gas Cosmology. We derive the equations governing the linear perturbations of the dilaton-gravity background in the presence of string matter sources. We focus on long wavelength fluctuations and find that there are no instabilities. Thus, the predictions of Brane Gas Cosmology are robust against the introduction of linear perturbations. In particular, we find that the stabilization of the extra dimensions (moduli) remains valid in the presence of dilaton and string perturbations.

Figures (1)

• Figure 1: A comparison between the numerical background solutions obtained in stable (red or light line) and the analytical approximation used in this paper (green or dark line).