Late cosmology of brane gases with a two-form field

Abstract

We consider the effects of a two-form field on the late-time dynamics of brane gas cosmologies. Assuming thermal equilibrium of winding states, we find that the presence of a form field allows a late stage of expansion of the Universe even when the winding degrees of freedom decay into a pressureless gas of string loops. Finally, we suggest to understand the dimensionality of the Universe not as a result of the thermal equilibrium condition but rather as a consequence of the symmetries of the geometry.

Figures (2)

• Figure 1: Phase space $(f,l)$. These curves represent the numerical solutions of the equations of motion for an efficiency parameter of the winding mode decay $c=0.1$, and a gas of small loops with $\gamma=1/3$ (top) and $\gamma=0$ (bottom). The straight lines correspond to $H_o=0$, the dashed lines to $H_o=0.001$, and the dotted-dashed lines to $H_o=0.005$. The grey area, $f^2-3l^2<0$, represents a region where the total matter energy is negative. The border lines, $l=\pm f/\sqrt{3}$, are straight solutions with $E_w=E_l=U=0$ and therefore cannot be crossed by other trajectories.
• Figure 2: Phase space $(f,l)$. These curves represent the numerical solution of the equations of motion without winding mode annihilation ($c=0$). The straight line correspond to $H_o=0$, the dashed line to $H_o=0.001$, and the dotted-dashed line to $H_o=0.005$.