Late-time dynamics of brane gas cosmology

Brane gas cosmology is a scenario inspired by string theory which proposes a simple resolution to the initial singularity problem and gives a dynamical explanation for the number of spatial dimensions of our Universe. In this work we study analytically and numerically the late-time behavior of these types of cosmologies taking proper care of the annihilation of the winding modes. This helps us clarify and extend several aspects of their dynamics. We find that the decay of the winding states into nonwinding states behaving like a gas of ordinary nonrelativistic particles precludes the existence of a late expansion phase of the Universe and obstructs the growth of three large spatial dimensions as we observe today. We propose a generic solution to this problem by considering the dynamics of a gas of nonstatic branes. We also obtain a simple criterion for the initial conditions to ensure the small string coupling approximation throughout the whole dynamical evolution, and consequently the consistency of an effective low-energy description. Finally, we reexamine the general conditions for a loitering period in the evolution of the Universe that could serve as a mechanism to resolve the brane problem---a problem equivalent to the domain wall problem in standard cosmology--- and discuss the scaling properties of a self-interacting network of winding modes taking into account the effects of dilaton dynamics.