We demonstrate that a gas of wrapped branes in the early Universe can help
resolve the cosmological Dine-Seiberg/Brustein-Steinhardt overshoot problem in
the context of moduli stabilization with steep potentials in string theory.
Starting from this mechanism, we propose a cosmological model with a natural
setting in the context of an early phase dominated by brane and string gases.
The Universe inflates at early times due to the presence of a wrapped two brane
(domain wall) gas and all moduli are stabilized. A natural graceful exit from
the inflationary regime is achieved. However, the basic model suffers from a
generalized domain wall/reheating problem and cannot generate a scale invariant
spectrum of fluctuations without additional physics. Several suggestions are
presented to address these issues.Comment: 7 pages, 5 figures, REVTeX; References added, note adde