  We have investigated the finite temperature systems of non-BPS D-branes and
D-brane-anti-D-brane pairs in the previous papers. It has been shown that
non-BPS D9-branes and D9-anti-D9 pairs become stable near the Hagedorn
temperature on the basis of boundary string field theory. This implies that
there is a possibility that these spacetime-filling branes exist in the early
universe. We study the time evolution of the universe in the presence of
non-BPS D9-branes on the basis of boundary string field theory in this paper.
We try to construct the following scenario for the early universe: The universe
expands at high temperature and the open string gas on the non-BPS D9-branes
dominates the total energy of the system at first. The temperature decreases as
the universe expands. Then the non-BPS D9-branes become unstable at low
temperature and decay through tachyon condensation. We obtain some classical
solutions for Einstein gravity and dilaton gravity in the very simple cases.
