In this paper we propose a new mechanism of inflating the Universe with non
-BPS D4-branes which decay into stable D3-branes via tachyon condensation.
In a single brane scenario the tachyon potential is very steep and unable t
o support inflation. However, if the universe lives in a stack of branes pr
oduced by a set of noninteracting unstable D4-branes, then the associated s
et of tachyons. may drive inflation along our 3 spatial dimensions. After t
achyon condensation the Universe is imagined to be filled with a set of par
allel stable D3-branes. We study the scalar density perturbations and rehea
ting within this setup. (C) 2001 Elsevier Science B.V. All rights reserved.