We propose a new brane world scenario. In our model, the Universe starts as a small bulk filled with a dense gas of branes. The bulk is bounded by two orbifold fixed planes. An initial stage of isotropic expansion ends once a weak potential between the orbifold fixed planes begins to dominate, leading to contraction of the extra spatial dimensions. Depending on the form of the potential, one obtains either a non-inflationary scenario which solves the entropy and horizon problem, or an improved brane-antibrane inflation model.