Two-brane system in a vacuum bulk with a single equation of state

We study the cosmology of a two-brane model in a five-dimensional spacetime, where the extra spatial coordinate is compactifed on an orbifold. Additionally, we consider the existence on each brane of matter fields that evolve in time. Solving the Einstein equations in a vacuum bulk, we can show how the matter fields in both branes are connected and they do not evolve independently