Cosmologies of multiple spherical brane-universe model

The Friedmann-Robertson-Walker metric with spherical topology is calculated as an effective metric at the brane in a multiple brane D-dimensional spacetime scenario. In this model the radius of the brane is the cosmological scale factor, and its evolution is calculated from the viewpoint of the observers on their respective branes. The cosmology of the brane-universe is analyzed in cases where the anisotropic pressure has a cosmological-constant-like state equation. The pressure values needed to distinguish the oscillating, expanding or collapsing solutions are found, and the minimum value of a brane-universe mass to prevent a collapse into a black hole is also calculated. As a result, we find solutions indicating a bouncing universe, and solutions with more than one oscillatory phase. To validate the analytical results, the equation of motion is solved numerically to show the different cosmological scenarios.