Cosmology of Randall-Sundrum models with an extra dimension stabilized by balancing bulk matter

We provide the cosmological solutions for Randall-Sundrum models with the bulk energy-momentum $\hat T^5_5$ incorporated. It alters the Friedmann equation for the brane scale factor. We make a specific choice of $\hat T^5_5$ which is adjusted to stabilize the extra dimension. This makes it possible to compactify the extra dimension with a single positive tension brane, and this model provides a RS-type solution to the cosmological constant problem. When the same idea is applied to the RS model with two branes, the wrong sign of Friedmann equation for the negative tension brane can be resolved and usual FRW cosmology is reproduced for the brane.