Brane world cosmologies with varying speed of light

We study cosmologies in the Randall-Sundrum models, incorporating the possibility of time-varying speed of light and Newton's constant. The cosmologies with varying speed of light (VSL) were proposed by Moffat and by Albrecht and Magueijo as an alternative to inflation for solving the cosmological problems. We consider the case in which the speed of light varies with time after the radion or the scale of the extra dimension has been stabilized. We elaborate on the conditions under which the flatness problem and the cosmological constant problem can be resolved. Particularly, the VSL cosmologies may provide a possible mechanism for bringing the quantum corrections to the fine-tuned brane tensions after the SUSY breaking under control. (author)