Brane world cosmologies with varying speed of light

We study cosmologies in the Randall-Sundrum (RS) models, incorporating the possibility of a 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 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. We find that the RS models are more restrictive about possible desirable VSL cosmological models than standard general relativity. Particularly, VSL cosmologies may provide us with a possible mechanism for bringing quantum corrections to fine-tuned brane tensions after the SUSY breaking under control.