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