  We consider the cosmological implications of light travelling faster in the
early Universe. We propose a prescription for deriving corrections to the
cosmological evolution equations while the speed of light $c$ is changing. We
then show how the horizon, flatness, and cosmological constant problems may be
solved. We also study cosmological perturbations in this scenario and show how
one may solve the homogeneity and isotropy problems. As it stands, our scenario
appears to most easily produce extreme homogeneity, requiring structure to be
produced in the Standard Big Bang epoch. Producing significant perturbations
during the earlier epoch would require a rather careful design of the function
$c(t)$. The large entropy inside the horizon nowadays can also be accounted for
in this scenario.
