  It is shown that varying speed of light cosmology follows from a
string-inspired minimal length uncertainty relation. Due to the reduction of
the available phase space volume per quantum mode at short wavelengths, the
equation of state of ultrarelativistic particles stiffens at very high
densities. This causes a stronger than usual deceleration of the scale factor
which competes with a higher than usual propagation speed of the particles.
Various measures for the effective propagation speed are analyzed: the group
and phase velocity in the high energy tail, the thermal average of the group
and phase velocity, and the speed of sound. Of these three groups, only the
first provides a possible solution to the cosmological horizon problem.
