The inflation model is apparently needed to explain why the universe is homogeneous at large scales as there would be not be enough time for photons to travel between points if inflation had been constant.

Feynman's QED series says that there are small probability amplitudes for photons travelling faster than the usual speed of light.

In the early universe where space was small in each dimension, wouldn't the Uncertainty Principle have caused photons' velocity to fluctuate wildly and be above the general speed of light much more often than normal, thereby allowing signals to move from one part of the early universe to another very quickly and removing the need for an exponential inflation theory? Please can someone inform me what is wrong with this logic =)