We know that immediately after the Big Bang space was opaque to light. As space expanded, light could travel. However I would think that as space expanded at some de sites the light would be much slower than it is today so that the speed of light was much lesser at the beginning? If so when we peer at the edge of the visible universe won't this "slower" light interfere with the "faster" light and give larger readings for the size of the universe?
I think there is no more "slow" light from the begining od the universe remaining because photon has accelerated after expansion to reach their current speed. Maybe I'm wrong but to me it seems to be the right way to think.
As far as I know the Speed of light has Always been constant. But some scientists suggest that the physical constants might Change slightly over time. The Situation in Inflation seems to be a bit different.