I do not think the experimental curve will alter.
The theoretical curve will not change because the mass of the photon will be very small to make any change.
It would be an ideal Bose gas with the difference that average particle number is now conserved and thus there is a non-zero chemical potential. You can just look up the solution for this textbook case.
As a striking consequence, we should not be able to detect the cosmic background radiation because its intensity would be suppressed for distances larger than the Compton wavelength of the photon. In any event, it would be described by an ideal Bose gas with massive particles, as pointed out by Christian Binek, and could undergo Bose-Einstein condensation at low temperatures.
You may be right if we want to get it theoretically.
However, the experimental limit for the photon mass is very law.
I wonder what will be the photon to baryon ration if we take into account the photon mass?
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