Light may not travel at ‘the speed of light’ unless its mass equivalent is zero and its wavelength is infinite if it follows the equation: c2 + V ^2 = G x mass / radius, where V is its absolute velocity. However, as the mass equivalency difference between visible light and gamma rays is so small, the speeds would have to be known to at least 15 significant figures to distinguish between them. Even a cosmological event at the edge of the universe releasing both visible light and gamma rays would result in an immeasurable arrival time difference. The entire electromagnetic spectrum travels at the same speed within our measuring capability.
However, this would not be true for enormously energetic photons according to the above equation. Perhaps, the most extreme case would be for a photon such as described in ‘an exercise’. Photons approaching even a fraction of that mass equivalency would be undetectable because of their almost infinitesimal wavelength and pass through ordinary matter.
There are no known cosmological events capable of producing such massively energetic photons. However, that may not be true during the conditions of the Big Bang. Once formed, they could still be existence today. Their properties should resemble those attributed to ‘dark matter’. That possibility should be taken into serious consideration.