Could the accelleration of the expanding universe be caused by the photons inflating it.
Sure. This as well as many, many other theories are all possible. The problem here is that if the answer to this question was available, it would be searchable. It is still in speculation and at this time, science is studying by way of the proton accelerator projects, such as the LHC (Large Hadron Collider) what causes this acceleration and how it all "began". This, too, while provable as being in existence, is still only a theory of why it is happening now. One of the ideas is to recreate an event, such as the one labeled the "Big Bang" and see what happens to those particles. This would give a much greater understanding of the process from the beginning. If a notable increase is observed at other levels of expansion, it will give more indication of pattern acceleration and a likelihood that is what is continuing now.
