We know galaxies are moving apart from each other due to the ability to look at the color shift of those galaxies.
The fact that galaxies are moving apart seems to be most-widely attributed to the idea that the universe itself is expanding or, that a Big Bang (explosion) occurred, propelling matter in every direction.
According to this question, a body could be propelled by emitting photons, (and, from my understanding this expands to other EM waves as well). It seems to go with it that being hit with photons and radiation would push us as well. (but correct me if I am wrong - because it is a basis for the rest)
If you imagine a roughly spherical shape of points, which aren't close enough to affect each other with gravity, all emitting photons or radiation, it seems to suggest that the points would start to move away from each other. The reasoning behind this is that the sum of being hit by all the other points' radiation would push a point in the direction opposite of where most of the other points are located.
Since the universe has existed for, well, a bit of an understatement: a long time, this could have built up momentum photon by photon over all these years between the galaxies?
Are there arguments which go against this possibility? Does this theory already exist and does it have a name?