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Does electromagnetic radiation actually carry kinetic energy?

Looking around the web gives different answers. I have seen explanations like radiation pressure experiments as evidence, but this has been argued being effects from energy absorbed by the recipient.

In case it does not carry kinetic energy, the universe dynamics are challenged.

In my understanding, based on the law of energy conservation, the universe rest mass energy, the rest mass kinetic energy and electromagnetic radiation should equate over the universe different epochs.

In early epochs with electromagnetic radiation dominating over rest mass energy, the expansion rate/ kinetic energy must have been much higher in order for the energies to equate? At the moment just after singularity, the expansion rate must have been close to C? As rest mass start dominate expansion speed decreases? Energy equation is balanced by the speed of expansion/kinetic energy? G?

What we actually see looking out in universe, back in time, to a point in time were most rest mass in fact already was created is a quite steady expansion rate (arguably some acceleration in “recent” times)