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If the electron is moving at relativistic speed relative to comoving observers, yes. But the number of electrons that were doing that for the vast majority of the universe's history were negligible. "Cold" matter, i.e., matter that is at rest relative to comoving observers, does not redshift as the universe expands.The redshift mechanism reduces the kinetic energy of a electron, too, when it moves in an expanding universe.

We don't know that it is a scalar field. A cosmological constant, which is the simplest explanation for accelerating expansion, is not a scalar field; it's just a constant.What about a scalar field which some people claim, is causing the acceleration of the expansion right now?

Correct.a field whose energy increases in an expanding universe is "exotic matter"

No, it isn't. We already know of one scalar field: the Higgs field. We also know that quantum vacuum fluctuations are exotic. And we know that only something with the characteristics of exotic matter (which includes a cosmological constant--that is also exotic) can account for accelerating expansion. So given that we observe accelerating expansion, we have no choice but to believe that something exotic exists.It is highly speculative to assume that such matter could exist.

Not as long as there are no interactions, which was the condition you imposed on the other fields. In the absence of interactions, the number of quanta is constant for any field.What about the energy content in the hypothetical scalar field? Is that energy contained in quanta of some kind? If yes, does the number of such quanta increase as the universe expands?

In a strongly interacting system, the number of quanta does not have to be constant. But you said earlier you wanted to ignore interactions. Which is it? And if you don't want to ignore interactions, what interactions do you think are happening in the vast empty regions of our expanding universe?The question is harder in a strongly interacting system

No, it isn't. It's an obvious consequence of the stress-energy tensor for scalar fields plus the absence of interactions.The hypothesis that a scalar field can grow its energy in an expanding universe is highly speculative.

You really should read the literature before making such a claim.Literature seems to ignore the fact that the hypothetical scalar fields in inflation and dark energy would be exotic matter