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I realize that there are theoretical reasons to reject the idea that the charges on electrons and protons may not be exactly equal and opposite; and I am not suggesting that they're not.

Edited 12/20/18: However, I would like to know: if there were a very, very tiny imbalance between the electron's charge and the proton's charge (on the order of one part in $10^{36}$ or less), would it result in a cosmic expansion that resembles the expansion attributed to dark energy?

The rationale is that all atoms would have a very slight net charge of the same sign if there were such an imbalance; and as a result there would be a very slight net repulsive electrostatic force between all nominally neutral atoms. If the imbalance were small enough, atoms should still form, gravity should be sufficient to bind most (nominally neutral) matter together on most scales, and most other phenomena should be as currently observed, but it seems that at cosmological distances there might be some observable effects.

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I don't think this idea works, for the simple reason that the electromagnetic and gravitational forces scale the exact same way: they are both proportional to their respective 'charge' and inverse square.

Since your idea implies most apparently neutral objects would have roughly the same charge to mass ratio (since it depends on just the electron density), if the repulsion effect were strong enough to beat gravity at cosmological scales, it would also beat gravity on everyday scales, because the ratio of the two would remain exactly the same. But we're not repelled from the Earth.

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  • $\begingroup$ From the Newtonian perspective that seems right, but the nonlinearity of gravity in GR should change the effective charge to mass ratio at extremely long or extremely short ranges. $\endgroup$ – S. McGrew Dec 20 '18 at 19:12
  • $\begingroup$ by the way, it would require only the teeniest amount of unbalanced charge to overwhelm gravity because the electromagnetic force is so much stronger than gravity... $\endgroup$ – niels nielsen Dec 20 '18 at 19:53
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    $\begingroup$ A sufficiently small imbalance would make an immeasurably small difference in the emission/absorption spectra of atoms, and the interaction between an electron and a proton would be unaffected for most practical purposes. If there were an observable effect, I would expect it to show up in cosmological observations or in the behavior of charged matter in the vicinity of black holes. "Neutral" matter falling into black holes would give black holes a substantial charge. E.g., a charge ratio of $rq=10^{36}$ gives a sun-sized black hole a net charge of ~$1.9x10^{38} Coulombs. $\endgroup$ – S. McGrew Dec 20 '18 at 22:12
  • $\begingroup$ @knzhou, here is a counter-argument to your comment. Your argument would seem to be correct except for two things. First, if matter neutrons and other neutral particles are considered to be elementary particles in their own right, having exactly zero charge. $\endgroup$ – S. McGrew Dec 23 '18 at 14:56
  • $\begingroup$ Sorry, hit the wrong key. Wanted to erase the comment and write this: First, I think you are considering only the interaction between an electron and a proton, not the interaction between two atoms. Second, it seems clear that if a universe were filled with very slightly charged, mostly uniformly distributed matter, it would experience an electrostatic pressure tending to make it expand. $\endgroup$ – S. McGrew Dec 23 '18 at 15:05
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I don't think this idea works. Two hand-wavy reasons:

  1. This would predict that everything would be repelled from everything else on cosmological scales, which isn't true. Most things are receding from us, but not everything (e.g. Andromeda is approaching the Milky Way).

  2. If there was an imbalance in electric charge in galaxies, why wouldn't free electrons be attracted to galaxies and neutralize it? For this same reason, electrically-charged black holes aren't as astronomically significant as their electrically-neutral black holes.

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  • $\begingroup$ In regards to your second point, if the Universe has a net electrical charge, there won't be enough free electrons to go around. $\endgroup$ – Mark Dec 21 '18 at 0:17
  • $\begingroup$ @Mark that assumes there's the same number of protons as electrons in the universe, which presumably might not be the case. $\endgroup$ – Allure Dec 21 '18 at 0:49
  • $\begingroup$ In regard to @Allure's first point, a very weak repulsion wouldn't prevent relative motion. After all, Andromeda would be repelled from all directions by surrounding galaxies. A charge surrounded (out to infinity) by other like charges should feel no net force. $\endgroup$ – S. McGrew Dec 21 '18 at 1:00
  • $\begingroup$ @S.McGrew wouldn't that predict that there'd be a roughly equal number of redshifted and blueshifted galaxies? $\endgroup$ – Allure Dec 21 '18 at 1:02
  • $\begingroup$ @allure, why do you think so? $\endgroup$ – S. McGrew Dec 21 '18 at 1:04

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