Why is the universe charge-neutral?

Question

The positive charges (such as from the protons) of the universe are almost neutralized by the negative charges (such as from the electrons).

Is there an explanation for this neutrality? Does it constitute a naturalness/fine-tuning problem? A likelier prior would be a universe with arbitrary charge density rather than the exact cancellation of positive and negative charges.

Well, one can entertain an anthropic "explanation": a charged universe would experience a much faster-accelerated expansion due to the repulsive nature of the charges, and we humans can not survive this charged universe.

That said, I am asking for a non-anthropic explanation of the fine-tuning of the neutral universe.

BTW, "charge conservation" could NOT be the answer since charge conservation states that if the initial condition of the universe is charge-neutral, then the universe stays charge-neutral. But it doesn't answer why the initial condition is charge-neutral. The initial condition of the universe could be any arbitrary charge density.

Answer 1

A nonzero net charge density is incompatible with the cosmological principle. Homogeneity implies a constant electromagnetic field, which implies via Gauss's law that the contained charge is zero. The universe was homogeneous to extremely high precision in the past, and charge is conserved. The reason for the homogeneity isn't known, but at least this argument shows that whatever can produce those conditions will also produce a neutral universe.

The problem with a charged homogeneous universe is closely related to the problem with Newton's static universe. In the gravitational case, you can argue that a universe with a constant nonzero mass density is observationally homogeneous (though not static), because the universality of gravity means it's impossible in practice to detect a constant gravitational field, and the field in any two local neighborhoods of the homogeneous universe differs by a constant. General relativity elevates that to an impossibility in principle. But that argument doesn't work for electromagnetism because you can detect a constant field by comparing its effect on charged and uncharged objects.

Answer 2

Charge conservation says that a universe which began charge-neutral would have remained charge-neutral. But why assume that it started out charge-neutral?

A better way to ask the question is to define the "charge asymmetry" of some volume as its net charge divided by the number of baryons it contains. We might compare this to the "baryon-antibaryon asymmetry" which describes the fact that there is more matter in the universe than antimatter. For the matter asymmetry, we normalize to the number of photons in the cosmic microwave background, since the antibaryons are no longer around. With this normalization, we find that the excess of matter over antimatter in the early universe was small, of order one part per billion ($10^{-9}$). Finding the differences between matter and antimatter which gave us this asymmetry and our matter-filled world is a major part of the experimental program of nuclear and particle physics.

For our charge asymmetry, we can compare Newton's and Coulombs laws for interacting baryons, $$ \begin{align} \frac{Gm_1m_2}{r^2} &\overset?= \frac{\alpha\hbar c \cdot q_1q_2}{r^2} \end{align} $$ to see that continuous matter becomes gravitationally unbound for one excess fundamental charge per about $10^{18}$ nucleons. The stability of the Earth tells you that the charge asymmetry in rocky matter is well below $10^{-18}$. The literature review by the Particle Data Group currently gives charge difference limits for electrons and protons of $$ \begin{align} \left| q_{e^+} + q_{e^-} \right| / e &< 4\times10^{-8} \\ \left| q_{p} + q_{\bar p} \right| / e &< 7\times10^{-10} \\ \left| q_{p} + q_{e^-} \right| / e &< 7\times10^{-21} \\ \left| q_{n} \right| /e &\lesssim 0.8\times10^{-21} \end{align} $$

This evidence is for the equality of charges for the fundamental particles. But it's also possible to imagine an unknown early-universe process which produced an initial charge asymmetry, which would then have been preserved as the universe evolved. We know that, for every $10^{9}$ early-universe antibaryons, there were roughly $10^9 + 1$ baryons. Suppose that, at its largest scales, the universe contains a few more protons than electrons. What limits do we set on this asymmetry? I'm pretty sure our upper limit of $10^{-21\text{-ish}}$ can be applied to the baryonic matter of a galaxy, perhaps a galaxy cluster. I can think of handwaving arguments for and against applying the same limit to the intergalactic medium.

This is more of an extended comment than an answer. In order to ask "why is" the universe charge-neutral, we must first have an answer to the "is" part. In modern physics we answer such questions by quantifying any possible non-neutrality, and setting upper limits. Our existing upper limits of $10^{-21}$ for non-neutral matter sound pretty impressive in isolation — but it's only one part in a thousand of the charge non-neutrality which would overbalance gravitational stability.

Answer 3

There is as of yet insufficient data to produce a meaningful answer.

I would certainly love to tell you that the universe is charge-neutral, because that would imply I know enough about the Universe to say that the number of negative charges exactly equals the number of positive charges in magnitude. Unfortunately, I'm not sure we're able to say that it is perfectly charge neutral. There could be a spare proton, or even a few spare quindecillion protons, somewhere out there imbalancing the Universe's net electric charge, and it would be basically impossible to tell from here. Obviously no such things exist nearby, but we can't rule it out for the entire Universe at large. Heck, we aren't even sure about the large-scale shape of the Universe (probably flat and expanding per FLRW, but we haven't gone to the corners and edges to check). Trying to say that it is charge-neutral would be shocking without further knowledge about what the Big Bang was like.

Of course, the best reason we have for why the Universe might be charge-neutral (if it is, which is strongly believed but again can't be proven really) is because the past timelike singularity of the Big Bang was also charge-neutral. When quarks and leptons W and Z bosons appeared (the only known charged particles), they should have appeared in roughly-equal quantities of particles and antiparticles, which would balance each other out electromagnetically. Again, that raises the question: where's the antimatter? If all kinds of particles were produced in even amounts, there should be more negative charge than positive charge, since up-type quarks have $Q=+2/3$ and down-type quarks have $Q=-1/3$ and leptons have $Q=-1$ (disregarding charged W bosons, which are ephemeral), leading to an overall charge per-set-of-particle of $-2/3$. Antimatter production during the Big Bang would rectify this, but we observe very little antimatter in the Universe compared to matter.

Ultimately, it comes down to "we don't know that it even is charge-neutral, and if it is, we're not sure exactly why". One can say that a charged Universe would not be able to form complex life and hence humans, but that's the boring anthropic answer that beats any question about why the Universe is the way it is. Yes, the Universe probably is charge-neutral from observations, but if it is, the antimatter imbalance problem would be key to understanding why.

If you're willing to accept a charge-conservation answer after all my blabbering, you can just say that the Big Bang singularity was perfectly neutral, and when it generated all the different particles, it could only do so in neutral combinations, leading to a charge-neutral Universe. Whether this includes a backwards-in-time antimass Universe is still up for debate.