I've always wondered why the number of protons in the Universe exactly matches the number of electrons. They are such different particles with totally different cross sections. So, first of all, is this true? And, secondly, how could it be that they have been produced in the same amount after the Big-Bang?
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It has been confirmed true to a high level of precision, since it only takes a tiny unbalance in charge would overwhelm gravity and tear apart the galaxy (or clusters of galaxies on a larger scale). There are more charged particles than simply electrons and protons, but since they account for almost all charged particles the universe, equality of charge is equivalent to equality of electrons and protons.
As to why there is charge conservation: we assume that there was perfect conservation of charge, even with all the crazy high energy physics that happened just after the big bang. Why so? If there wasn't, you could generate perpetual energy by allowing a proton to fall into a deep negative charge potential well, converting it into a negatively charged particle, allowing it to fly away, converting it back, etc. The energy required/released by converting a particle would not depend on the electric potential since conversion would be a local process that knows nothing about the global structure of the electrostatic potential you have set up.
However, what about initial charge distribution? It turns out that in the early universe there was a time of inflation for which the universe expanded without the soup of mass/energy being diluted; the expansion would have diluted any charge imbalance.
Note: the only way in which energy can be created/destroyed is by having the universe expand. However, energy will always be conserved in a closed system of constant size even if the universe expands.
Kevin Kostlan
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There is another conceptual problem of having a non-zero average charge density. If Gauss law for the divergence of the electric field is still valid, the electric field cannot be uniform: $\mathrm{div} \vec{E}=\rho/\epsilon_0$.
It is still possible to have a spherically symmetrical solution $\vec{E}=\vec{r}\rho/\epsilon_0$, i.e. electric field must grow linearly with the distance to the coordinate origin. But the universe then would have to have a center, which, as far as we know, it doesn't.
Pavlo. B.
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Accepting that long ago there would likely be equal numbers for the two polarities. Once one galaxy ever borrowed electrons from another, then it could coat a protostar with them thus presenting a negative electric field at the center of that host. That field would drive electrons away from atoms there and neutralize naked protons so that they could cluster. Consequential fusion would be devoid of the parity occurring with fusion within plasma. Hence a positron could be lost to converted energy and a durable negative bias could begin.
