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In this question OP asks for a prediction for the expansion or contraction, therefore a scale parameter $a(t)$, when Universe is not neutral but uniformly charged.

A result for this would be

In a homogeneous universe filled with charged dust the Faraday tensor must be zero everywhere by symmetry (in spite of the charge) making the Einstein-Maxwell equation reduce to the standard Einstein field equation. Electromagnetism plays no role in determining the spacetime geometry.

As DFJ states

However, intuitively I still think it is strange that a uniformly charged universe is the same as one with no charge.

I also find it odd. I'd like to ask you if (Question:) you are in knowledge of any models for a Universe that's "slightly" charged. With this I mean that: we do expect the Universe to be neutral because we see gravity as the force describing its dynamics despite Coulomb's law being $\sim39$ orders of magnitude stronger, but at the same time if positive or negative charges exceeds by only a small amount, this effect might not be noticeable when studying the motion of objects.

This might be equivalent to ask for a model of Universe being perturbed by a small amount of charge. How would it be?

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  • $\begingroup$ I don't think it's possible to find a translationally symmetric solution to the Maxwell equations for uniform charge. Having zero field violates the equations, after all. $\endgroup$
    – Javier
    Feb 22, 2022 at 17:46
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    $\begingroup$ I think a charged universe model will naturally give rise to a rotating universe model. Even if the universe had a slight non zero charge, there was a time close to Big Bang, when these charges were close to one another , and since it is statistically unlikely that they were symmetrically distributed, they must have gained a non zero torque in the process of acceleration of universe. We don't have evidence for rotating universe model, so it's unlikely that universe is charged $\endgroup$
    – KP99
    Feb 22, 2022 at 17:55

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