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It seems our universe is neutral in large scale.

There is CP violationwiki problem about matter and dark matter.
Similarly is there any theory about whether our universe is electrically neutral?

Cosmic rays are not neutral. However the atomic nucleus and electrons are just separated. There should be no charge excess in total.

What is the largest scale that is severely non-neutral?

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OK. I find a paper. arxiv.org/abs/1201.6585 This can partly answer my question. –  questionhang Jul 15 at 11:30
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@RoryAlsop A similar question already exists on Physics: physics.stackexchange.com/questions/83486/… –  Kyle Kanos Jul 18 at 13:44
    
Note that the paper by Düren (the one you quoted in your comment) has not appeared in any peer-reviewed journal. That is a serious indication that it didn't make it through the review process for some good reasons, e.g. it violates known observational constraints. –  Walter Sep 5 at 9:30
    
Do you mean areas of large and stable static charges? Because otherwise anywhere there is a magnetic field there is some imbalance which is generating the current and hence the field - there is good evidence of magnetic fields at galactic scale. But I guess that is not what you mean. –  adrianmcmenamin Nov 16 at 14:35
    
You mean it could be un-neutral in galactic scale? We do not care about time-scale here. Suppose there is an isolated galaxy which loses many of its electrons and can not get the electrons back for some kind of reason. –  questionhang Nov 16 at 18:39

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