Question

What mathematical evidence can you provide to support the assertion that the universe is electrically neutral on large scales?

Ryden, Barbara. Introduction to Cosmology (p. 47). Cambridge University Press. Kindle Edition.

Answer 1

There is no such evidence and never will be because it may or may not be true.

Actually there we observe some signs that the universe is charge neutral or almost neutral and no. of protons don't differ much from no. of electrons.

(1) lets suppose if the universe and cosmos have any net charge be it + or -, then there must be electric and magnetic fields associated with the charges that will be observable in the cosmic microwave background and technology today. but we haven't observed anything of this kind yet, which supports that almost neutrality is maintained in the universe or more specifically speaking in observable universe.

(2) As gravity is the typical and may be only important force when considering planatery distance and interaction scales. we have observed that this only force is enough to tell us most functions of universe. as we know that the electro-magnetic force is manyfolds strong than gravitational force, if the universe is having any charge then we must have observed Electromagnetic interactions at some lengths.