What is the overall electric charge of the universe?
It is impossible to conclusively measure the overall electric charge of the universe since the universe is infinite. However, the laws of physics, extrapolations of local measurements, and simple reasoning seem to all tell us that the overall electric charge of the universe is exactly zero. In other words, there is exactly as much positive electric charge in the universe as there is negative electric charge. The theoretical reason for making this conclusion is the Law of Conservation of Charge. Because of certain symmetries in the structure of the universe, the total electric charge of an isolated system is always conserved. This means that the total charge of an isolated system is the same at all points in time. The Law of Conservation of Charge is a fundamental, strict, universal law. In thousands to millions of different experiments, this law has never been observed to be violated, not even once. Furthermore, this law is the only logical way to explain the world around us. In short, this law just makes sense.
The Law of Conservation of Charge does not mean that electric charge can’t be created or destroyed. It just means that every time some negative electric charge is created, an equal amount of positive electric charge must be created at the same time so that the total charge of a system does not change. For instance, in the well-understood phenomenon of pair production, a gamma ray (a high-energy form of light) transforms into a regular matter particle and an antimatter particle that is the counterpart of the regular matter particle. Since an antimatter particle always has the opposite electric charge of its regular matter counterpart, the total charge of the two particles is zero. Therefore, pair production does not change the total electric charge of a system and is thus allowed by the Law of Conservation of Charge. As a more specific example of this, a gamma ray can transform into an electron and an anti-electron (i.e. a positron). The electron has an electric charge of -1 and the positron has an electron charge of +1. The total charge added to the system by the creation of the electron and the positron is: +1-1 = 0. The point is that the Law Conservation of Charge forces upon us the fact that every time an electron is created from a gamma ray, a positron must also be created. In this way, electric charge can be created and destroyed while the total charge of a system can stay constant. Pair production is routinely observed in the lab and in measurements of atmospheric cosmic ray air showers.
So what does conservation of charge have to do with the overall charge of the universe? According to modern science, the universe began by exploding out of nothing in what scientists call the Big Bang. Since the universe started as nothing, it started with zero electric charge. Therefore, the Law of Conservation of Charge tells us that the universe must still have a total electric charge of zero.
This makes sense from an observational standpoint. The electromagnetic force has just as long a range as the force of gravity and is much stronger than gravity. The reason that the electromagnetic force does not play much of a role on the astronomical scale is because stars and planets have a total electric charge of zero. If the earth and sun both had a large positive electric charge, then the electromagnetic repulsion between them would be far stronger than the gravitational attraction between them. In such a case, the earth would not orbit around the sun but would be thrown out of the solar system. The fact that moons form stable orbits around planets, planets form stable orbits around stars, and stars form stable orbits around galactic centers is direct observational evidence that moons, planets, and stars all have a total electric charge of zero. Since moons, planets, and stars are the things that make up the universe, it is only logical to deduce that the universe therefore has a total electric charge of zero.