Conservation of Charge vs. Conservation of Energy

Question

Is conservation of charge ever violated like conservation of energy is violated during cosmological expansion? I am trying to understand this with respect to Noether's Theorem.

Answer 1

With Noether’s theorem any conserved quantity is associated with some differential symmetry of the Lagrangian. For energy, the relevant symmetry is time translation symmetry. The laws of physics are generally symmetric under time translations, so usually energy is conserved. However, the LCDM model’s spacetime is not time translation symmetric, so on cosmological scales there is no conserved energy. (Note, locally energy is still conserved, including along the worldline of a redshifting photon, just not globally)

For charge conservation the Noether symmetry is the gauge invariance of the electromagnetic potential. That is an independent symmetry from the time translation symmetry, so you can still have charge conservation even in the LCDM model spacetime. As far as I know there is no known realistic scenario where the gauge invariance is lost and therefore charge is not conserved.

Answer 2

As far as the present is concerned charge has not been violated. However in the Big bang charge might have been violated because of the way quantum mechanics was not like today. Certain symmetries must have been broken and so charge might have been violated. Of course I am not too sure about this.