My knowlege and understanding is very limited but here is what I understand the numbers to be. Because we cannot see all of the universe or even know how big it might be, we have to talk in terms of energy density and matter density. In terms of overall matter/energy density dark matter accounts for 23% of the total, normal matter 4.6% and dark energy the rest. This means that if we look at just matter density it is about 20% / 80% split between normal and dark matter.
As a matter of interest, the idea of dark matter has been around since the 1920s or 1930s.
I can believe that matter exists that does not contain electrons and indead has no electrical charge. This would account for no observable interaction with normal matter. If this matter pushed instead of pulled in gravitational terms then I could see it causing the universe to expand. Over long periods it would be reasonable that this matter would be ejected from within solar systems so that we would see no evidence of expansion within our own solar system. It might also be ejected or squeezed out from galaxies. So, existing outside large structures, it would tend to push them together and away from each other. Assuming that this matter can interact gravitationaly with photons and that its density is not the same everywhere, we sould be able to spot something like gravitational lensing happening away from large structures. I expect that my thinking is flawed but at least I am thinking.