Assuming that during the “big bang” matter and anti-matter pair production and annihilation governed the first phase before the expansion and cool down of the universe, we would expect to find a universe consisting of both matter and anti-matter uniformly spread apart throughout space. That is obviously not the case as we can observe today and we expect to find some new kind of anti-symmetry between matter and anti-matter. In this paper we will show a paradox that leads to the conclusion that anti-matter must have "anti-gravity". Based on this conclusion we claim that matter and anti-matter preserve two new conservation laws: 1. Conservation of gravity, 2. Conservation of time. Based on these new conservation laws we predict that anti-matter is uniformly spread, as anti-atoms or anti-elementary particles, throughout space and it’s one of the main reasons for space expansion. We strongly believe that future tests on the influence of anti-matter on gravity and time will prove this theory. .