I fail to see an experiment clarifying the properties of antimatter gravity and so far I've only heard of 2 speculations: i) Antimatter gravity is the same as matter gravity, as gravity is a property of mass, ii) Antimatter and matter repel each other, but antimatter pulls itself together in the same way as matter does. I'm thinking of something else:
Matter gravity --> A "force" that pulls "everything"
Antimatter gravity --> A "force" that repels "everything"
In the beggining of the universe, a gravitational effect like this, would make the concetration of matter higher at the center of the universe "globe", while antimatter would mainly concetrate far from it. There would be 3 types of reactions :
Energy ---> Matter + Antimatter
Matter + Antimatter ---> Energy
Mass ---> Energy
Since more matter than antimatter would be at the center (hotter area), the matter mass would disappear at higher rates than the antimatter mass and we would therefore have more antimatter than matter as a total. As matter kept decaying at higher rates, the "repel forces" of the antimatter gravity were becoming dominant, pushing the universe to expand.
And the present situation would be:
1) Antimatter is more than matter.
2) Matter continues to decay into energy due to its gravitational effect, and antimatter becomes increasingly dominant
3) We can't detect the antimatter because its gravitational effect makes it spread through the entire universe in the form of single individual particles
4) Dark Energy probably is the gravitational effect of this antimatter