| MadSci Network: Astronomy |
First of all, your statement that antimatter and matter are repulsed by each other is incorrect. To illustrate this, consider a electron and an anti-electron (positron). Just from basic electrostatic principles, they will actually attract each other due to the difference in charge parity (sign) between them.
Modern cosmological theories involve a period of baryosynthesis (a time when all the baryons were created). There are processes that give rise to the observed imbalance between matter and anti-matter in todays universe.
Taking this into account though, there are theories in which there is 'shadow' matter that does not interact with us except through gravitational forces. This theory is one of the dark matter solutions.
Having said all of this, it is possible that another Universe could exist that was anti-matter dominated. Very little would be different to an occupant of this universe except he/she/it would see electrons spiralling a different way in their cloud chambers!
I hope that this has helped.
Try the links in the MadSci Library for more information on Astronomy.