Based on Heisenberg’s uncertainty principle it is concluded that the vacuum is filed with matter and anti-matter virtual pairs (“quantum foam”) that pop out and annihilate back in a very short period of time. When this quantum effects happen just outside the "event horizon" of a black hole, there is a chance that one of these virtual particles will pass through the event horizon and be sucked forever into the black hole while its partner virtual particle remains outside the event horizon free to float in space as a real particle (Hawking Radiation). In our previous work [1], we claim that antimatter particle has anti-gravity characteristic, therefore, we claim that during the Hawking radiation procedure, virtual matter particles have much larger chance to be sucked by gravity into the black hole then its copartner the anti-matter (anti-gravity) virtual particle. This leads us to the conclusion that hawking radiation is a significant source for continuous generation of mostly new anti-matter particles, spread in deep space, contributing to the expansion of space through their anti-gravity characteristic.