Actually, standard gravity does have a repulsive phase. (Note that this has nothing whatsoever to do with these antigravity claims, for which there is neither theoretical support nor verified experimental evidence.) If we postulate a scalar field (such as electric potential, but with a fixed global energy minimum at some value of the field), and further postulate that it is possible to place a region of vacuum stably into a higher potential state (that is, that there would exist a deep local energy minimum at some different value of the field), then gravity becomes repulsive. This causes the region of space to inflate--a new Big Bang!
I've heard that some theorists now believe that such a metastable "false vacuum" is not necessary for inflation. If a region of vacuum can be kicked unstably into a higher potential, it can "surf" along at the higher potential as the space inflates, just as a surfer maintains his elevation on a wave while falling down its slope the whole time.