As far as our current understanding of gravity, no. The common analogy is a rubber sheet with marbles. The sheet can only be pulled downwards, so you cannot have a repelling force.
To pull the sheet upwards would require something like inverse gravity, which is not yet known to current physics.
Of course dark energy seems to look like this, but as the origin of dark energy is currently completely unknown, it is not useful to speculate on this at this point in time.
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