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Except for those galaxies which are gravitationally bound like our local group of galaxies, everything is effectively moving away from everything else. On a large scale, visible universe scale the proper motion of galaxies is far smaller than the expansion of space time. Eventually many billions of years from now, except for a handfull of galaxies we will be alone in space.
Whether the expansion continues, stops or starts to contract depends on the amount of matter in the universe. Currently scientists believe there is not enough matter in the universe to stop the expansion.
Worse still, normal matter only accounts for 5% of the matter and dark matter maybe 25% more of the matter in the universe. People believe the remaining 70% is made up of dark energy and unfortunately this has the effect of negative gravity and is causing the expansion to speed up.
Cheers
Paul
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