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The Virgo Cluster is currently red-shifted by 0.003 according to Wikipedia; this indicates that the cluster is expanding. Will the cluster's enormous gravity eventually "win" and pull the milky way/local group back toward itself, or will our current recessional velocity combined with dark energy cause us to recede off to infinity?

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It would seem so. The local group is part of the Virgo cluster and as such is considered to be gravitationally bound. Although the Virgo cluster and the local group are currently moving apart, the mass if the Virgo cluster will likely slow and reverse the recession over time, with the local group ultimately merging with the cluster.

References: http://astronomy.swin.edu.au/cosmos/V/Virgo+Cluster http://heasarc.nasa.gov/docs/cosmic/local_supercluster_info.html

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    $\begingroup$ However, this says no: arxiv.org/abs/astro-ph/0204249 $\endgroup$
    – Kevin Kostlan
    Apr 26, 2014 at 12:55
  • $\begingroup$ @Kevin that seems to be considering the effects of endless expansion (as opposed to bang/crunch). Of course in such a universe the local group would become isolated; in even more distant times even the components of the local group would drift apart. Expansion will tear apart all gravitational bonds given enough time. The original question was in regard to gravitational binding. $\endgroup$
    – ntremble
    Apr 26, 2014 at 13:13
  • $\begingroup$ No dark energy does not grow with time (no "phantom energy"). Dark energy is constant but matter dilutes, thus we say dark energy will "dominate" the future universe. However, structures dense enough now to resist expansion are stable (until some internal mechanisms, such as proton decay, destroy them in the FAR future), "Brooklyn is not expanding". $\endgroup$
    – Kevin Kostlan
    Apr 26, 2014 at 13:16
  • $\begingroup$ The confusing part is that there seems to be a gravitationally bound Virgo cluster, of which we are not part, and a gravitationally unbound Virgo supercluster, of which we are part. $\endgroup$
    – Stephane Bersier
    Sep 3, 2019 at 2:39

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