Estimates for the number of visible galaxy-spanning civilizations and
  the cosmological expansion of life
  If advanced civilizations appear in the universe with an ability and desire
to expand, the entire universe can become saturated with life on a short
timescale, even if such expanders appear rarely. Our presence in an apparently
untouched Milky Way thus constrains the appearance rate of galaxy-spanning
Kardashev type III (K3) civilizations, if it is assumed that some fraction of
K3 civilizations will continue their expansion at intergalactic distances. We
use this constraint to estimate the appearance rate of K3 civilizations for 81
cosmological scenarios by specifying the extent to which humanity is a
statistical outlier. We find that in nearly all plausible scenarios, the
distance to the nearest visible K3 is cosmological. In searches for K3 galaxies
where the observable range is limited, we also find that the most likely
detections tend to be expanding civilizations who have entered the observable
range from farther away. An observation of K3 clusters is thus more likely than
isolated K3 galaxies.
