Estimates for the number of visible galaxy-spanning civilizations and the cosmological expansion of life
S. Jay Olson

TL;DR
This paper estimates the frequency and distribution of galaxy-spanning civilizations in the universe, suggesting that such civilizations are likely rare and often observable as clusters rather than isolated entities.
Contribution
It introduces a method to constrain the appearance rate of K3 civilizations across various cosmological scenarios using the absence of observed galaxy-spanning life.
Findings
Most K3 civilizations are likely beyond current observable range.
Detectable civilizations are more likely to be in clusters than isolated.
The nearest visible K3 civilization is probably at a cosmological distance.
Abstract
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…
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