On the Likelihood of Observing Extragalactic Civilizations: Predictions from the Self-Indication Assumption

Ambitious civilizations that expand for resources at an intergalactic scale could be observable from a cosmological distance, but how likely is one to be visible to us? The question comes down to estimating the appearance rate of such things in the cosmos --- a radically uncertain quantity. Despite this prior uncertainty, anthropic considerations give rise to Bayesian updates, and thus predictions. The Self-Sampling Assumption (SSA), a school of anthropic probability, has previously been used for this purpose. Here, we derive predictions from the alternative school, the Self-Indication Assumption (SIA), and point out its features. SIA favors a higher appearance rate of expansionistic life, but our existence at the present cosmic time means that such life cannot be too common (else our galaxy would long ago have been overrun). This combination squeezes our vast prior uncertainty into a few orders of magnitude. Details of the background cosmology fall out, and we are left with some stark conclusions. E.g. if the limits to technology allow a civilization to expand at speed $v$, the probability of at least one expanding cosmological civilization being visible on our past light cone is $1-\frac{v^3}{c^3}$. We also show how the SIA estimate can be updated from the results of a hypothetical full-sky survey that detects "$n$" expanding civilizations (for $n \geq 0$), and calculate the implied final extent of life in the universe.