Here is our main paper on the subject, in Astrophysical Journal:
“If Loud Aliens Explain Human Earliness, Quiet Aliens Are Also Rare” (version 3) by Robin Hanson, Daniel Martin, Calvin McCarter, and Jonathan Paulson, September 7th, 2021.
If life on Earth had to achieve n “hard steps” to reach humanity’s level, then the chance of this event rose as time to the n-th power. Integrating this over habitable star formation and planet lifetime distributions predicts >99% of advanced life appears after today, unless n < 3 and max planet duration <50Gyr. That is, we seem early. We offer this explanation: a deadline is set by “loud” aliens who are born according to a hard steps power law, expand at a common rate, change their volumes’ appearances, and prevent advanced life like us from appearing in their volumes. “Quiet” aliens, in contrast, are much harder to see. We fit this three- parameter model of loud aliens to data: 1) birth power from the number of hard steps seen in Earth history, 2) birth constant by assuming a uniform distribution over our rank among loud alien birth dates, and 3) expansion speed from our not seeing alien volumes in our sky. We estimate that loud alien civilizations now control 40- 50% of universe volume, each will later control ∼105 - 3x107 galaxies, and we could meet them in ∼200Myr – 2Gyr. If loud aliens arise from quiet ones, a depressingly low transition chance (< ∼10−4) is required to expect that even one other quiet alien civilization has ever been active in our galaxy. Which seems bad news for SETI. But perhaps alien volume appearances are subtle, and their expansion speed lower, in which case we predict many long circular arcs to find in our sky.
(See also prior version 2 “If Loud Aliens Explain Human Earliness, Quiet Aliens Are Also Rare”, February 1, 2021.)
(See also prior version 1 “A Simple Model of Grabby Aliens”, February 1, 2021.)