Nucleation Rates Below a Maximum Temperature: How a Density Ceiling Truncates Thermal Bubble Formation

Nucleation occurs at 95.1 GeV, where the exponent has fallen to S3/T = 144. At 95 GeV the rate itself is 1.35e-51 GeV^4, still far below one event per Hubble four-volume, which illustrates how abruptly the rate turns on as the universe cools: a five percent change in temperature moves the exponent by tens and the rate by many orders of magnitude. The ceiling temperature implied by the bound density is 1.05e+09 GeV, roughly eight orders of magnitude above the nucleation temperature of this benchmark. Integrating the formal nucleation probability over all temperatures, the fraction contributed by temperatures above the ceiling is 0.00e+00. The ceiling therefore leaves electroweak-scale nucleation numerically untouched, while removing a formally divergent-looking tail that an unrestricted integral would otherwise include. This study is simulated and computed from stated assumptions; it is not a measurement.