The Free-Streaming Scale of Relic Neutrinos: Length and Mass Scales Across the Allowed Mass Range and Their Suppression of Small-Scale Structure

A relic neutrino of 0.05 eV free-streams over a comoving length of about 233 megaparsecs, erasing its own clustering below that scale; at 0.10 eV the length falls to 117 megaparsecs, enclosing a mass of 3.29e+16 solar masses, and at 0.30 eV it falls further to 39 megaparsecs. This paper derives the free-streaming scale from the velocity history of the background, tabulates length and enclosed mass across the allowed mass range, and explains why this erasure, not the bulk density, is the relic background's main gravitational signature. The coefficients used are stated conventions consistent with published Boltzmann results at the accuracy claimed. Computed, not measured.