Anthropic origin of the neutrino mass from cooling failure

The sum of active neutrino masses is well constrained, 58meV≤mν 0.23eV, but the origin of this scale is not well understood. Here we investigate the possibility that it arises by environmental selection in a large landscape of vacua. Earlier work noted the detrimental effects of neutrinos on large-scale structure. However, using Boltzmann codes to compute the smoothed density contrast on Mpc scales, we find that dark matter halos form abundantly for mν 10eV. This finding rules out an anthropic origin of mν, unless a different catastrophic boundary can be identified. Here we argue that galaxy formation becomes inefficient for mν 10eV. We show that in this regime, structure forms late and is dominated by cluster scales, as in a top-down scenario. This is catastrophic: baryonic gas will cool too slowly to form stars in an abundance comparable to our Universe. With this novel cooling boundary, we find that the anthropic prediction for mν agrees at better than 2σ with current observational bounds. A degenerate hierarchy is mildly preferred.