Anthropic Origin of the Neutrino Mass from Cooling Failure

The sum of active neutrino masses is well constrained, $58$ meV $\leq m_\nu \lesssim 0.23$ eV, 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 had 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 $m_\nu \gtrsim 10$ eV. This finding rules out an anthropic origin of $m_\nu$, unless a different catastrophic boundary can be identified. Here we argue that galaxy formation becomes inefficient for $m_\nu \gtrsim 10$ eV. 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 $m_\nu$ agrees at better than $2\sigma$ with current observational bounds. A degenerate hierarchy is mildly preferred.