Anthropic Origin of the Neutrino Mass from Cooling Failure

Abstract

Given a large landscape of vacua that statistically favors large values of the neutrino mass sum, $m_\nu$, I will present the probability distribution over $m_\nu$ obtained by weighting this prior by the amount of galaxies that are produced. Using Boltzmann codes to compute the smoothed density contrast on Mpc scales, we find that large dark matter halos form abundantly for $m_\nu \gtrsim 10$\,eV. However, in this regime structure forms late and is dominated by cluster scales, as in a top-down scenario. I will argue that this change of regime is catastrophic: baryonic gas will cool too slowly to form stars in an abundance comparable to our universe. Upon implementing this cooling boundary, the anthropic prediction for $m_\nu$ is consistent at better than $2\sigma$ with the entire range of values allowed by current experimental bounds, $58$\,meV $\leq m_\nu \lesssim 0.23$\,eV. A degenerate hierarchy is mildly preferred. Without a catastrophic boundary at or below $10$\,eV, the theoretical expectation would conflict strongly with the observed mass range. Thus the asserted cooling failure can be regarded as a prediction of the anthropic solution to the neutrino mass problem.