Anthropic predictions for vacuum energy and neutrino masses in the light of WMAP-3

Abstract

Anthropic probability distributions for the cosmological constant and for the sum of neutrino masses are updated using the WMAP-3 data release. The new distribution for Lambda is in a better agreement with observation than the earlier one. The typicality of the observed value, defined as the combined probability of all values less likely than the observed, is no less than 22%. We discuss the dependence of our results on the simplifying assumptions used in deriving the distribution for Lambda and show that the agreement of the anthropic prediction with the data is rather robust. The distribution for the sum of the neutrino masses is peaked at 1 eV, suggesting degenerate masses, but a hierarchical mass pattern is still marginally allowed at a 2 sigma level.