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

Anthropic probability distributions for the cosmological constant. and for the sum of neutrino masses m. are updated using the WMAP-3 data release. The new distribution for. 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 one, is no less than 22%. We discuss the dependence of our results on the simplifying assumptions used in deriving the distribution for. and show that the agreement of the anthropic prediction with the data is rather robust. The distribution for m. is peaked at m(v) similar to 1 eV, suggesting degenerate neutrino masses, but a hierarchical mass pattern is still marginally allowed at a 2s level.