Testing anthropic reasoning for the cosmological constant with a realistic galaxy formation model

The anthropic principle is one of the possible explanations for the cosmological constant ($\Lambda$) problem. In previous studies, a dark halo mass threshold comparable with our Galaxy must be assumed in galaxy formation to get a reasonably large probability of finding the observed small value, $P(<$$\Lambda_{\rm obs})$, though stars are found in much smaller galaxies as well. Here we examine the anthropic argument by using a semi-analytic model of cosmological galaxy formation, which can reproduce many observations such as galaxy luminosity functions. We calculate the probability distribution of $\Lambda$ by running the model code for a wide range of $\Lambda$, while other cosmological parameters and model parameters for baryonic processes of galaxy formation are kept constant. Assuming that the prior probability distribution is flat per unit $\Lambda$, and that the number of observers is proportional to stellar mass, we find $P(<$$\Lambda_{\rm obs}) = 6.7 \%$ without introducing any galaxy mass threshold. We also investigate the effect of metallicity; we find $P(<$$\Lambda_{\rm obs}) = 9.0 \%$ if observers exist only in galaxies whose metallicity is higher than the solar abundance. If the number of observers is proportional to metallicity, we find $P(<$$\Lambda_{\rm obs}) = 9.7 \%$. Since these probabilities are not extremely small, we conclude that the anthropic argument is a viable explanation, if the value of $\Lambda$ observed in our universe is determined by a probability distribution.