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

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