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The observed value $\Lambda_{\rm obs}$ of the cosmological constant $\Lambda$ is extremely smaller than theoretical expectations, and the anthropic argument has been proposed as a solution to this problem because galaxies do not form when $\Lambda \gg \Lambda_{\rm obs}$. However, the contemporary galaxy formation theory predicts that stars form even with a high value of $\Lambda / \Lambda_{\rm obs} \sim$ 50, which makes the anthropic argument less persuasive. Here we calculate the probability distribution of $\Lambda$ using a model of cosmological galaxy formation, considering extinction of observers caused by radiation from nearby supernovae. The life survival probability decreases in a large $\Lambda$ universe because of higher stellar density. Using a reasonable rate of lethal supernovae, we find that the mean expectation value of $\Lambda$ can be close to $\Lambda_{\rm obs}$, and hence this effect may be essential to understand the small but nonzero value of $\Lambda$. It is predicted that we are located on the edge of habitable regions about stellar density in the Galaxy, which may be tested by future exoplanet studies., Comment: 13 pages, 2 figures. the version accepted to Astrobiology more...

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., Comment: 6 pages, 4 figures, accepted for publication in MNRAS more...