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

TL;DR

This study uses a realistic galaxy formation model to evaluate the anthropic explanation for the small observed value of the cosmological constant, finding it remains a plausible explanation under various assumptions.

Contribution

It introduces a semi-analytic galaxy formation model to assess anthropic probability distributions of the cosmological constant without relying on galaxy mass thresholds.

Findings

Probability of observed $\\Lambda$ is around 6.7% to 9.7% depending on assumptions.

Anthropic explanation remains viable with realistic galaxy formation modeling.

Metallicity considerations slightly increase the probability estimate.

Abstract

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.