Anthropic Prediction of the Dark Matter Abundance

I use Bousso’s causal diamond measure to make a statistical prediction for the dark matter abundance, assuming an axion with a large decay constant fa ≫ 10 GeV. Using a crude approximation for observer formation, the prediction agrees well with observation: 25% of observers see less dark matter than we do while 75% of observers see more dark matter. Larger values of the dark matter ratio are disfavored by an elementary effect: increasing the amount of dark matter decreases the number of baryons inside one horizon volume. Thus the prediction does not depend on detailed assumptions about the requirements for life. The key assumption is that the number of observers per baryon is a mild function of the dark matter ratio for values near the observed value.