Predicting the cosmological constant with the scale-factor cutoff measure

It is well known that anthropic selection from a landscape with a flat prior distribution of cosmological constant Λ gives a reasonable fit to observation. However, a realistic model of the multiverse has a physical volume that diverges with time, and the predicted distribution of Λ depends on how the spacetime volume is regulated. A very promising method of regulation uses a scale-factor cutoff, which avoids a number of serious problems that arise in other approaches. In particular, the scale-factor cutoff avoids the “youngness problem” (high probability of living in a much younger universe) and the “Q and G catastrophes” (high probability for the primordial density contrast Q and gravitational constant G to have extremely large or small values). We apply the scale-factor cutoff measure to the probability distribution of Λ, considering both positive and negative values. The results are in good agreement with observation. In particular, the scale-factor cutoff strongly suppresses the probability for values of Λ that are more than about 10 times the observed value. We also discuss qualitatively the prediction for the density parameter Ω, indicating that with this measure there is a possibility of detectable negative curvature.