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 Lambda 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 Lambda 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 Lambda, 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 Lambda that are more than about 10 times the observed value. We also discuss qualitatively the prediction for the density parameter Omega, indicating that with this measure there is a possibility of detectable negative curvature.