Anthropic predictions: the case of the cosmological constant

TL;DR

Anthropic reasoning is applied to the cosmological constant within an inflation-generated multiverse. The core method defines ${\cal P}(\rho_v) \propto n_{obs}(\rho_v)\,{\cal P}_{prior}(\rho_v)$ and uses the mediocrity principle to expect typical observers measure $\rho_v$ within a 95% interval. The analysis shows that the observed $\rho_v^*$ lies inside the 95% confidence region even though the distribution's median can be higher; sensitivity to prior choices and to additional varying parameters is discussed. The paper also derives predictions for the equation of state, discusses particle-physics implications, and emphasizes that anthropic models are falsifiable despite yielding probabilistic rather than sharp predictions.

Abstract

Anthropic models can give testable predictions, which can be confirmed or falsified at a specified confidence level. This is illustrated using the successful prediction of the cosmological constant as an example. The history and the nature of the prediction are reviewed. Inclusion of other variable parameters and implications for particle physics are briefly discussed.

Figures (1)

• Figure 1: The logarithmic probability distribution $d{\cal P}/d(\log\rho_v)$. The lightly and densely shaded areas are the regions excluded at 68% and 95% level, respectively. The uncertainty in the observed value $\rho_v^*$ is indicated by the vertical strip.