Making predictions in the multiverse

TL;DR

The paper analyzes how to make predictions in an eternally inflating multiverse by regulating infinities with geometric cutoffs (measures). It surveys local (causal diamond, census taker) and global (proper time, scale factor, lightcone time) measures, highlighting equivalences and observational constraints that prune the landscape of viable proposals. A holographic-inspired approach yields the new lightcone time cutoff via bulk-boundary mapping and a Yamabe-fixed boundary metric, suggesting a pathway to deriving measures from quantum gravity. Ultimately, two main strategies—the lightcone time/causal diamond family and the scale factor/fat geodesic family—emerge as compatible with current data, but both carry conceptual challenges (end-of-time, negative-$\Lambda$ tendency) that motivate further theoretical development and empirical scrutiny.

Abstract

I describe reasons to think we are living in an eternally inflating multiverse where the observable "constants" of nature vary from place to place. The major obstacle to making predictions in this context is that we must regulate the infinities of eternal inflation. I review a number of proposed regulators, or measures. Recent work has ruled out a number of measures by showing that they conflict with observation, and focused attention on a few proposals. Further, several different measures have been shown to be equivalent. I describe some of the many nontrivial tests these measures will face as we learn more from theory, experiment, and observation.

Figures (3)

• Figure 1: To compute the lightcone time of an event, construct its future lightcone and project back to the initial surface $\Sigma_0$ along the geodesic congruence. The resulting volume on $\Sigma_0$ gives the lightcone time of the event. Figure courtesy of Raphael Bousso.
• Figure 2: Conformal diagrams for bubbles with positive and negative cosmological constant. The Bousso wedges indicate the null directions in which the sizes of spheres are increasing. The tips of the wedges point in the direction of increase. Entropy bounds dictate that if we think of the wedges as arrows, they point towards the natural holographic screens sbound. One can see that future infinity is a natural holographic screen for the $\Lambda>0$ bubble (left), but not for the $\Lambda<0$ bubble.
• Figure 3: In both global (left) and local (right) cutoffs, a finite fraction of observers born before the cutoff run into the cutoff before they die. The fraction of observers who are cut off does not go to zero as the cutoff is taken later and later.