Abstract
An unresolved question in inflationary cosmology is the assignment of probabilities to different types of events that can occur in the eternally inflating multiverse. We explore the possibility that the resolution of this ``measure problem" may rely on non-standard dynamics in regions of high curvature. In particular, ``big crunch" singularities at the future boundary of bubbles with negative vacuum energy density may lead to bounces, where contraction is replaced by inflationary expansion driven by different vacua in the landscape. Similarly, singularities inside of black holes might be gateways to other inflating vacua. This would drastically affect the global structure of the inflating multiverse. We consider a measure based on a probe geodesic which undergoes an infinite number of passages through crunches. This can be thought of as the world-line of an eternal ``watcher", collecting data in an orderly fashion. We compare this to previous approaches to the measure problem. The watcher's measure is independent of initial conditions and does not suffer from ambiguities associated with the choice of a cut-off surface. Another potential benefit from passing through crunches is that the observations collected by the watcher may easily depart from ergodicity, in very generic landscapes. This may significantly alleviate the problem of Boltzmann Brain dominance.