The Measure Problem and Challenges in String Compactifications

The Measure Problem is a fundamental theoretical challenge that arises when studying theories al- lowing for a landscape of different vacua. String theory, with its large number of four-dimensional solutions, is a prominent example. The Measure Problem refers to the issue of how to predict the outcome of future measurements – one of the most fundamental tasks in theoretical physics. In a land- scape scenario, simple event counting is generally insufficient for making predictions. A probability measure on the space of possible measurement outcomes is required. We propose a probability mea- sure, the Local Wheeler-DeWitt Measure, based on fundamental principles of quantum mechanics and semiclassical gravity. We use this measure to predict the scale of inflation to be observed in the future, mainly focusing on the string landscape. Furthermore, we develop a general framework for studying spacetime decays to nothing and the creation of universes from nothing, involving end-of-the-world (ETW) branes. This is necessary because measurement predictions are sensitive to vacuum decay and vacuum creation rates. We explicitly construct an ETW brane for the best-understood part of the string landscape, capable of causing spacetime decay or creation processes. Finally, we propose a new mechanism for universe creation from nothing, utilizing ETW branes in purely off-shell configurations.