A Local Wheeler-DeWitt Measure for the String Landscape

TL;DR

This paper proposes a new measure for the string landscape using a local Wheeler-DeWitt wave function, incorporating sources to account for different vacua and avoiding the global multiverse picture.

Contribution

It introduces a local Wheeler-DeWitt measure for the string landscape that accounts for various vacua and inhomogeneous sources, differing from traditional global approaches.

Findings

Derives a time-independent wave function for the multiverse

Incorporates sources consistent with semiclassical intuition

Results in a local measure focusing on static patches

Abstract

According to the `Cosmological Central Dogma', de Sitter space can be viewed as a quantum mechanical system with a finite number of degrees of freedom, set by the horizon area. We use this assumption together with the Wheeler-DeWitt (WDW) equation to approach the measure problem of eternal inflation. Thus, our goal is to find a time-independent wave function of the universe on a total Hilbert space defined as the direct sum of a variety of subspaces: A finite-dimensional subspace for each de Sitter vacuum and an infinite-dimensional subspace for each terminal Minkowski or AdS vaccuum. We argue that, to be consistent with semiclassical intuition, such a solution requires the presence of sources. These are implemented as an inhomogenous term in the WDW equation, induced by the Hartle-Hawking no-boundary or the Linde/Vilenkin tunneling proposal. Taken together, these steps unambiguously lead to what we would like to think of as a `Local WDW measure,' where `local' refers to the fact that the dS part of the resulting wave function describes a superposition of static patches. The global 3-sphere spatial section of the entire multiverse makes no appearance.