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A Local Wheeler-DeWitt Measure for the String Landscape

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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. I will discuss how this assumption, together with the Wheeler-DeWitt (WDW) equation, can be used to approach the measure problem of eternal inflation. It turns out that one is searching for 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. I will 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 multiverse geometry makes no explicit appearance.

This talk is part of the Cosmology Lunch series.

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