Observers, $\alpha$-parameters, and the Hartle-Hawking state

TL;DR

This paper explores how observer fluctuations in the Hartle-Hawking state influence cosmological transitions, holography, and the nature of the Hilbert space, revealing new insights into quantum cosmology and the landscape.

Contribution

It introduces a third-quantized framework for fluctuating observers in the Hartle-Hawking state without relying on $eta$-parameters, and clarifies holographic and path integral relationships.

Findings

Dominant cosmological transitions can involve universe annihilation and creation.

Observer decoherence enables a third-quantized description from a one-dimensional Hilbert space.

In landscape scenarios, observers are almost always found in dS space, not AdS.

Abstract

In this paper we extend recent ideas about observers and closed universes to theories where observers can be fluctuated into existence in the Hartle-Hawking state. This introduces a phenomenon that was not considered in these earlier discussions: the dominant transition from one cosmological state to another can go through a fluctuation that annihilates the universe and creates a new one. We nonetheless argue that the observer decoherence rule allows for the third-quantized description of such a theory to emerge from a factorizing holographic theory with a one-dimensional Hilbert space, without any need for $\alpha$-parameters. We also point out a close analogy between the observer rule in this context and the coarse-graining of the spectral form factor at late times for AdS black holes. Along the way we clarify several aspects of the relationship between holography, the gravitational path integral, and $\alpha$-parameters. We also explain why string theory scattering amplitudes do not lead to a one-dimensional Hilbert space on the worldsheet, despite being computed by a gravitational path integral with a sum over topology. Finally we point out that using the path integral to compute integrated local operators conditioned on an observer in the context of a theory with a landscape can lead to rather surprising conclusions. For example we argue that in a landscape with one AdS minimum and one dS minimum, both of which can support observers, an observer almost surely finds themself in dS and not AdS even if the boundary conditions are dual to a state with an observer in AdS.