Two Wave Functions and dS/CFT on S^1 x S^2

Abstract

We evaluate the tunneling and Hartle-Hawking wave functions on S^1 x S^2 boundaries in Einstein gravity with a positive cosmological constant. In the large overall volume limit the classical predictions of both wave functions include an ensemble of Schwarzschild-de Sitter black holes. We show that the Hartle-Hawking tree level measure on the classical ensemble converges in the small S^1 limit. A divergence in this regime can be identified in the tunneling state. However we trace this to the contribution of an unphysical branch of saddle points associated with negative mass black holes. Using a representation in which all saddle points have an interior Euclidean anti-de Sitter region we also generalise the holographic formulation of the semiclassical Hartle-Hawking wave function to S^1 x S^2 boundaries.

arXiv comment25 pages, 14 figures, version 2. Revisions according to the JHEP editor

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• Jackiw-Teitelboim and Kantowski-Sachs quantum cosmology
• Late-time Structure of the Bunch-Davies FRW Wavefunction
• Holographic Tunneling Wave Function
• Jackiw-Teitelboim Gravity and Lorentzian Quantum Cosmology
• Lorentzian Condition in Holographic Cosmology
• A correspondence between strings in the Hagedorn phase and asymptotically de Sitter space
• Holographic renormalization in no-boundary quantum cosmology
• The Fate of Nucleated Black Holes in de Sitter Quantum Gravity