Norm of the no-boundary state

2025/06/25 by Jordan Cotler, Cotler, Jordan, Kristan Jensen +1 · 3 citations
Mathematics · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2506.20547

openalex publication_date 2025/06/25 · openalex created_date 2025/10/09 · openalex updated_date 2026/07/28

Abstract

We consider Einstein gravity with positive cosmological constant coupled to matter in an asymptotically de Sitter universe with sphere boundary at timelike infinity. In this setting we show that, to one-loop order and at late time, the norm of the no-boundary state vanishes, going as e^S₀ \fracZ S₀^-d(d+1)/4vol(SO(d,1)) with S₀ the tree-level entropy of the static patch, d the spacetime dimension, and Z non-negative. We show that the presence of an observer stabilizes the norm to a large, positive value.

Citations

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Cited by

• Quantum Liouville Cosmology
• The Hilbert space of gauge theories: group averaging and the quantization of Jackiw-Teitelboim gravity
• A Quantum Gravitational Mechanism for Isotropization of de Sitter Cosmologies

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