Norm of the no-boundary state
Abstract
A bstract 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 $$ {e}^{S_0}\frac{Z{S}_0^{-d\left(d+1\right)/4}}{\textrm{vol}\left(\textrm{SO}\left(d,1\right)\right)} $$ e S 0 Z S 0 − d d + 1 / 4 vol SO d 1 with S 0 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.
Fields of Study & Subjects
Cosmology and Gravitation Theories
Black Holes and Theoretical Physics
Noncommutative and Quantum Gravity Theories
Publication details
- Journal / source
- Journal of High Energy Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 2026
- Issue
- 3
- Publication date
- 19 March 2026
- Language
- EN