Norm of the no-boundary state

TL;DR

This paper analyzes the norm of the no-boundary state in asymptotically de Sitter universes, showing it vanishes at one-loop order but can be stabilized to a positive value by an observer, with implications for quantum cosmology.

Contribution

It demonstrates that the no-boundary state's norm vanishes at one-loop order in de Sitter space and reveals how an observer can stabilize it to a positive value.

Findings

The norm of the no-boundary state vanishes at late times and one-loop order.

Presence of an observer stabilizes the norm to a large positive value.

The norm scales with the exponential of the static patch entropy.

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 $e^{S_0} \frac{Z S_0^{-d(d+1)/4}}{\text{vol}(SO(d,1))}$ 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.