Higher-loop norm of the no-boundary state

TL;DR

This paper proves that the norm of the de Sitter no-boundary state, including all quantum corrections, vanishes at all orders in perturbation theory, impacting the understanding of quantum cosmology.

Contribution

It demonstrates that the norm of the no-boundary state is zero to all orders in perturbation theory, extending previous one-loop results.

Findings

The norm vanishes at one loop.

The norm vanishes to all orders in perturbation theory.

Implications for quantum cosmology and the stability of the no-boundary state.

Abstract

The leading contribution to the de Sitter no-boundary state comes from geometries with spherical spatial slices, including the Hartle-Hawking geometry and fluctuations around it. Recent work showed that this leading contribution has vanishing norm at one loop. Here we show that the norm in fact vanishes to all orders in perturbation theory.