The Boundedness of Euclidean Gravity and the Wavefunction of the Universe

TL;DR

This paper demonstrates that including back-reaction and decoherence effects in Euclidean quantum gravity renders the wavefunction of the universe normalizable, enabling meaningful probability comparisons in the string landscape.

Contribution

It introduces a correction to the Euclidean action accounting for back-reaction and decoherence, ensuring the wavefunction's boundedness and normalizability in quantum cosmology.

Findings

The Euclidean action becomes bounded from below with back-reaction.

Decoherence is essential for the consistency of quantum gravity.

The improved wavefunction allows probability comparisons in the string landscape.

Abstract

When the semi-positive cosmological constant is dynamical, the naive Euclidean Einstein action is unbounded from below and the Hartle-Hawking wavefunction of the universe is not normalizable. With the inclusion of back-reaction (a crucial point), the presence of the metric perturbative modes (as well as matter fields) as the environment (that is, to be integrated or traced out) introduces a correction term that provides a bound to the Euclidean action. So the improved wavefunction is normalizable. That is, decoherence plays an essential role in the consistency of quantum gravity. In the spontaneous creation of the universe, this improved wavefunction allows one to compare the tunneling probabilities from absolute nothing (i.e., not even classical spacetime) to various vacua (with different large spatial dimensions and different low energy spectra) in the stringy cosmic landscape.