Comment on Coleman-DeLuccia Instantons

TL;DR

This paper analyzes the properties of causal diamonds in Coleman-DeLuccia instantons, demonstrating their finite area and proposing quantum models that align with detailed balance principles, with implications for quantum gravity models.

Contribution

It completes an argument about causal diamond areas in instantons and introduces quantum models consistent with detailed balance for different causal diamond sizes.

Findings

Causal diamonds in instantons have finite area.

Quantum models can mimic instanton transition probabilities.

Implications for the validity of certain quantum gravity potentials.

Abstract

We complete an old argument that causal diamonds in the crunching region of the Lorentzian continuation of a Coleman-Deluccia instanton for transitions out of de Sitter space have finite area, and provide quantum models consistent with the principle of detailed balance, which can mimic the instanton transition probabilities for the cases where this diamond is larger or smaller than the causal patch of de Sitter space. We review arguments that potentials which do not have a positive energy theorem when the lowest de Sitter minimum is shifted to zero, may not correspond to real models of quantum gravity.