A geometric solution to the coincidence problem, and the size of the landscape as the origin of hierarchy

TL;DR

This paper proposes a geometric approach to the coincidence problem, linking the universe's size and hierarchy to the landscape's metastable vacua, without relying on observer-based assumptions.

Contribution

It introduces a novel geometric solution connecting the universe's size and hierarchy to the landscape's metastable vacua, independent of observer conditions.

Findings

Causal patch measure predicts vacuum energy and matter density coincidence.

The universe's size is rooted in the number of metastable vacua.

Provides a geometric perspective on the hierarchy problem.

Abstract

Without assuming necessary conditions for observers such as galaxies or entropy production, we show that the causal patch measure predicts the coincidence of vacuum energy and present matter density. Their common scale, and thus the enormous size of the visible universe, has its origin in the number of metastable vacua in the landscape.