Global-Local Duality in Eternal Inflation

TL;DR

This paper proves the equivalence of two different measures used in eternal inflation, linking the light-cone time cut-off and the causal patch through a geometric duality rooted in holography.

Contribution

It establishes a complete equivalence between two seemingly different measures of eternal inflation, revealing an underlying geometric duality.

Findings

Proves the equivalence of light-cone time cut-off and causal patch measures.

Identifies a geometric relation underlying the duality.

Supports the holographic motivation for these measures.

Abstract

We prove that the light-cone time cut-off on the multiverse defines the same probabilities as a causal patch with initial conditions in the longest-lived metastable vacuum. This establishes the complete equivalence of two measures of eternal inflation which naively appear very different (though both are motivated by holography). The duality can be traced to an underlying geometric relation which we identify.