New Local Duals in Eternal Inflation

TL;DR

This paper demonstrates that global-local duality in eternal inflation is a general phenomenon, showing how various global cutoffs have equivalent local duals based on the fundamental spacetime region, with implications for understanding measure problems.

Contribution

It establishes the generality of global-local duality in eternal inflation and derives local duals for several important global cutoffs.

Findings

Global-local duality is more general than previously thought.

Derived local duals for the New Scale Factor and CAH cutoffs.

Provided insights into the youngness problem via local duals.

Abstract

Global-local duality is the equivalence of seemingly different regulators in eternal inflation. For example, the light-cone time cutoff (a global measure, which regulates time) makes the same predictions as the causal patch (a local measure that cuts off space). We show that global-local duality is far more general. It rests on a redundancy inherent in any global cutoff: at late times, an attractor regime is reached, characterized by the unlimited exponential self-reproduction of a certain fundamental region of spacetime. An equivalent local cutoff can be obtained by restricting to this fundamental region. We derive local duals to several global cutoffs of interest. The New Scale Factor Cutoff is dual to the Short Fat Geodesic, a geodesic of fixed infinitesimal proper width. Vilenkin's CAH Cutoff is equivalent to the Hubbletube, whose width is proportional to the local Hubble volume. The famous youngness problem of the Proper Time Cutoff can be readily understood by considering its local dual, the Incredible Shrinking Geodesic.