The Eternal Sunshine of the Spotless Mind

TL;DR

This paper investigates how introducing a preferred time-slicing in de Sitter space affects the youngness paradox in eternal inflation, showing it is a gauge artifact unless a physical clock is added.

Contribution

It extends the worldline measure to include time-ordered bubble formation and demonstrates the impact of a physical clock on the youngness paradox in eternal inflation.

Findings

The youngness paradox is a gauge artifact in unbroken de Sitter space.

Adding a physical clock introduces a preferred slicing, making the paradox more persistent.

The measure clarifies the role of memory and observer dependence in inflationary universes.

Abstract

We extend the worldline measure for pocket formation in eternal inflation to allow for time-ordered bubble formation. Such a time-ordering is equivalent to imposing a preferred time-slicing on the "parent" de Sitter space. Using this measure, we describe a covariant version of the youngness paradox and show that the youngness paradox is a gauge artifact if the parent spacetime is an unbroken de Sitter space, due to the lack of an explicit time-ordering for the bubble nucleation events. We then show that one can add a "clock" to the de Sitter space, in the form of a vector field with a spontaneously broken symmetry that defines a unique timelike direction accessible to all observers. Once this is done, the existence of a preferred slicing means that the youngness paradox cannot be easily resolved. We use this to elucidate the apparent "persistence of memory" discussed recently by Garriga, Guth and Vilenkin, for inflationary universes produced by bubble nucleation.