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Probabilities in the landscape

Alexander Vilenkin

TL;DR

In an eternally inflating multiverse with a vast string landscape of vacua, predicting observed constants requires a gauge-invariant measure. The paper advocates a pocket-based approach that computes a local volume distribution $P^{(V)}(X)$ inside a representative pocket and couples it to bubble counting via a bubble abundance $p_j$ and a reference length $R_j$, yielding $P_j^{(V)} \propto p_j R_j^3$. It provides concrete methods to define $p_j$ (via a comoving-size cutoff or worldlines) and $R_j$ (via early-time universes or curvature scales), and generalizes to continuous variables $X$ with $P_j^{(V)}(X) \propto p_j \hat{P}_j(X) R_j^3(X)$. The approach aims to deliver a practical, largely gauge-invariant framework for predicting observer distributions across vacua, while acknowledging non-uniqueness and inviting empirical tests and comparisons with alternative proposals.

Abstract

I review recent progress in defining probability distributions in the inflationary multiverse.

Probabilities in the landscape

TL;DR

In an eternally inflating multiverse with a vast string landscape of vacua, predicting observed constants requires a gauge-invariant measure. The paper advocates a pocket-based approach that computes a local volume distribution inside a representative pocket and couples it to bubble counting via a bubble abundance and a reference length , yielding . It provides concrete methods to define (via a comoving-size cutoff or worldlines) and (via early-time universes or curvature scales), and generalizes to continuous variables with . The approach aims to deliver a practical, largely gauge-invariant framework for predicting observer distributions across vacua, while acknowledging non-uniqueness and inviting empirical tests and comparisons with alternative proposals.

Abstract

I review recent progress in defining probability distributions in the inflationary multiverse.

Paper Structure

This paper contains 9 sections, 12 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Problem with global-time measure
  3. A pocket-based measure
  4. Counting pockets
  5. Bubble abundance $p_j$
  6. An equivalent proposal
  7. Reference length $R_j$
  8. Continuous variables
  9. Discussion

Figures (2)

  • Figure 1: A schematic conformal diagram for a comoving region in an eternally inflating universe. Bubbles of different vacua are represented by different shades of gray. The upper boundary of the diagram $i_+$ is the future timelike infinity. A surface of constant global time $\Sigma$ cuts through the entire region and intersects many bubbles.
  • Figure 2: A comoving region with a single type of bubble. Bubbles differ by details of the scalar field distribution, but are statistically identical. Each pocket is internally an infinite open universe. Constant-time surfaces within pockets, shown by dashed lines, are infinite spacelike surfaces.