Predictions in eternal inflation

TL;DR

This paper discusses the challenges of making statistical predictions in models of eternal inflation and the string landscape, highlighting issues like cutoff dependence and various approaches to address them.

Contribution

It reviews the development of mathematical techniques and proposals for extracting predictions in eternal inflation and string landscape models.

Findings

Identifies problems with volume cutoff dependence and initial conditions.

Reviews approaches for statistical predictions in eternal inflation.

Provides examples of applying different techniques.

Abstract

In generic models of cosmological inflation, quantum fluctuations strongly influence the spacetime metric and produce infinitely many regions where the end of inflation (reheating) is delayed until arbitrarily late times. The geometry of the resulting spacetime is highly inhomogeneous on scales of many Hubble sizes. The recently developed string-theoretic picture of the "landscape" presents a similar structure, where an infinite number of de Sitter, flat, and anti-de Sitter universes are nucleated via quantum tunneling. Since observers on the Earth have no information about their location within the eternally inflating universe, the main question in this context is to obtain statistical predictions for quantities observed at a random location. I describe the problems arising within this statistical framework, such as the need for a volume cutoff and the dependence of cutoff schemes on time slicing and on the initial conditions. After reviewing different approaches and mathematical techniques developed in the past two decades for studying these issues, I discuss the existing proposals for extracting predictions and give examples of their applications.