Uniform probability in cosmology

TL;DR

This paper explores the measure problem in cosmology, especially in inflation theory, highlighting foundational issues with uniform probabilities on infinite spaces and suggesting multiple consistent approaches for assigning probabilities.

Contribution

It introduces foundational probability issues in cosmology to philosophers and physicists, connecting them with classical probability theory and proposing a pluralist approach.

Findings

Identifies the origin of the measure problem as a paradox involving uniformity on infinite spaces.

Highlights multiple consistent methods for handling uniform probabilities in cosmology.

Encourages a pluralist stance to improve probability assignments in cosmological models.

Abstract

Problems with uniform probabilities on an infinite support show up in contemporary cosmology. This paper focuses on the context of inflation theory, where it complicates the assignment of a probability measure over pocket universes. The measure problem in cosmology, whereby it seems impossible to pick out a uniquely well-motivated measure, is associated with a paradox that occurs in standard probability theory and crucially involves uniformity on an infinite sample space. This problem has been discussed by physicists, albeit without reference to earlier work on this topic. The aim of this article is both to introduce philosophers of probability to these recent discussions in cosmology and to familiarize physicists and philosophers working on cosmology with relevant foundational work by Kolmogorov, de Finetti, Jaynes, and other probabilists. As such, the main goal is not to solve the measure problem, but to clarify the exact origin of some of the current obstacles. The analysis of the assumptions going into the paradox indicates that there exist multiple ways of dealing consistently with uniform probabilities on infinite sample spaces. Taking a pluralist stance towards the mathematical methods used in cosmology shows there is some room for progress with assigning probabilities in cosmological theories.