Some Generalities About Generality

TL;DR

This paper surveys the concept of generality in cosmology, using counting arguments to analyze Einstein's equations and discussing implications for singularities, models, and universe descriptions.

Contribution

It introduces a systematic approach using counting arguments to characterize the general solutions of Einstein's equations across various cosmological contexts.

Findings

Counting arguments help identify the degrees of freedom in Einstein's solutions.

Applications include insights into singularities and isotropisation.

The work clarifies the parameter complexity of general cosmological models.

Abstract

We survey a variety of cosmological problems where the issue of generality has arisen. This is aimed at providing a wider context for many claims and deductions made when philosophers of science choose cosmological problems for investigation. We show how simple counting arguments can be used to characterise parts of the general solution of Einstein's equations when various matter fields are present and with different spatial topologies. Applications are described to the problem of singularities, static cosmological models, cosmic no hair theorems, the late-time isotropisation of cosmological models, and the number of parameters needed to describe a general astronomical universe.