The Structure and Interpretation of Cosmology: Part I - General Relativistic Cosmology

TL;DR

This paper reviews and clarifies the mathematical foundations of modern general relativistic cosmology, focusing on models, topology, geometry, and their connection to observations, with future work on inflationary and quantum cosmology.

Contribution

It provides a detailed mathematical analysis of cosmological models, emphasizing topological and geometrical aspects, and links formalism with astronomical observations.

Findings

Clarification of Friedmann-Robertson-Walker models

Mathematical formalism linked to observations

Focus on topological and geometrical structures

Abstract

The purpose of this work is to review, clarify, and critically analyse modern mathematical cosmology. The emphasis is upon mathematical objects and structures, rather than numerical computations. This paper concentrates on general relativistic cosmology. The opening section reviews and clarifies the Friedmann-Robertson-Walker models of general relativistic cosmology, while Section 2 deals with the spatially homogeneous models. Particular attention is paid in these opening sections to the topological and geometrical aspects of cosmological models. Section 3 explains how the mathematical formalism can be linked with astronomical observation. In particular, the informal, observational notion of the celestial sphere is given a rigorous mathematical implementation. Part II of this work will concentrate on inflationary cosmology and quantum cosmology.