The structure and interpretation of cosmology: Part I—general relativistic cosmology

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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.

Section snippets

Geometry and topology

Let us review and clarify the topological and geometrical aspects of the Friedmann–Robertson–Walker (FRW) models of general relativistic cosmology. Whilst doing so will contribute to the overall intention of this paper to clarify, by means of precise mathematical concepts, the notions of modern cosmology, there are further philosophical motivations: firstly, to emphasise the immense variety of possible topologies and geometries for our universe, consistent with empirical (i.e. astronomical)

Spatially homogeneous cosmologies

As a continuation to the rationale of the opening section, the philosophical purpose of this section is to explain and emphasise the immense variety of spatially homogeneous cosmological models which are consistent with astronomical observation, or which serve to highlight the variety of possible universes similar to our own. This section will also clarify the Bianchi classification, and the relationship between the spatially homogeneous models and the FRW models.

The spatially homogeneous class

The epistemology of cosmology

To elucidate the nature and scope of astronomical and cosmological knowledge, the philosophical purpose of this section is to precisely clarify, using the concept of the celestial sphere, the relationship between general relativity and astronomical observation and measurement. En route, the nature of colour in astronomical observation is clarified, and an iconoclastic scenario suggested by Arp, Burbidge, Hoyle, Narlikar, and Wickramasinghe (1990) is used as a case study of the relationship

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