The purpose of this paper is to review, clarify, and critically analyse modern mathematical cosmology. The emphasis is upon the mathematical structures involved, rather than numerical computations. 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 to the topological and geometrical aspects of these models. Section 3 explains how the mathematical formalism can be linked with astronomical observation. Sections 4 and 5 provide a (...) critical analysis of Inflationary Cosmology and Quantum Cosmology, with particular attention to the claims made that these theories can explain the creation of the universe. (shrink)

Where does the road to reality lie? This fundamental question is addressed in this collection of essays by physicists and philosophers, inspired by the original ideas of Sir Roger Penrose, the English mathematical physicist and philosopher of science. The topics range from black holes and quantum information to the very nature of mathematical cognition itself. *** Librarians: ebook available on ProQuest and EBSCO [Subject: Philosophy, Physics, Mathematics, Cosmology].

The claim of inflationary cosmology to explain certain observable facts, which the Friedmann-Roberston-Walker models of `Big-Bang' cosmology were forced to assume, has already been the subject of significant philosophical analysis. However, the principal empirical claim of inflationary cosmology, that it can predict the scale-invariant power spectrum of density perturbations, as detected in measurements of the cosmic microwave background radiation, has hitherto been taken at face value by philosophers. The purpose of this paper is to expound the theory of density perturbations (...) used by inflationary cosmology, to assess whether inflation really does predict a scale-invariant spectrum, and to identify the assumptions necessary for such a derivation. The first section of the paper explains what a scale invariant power-spectrum is, and the requirements placed on a cosmological theory of such density perturbations. The second section explains and analyses the concept of the Hubble horizon, and its behaviour within an inflationary space-time. The third section expounds the inflationary derivation of scale-invariance, and scrutinises the assumptions within that derivation. The fourth section analyses the explanatory role of `horizon-crossing' within the inflationary scenario. (shrink)

The purpose of this paper is to elucidate, by means of concepts and theorems drawn from mathematical logic, the conditions under which the existence of a multiverse is a logical necessity in mathematical physics, and the implications of Gödel’s incompleteness theorem for theories of everything.Three conclusions are obtained in the final section: (i) the theory of the structure of our universe might be an undecidable theory, and this constitutes a potential epistemological limit for mathematical physics, but because such a theory (...) must be complete, there is no ontological barrier to the existence of a final theory of everything; (ii) in terms of mathematical logic, there are two different types of multiverse: classes of non-isomorphic but elementarily equivalent models, and classes of model which are both non-isomorphic and elementarily inequivalent; (iii) for a hypothetical theory of everything to have only one possible model, and to thereby negate the possible existence of a multiverse, that theory must be such that it admits only a finite model. (shrink)