Abstract
An elementary survey of mathematical cosmology is presented. We cover certain key ideas and developments in a qualitative way, from the time of the Einstein static universe in 1917 until today. We divide our presentation into four main periods, the first one containing important cosmologies discovered until 1960. The second period (1960–80) contains discussions of geometric extensions of the standard cosmology, singularities, chaotic behaviour and the initial input of particle physics ideas into cosmology. Our survey for the third period (1980–2000) continues with brief descriptions of the main ideas of inflation, the multiverse, quantum, Kaluza-Klein and string cosmologies, wormholes and baby universes, cosmological stability and modified gravity. The last period that ends today includes various more advanced topics such as M-theoretic cosmology, braneworlds, the landscape, topological issues, the measure problem, genericity, dynamical singularities and dark energy. We emphasize certain threads that run throughout the whole period of development of theoretical cosmology and underline their importance in the overall structure of the field. This is Part A of our survey covering the first two periods of development of the subject. The second part will include the third and fourth periods. We end this outline with an inclusion of the abstracts of all papers contributed to the Philosophical Transactions of the Royal Society A theme issue, ‘The Future of Mathematical Cosmology’.This article is part of the theme issue ‘The future of mathematical cosmology, Volume 1’.
Highlights
100 years of mathematical cosmology: Models, theories, and problems, Part ASpiros Cotsakis1,2 and A
We shall use the phrases ‘mathematical cosmology’ and ‘theoretical cosmology’ as having a very similar meaning, a possible difference being that of the amount of mathematical rigor contained in the presentation of the results
We shall present a panorama of cosmological models that aim at describing some aspect of the universe
Summary
100 years of mathematical cosmology: Models, theories, and problems, Part ASpiros Cotsakis1,2 and A. — The ‘universes’ as solutions of the field equations — The cosmological constant and vacuum energy — Homogeneity of the universe — Inhomogeneous and anisotropic cosmologies — Expansion and contraction — Evolution vs steady state — Big bang vs bouncing models — Gravitational stability and perturbations — Hot big bang — Causality and time travel — Local vs global structure
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