100 years of mathematical cosmology: Models, theories, and problems

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 parts, the first part 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 which 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. 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'.

91 pages

References in corpus (11)

• Dark torsion as the cosmic speed-up
• Beyond the Cosmological Standard Model
• Einstein's Other Gravity and the Acceleration of the Universe
• A Short Review of Loop Quantum Gravity
• Conformal transformation in $f(T)$ theories
• A Safe Beginning for the Universe?
• The roots of scalar-tensor theory: an approximate history
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• On the cosmological singularity
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Cited by in corpus (8)

• Is the Observable Universe Consistent with the Cosmological Principle?
• Legendre scalarization in gravity and cosmology
• Dispersive Friedmann universes and synchronization
• A universe born in a metastable false vacuum state needs not die
• Structural stability and general relativity
• Friedmann-Lemaître universes and their metamorphoses
• Sudden Shock Waves in modified gravity
• Cosmology in the presence of diffeomorphism-violating, nondynamical background fields