Titlebook: Cosmological Crossroads; An Advanced Course i Spiros Cotsakis,Eleftherios Papantonopoulos Textbook 2002 Springer-Verlag Berlin Heidelberg 2

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Cosmological Singularitiesund from tensor and causal geometry to understand the theorems is supplied, the mathematical notion of a cosmology is described in some detail and issues related to the range of validity of general relativity are also discussed.

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Introduction to Cosmological Dynamical Systemsa brief review of the basic mathematical formalism of the theory of finite dynamical systems. We write the field equations in a form suitable for the dynamical system approach and analyze the general properties of the system of DEs describing the evolution of the models. Finally we discuss without t

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Cosmological Perturbationsn theory and of structure formation scenarios. We present both the Newtonian and the general relativistic approaches, derive the key equations and then apply them to a number of characteristic cases. The gauge problem in cosmology and ways to circumvent it are also discussed. We outline the basic fr

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Dark Matter: A Particle Theorist’s Viewpointosmological observations suggest that the Matter-Energy density of the Universe is close to its critical density, . = 1, whose large amount (. 70%) is Dark Energy of uknown origin. The baryonic density comprises only the . 5% while the rest is due to Dark Matter of unknown composition. Modern partic

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Quantum Cosmologyroups are revealed as the key element through which G.C.T.’s can be used for a general treatment of these problems. At the classical level, the time dependent automorphisms lead to significant simplifications of the line element for the generic spatially homogeneous geometry, without loss of general

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Inflationary Cosmologyussed together with their resolution by inflationary cosmology. Inflation, the subsequent oscillation and decay of the inflaton, and the resulting ‘reheating’ of the universe are studied. The density perturbations produced by inflation and the temperature fluctuations of the cosmic background radiat

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