Inflation and the Theory of Cosmological Perturbations

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The hypothesis that the Universe underwent a period of exponential expansion at very early times has become the most popular theory of the early Universe. Not only does it solve some of the problems of standard big bang cosmology, but it also provides a causal theory for the origin of primordial density fluctuations which may explain the observed density inhomogeneities and cosmic microwave fluctuations in the Universe. In these lectures, a review of the basic principles of inflationary cosmology is given, focusing on the theory of the origin and growth of cosmological perturbations. The lectures also focus on some recent progress in inflationary cosmology (in particular on an improved theory of reheating), and on several problems with the present inflationary Universe models. A couple of possible approaches to resolve these issues are suggested.