Cosmological attractors and no-hair theorems.
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Interest in the attracting property of de Sitter space-time has grown during the 'inflationary era' of cosmology. In this dissertation we discuss the more important attempts to prove the so called 'cosmic no-hair conjecture' ie the proposition that all expanding universes with a positive cosmological constant asymptotically approach de Sitter space-time. After reviewing briefly the standard FRW cosmology and the success of the inflationary scenario in resolving most of the problems of standard cosmology, we carefully formulate the cosmic no-hair conjecture and discuss its limitations. We present a proof of the cosmic no-hair theorem for homogeneous space-times in the context of general relativity assuming a positive cosmological constant and discuss its generalisations. Since, in inflationary cosmology, the universe does not have a true cosmological constant but rather a vacuum energy density which behaves like a cosmological term, we take into account the dynamical role of the inflaton field in the no-hair hypothesis and examine the no-hair conjecture for the three main inflationary models, namely new inflation, chaotic inflation and power-law inflation. A generalisation of a well-known result of Collins and Hawking  in the presence of a scalar field matter source, regarding Bianchi models which can approach isotropy is given. In the context of higher order gravity theories, inflation emerges quite naturally without artificially imposing an inflaton field. The conformal equivalence theorem relating the solution space of these theories to that of general relativity is reviewed and the applicability of the no-hair theorems in the general framework of f (R) theories is developed. We present our comments and conclusions about the present status of the cosmic no-hair theorem and suggest possible paths of future research in the field.