Extra dimensions and dark matter

In this thesis we analyze the consequences of extra spacetime dimensions on the MSSM. We begin by reviewing the MSSM in four dimensions. We specify the superpotential and all the possible soft terms to break supersymmetry. After describing gravity-mediated susy breaking models, we present the mass spectrum of the MSSM. In particular we introduce the neutralinos as lightest supersymmetric particles. They are suitable candidates for dark matter. We present a pedagogical introduction to the method of the effective potential. We apply this method to the MSSM in order to obtain its renormalization group equations. We also do an analysis in terms of Feynman diagrams. We present the string-inspired model by Dienes, Dudas and Gherghetta [Nuclear Physics B537, 47 (1999)]. We treat different scenarios showing how extra dimensions give rise to `power-law' running of the parameters. We also analyze the possible implications of extra dimensions related to the dark matter problem. Extra dimensions affect also cosmology: we take care of this modifying the Friedmann equation. The result of the computation is that the neutralino is still the lightest supersymmetric particle and it is higgsino like in most of the parameter space.