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Nevertheless, long-standing open theoretical issues, as well as possible new observational ones arising from the explosive development of cosmology in the last two decades, offer the motivation and lead a large amount of research to be devoted in constructing various extensions and modifications. In this review all extended theories and scenarios are first examined under the light of theoretical consistency, and are then applied in various geometrical backgrounds, such as the cosmological and the spherical symmetric ones. Their predictions at both the background and perturbation levels, and concerningcosmology at early, intermediate and late times, are then confronted with the huge amount of observational data that astrophysics and cosmology has been able to offer in the last two decades. 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The extension of the SM with supersymmetry (SUSY) is considered a promising possibilities to explain dark matter.The nominated thesis describes a search for SUSY using data collected by the CMS experiment at the LHC. It utilizes a final state consisting of a photon, a lepton, and a large momentum imbalance probing a class of SUSY models that has not yet been studied extensively. 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