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In the framework of Supersymmetric Grand Unified Theories (SUSY GUTs), theuniverse undergoes a cascade of symmetry breakings, during which topologicaldefects can be formed. We address the question of the probability of cosmicstring formation after a phase of hybrid inflation within a large number ofmodels of SUSY GUTs in agreement with particle and cosmological data. We showthat cosmic strings are extremely generic and should be used to relatecosmology and high energy physics. This conclusion is employed together withthe WMAP CMB data to strongly constrain SUSY hybrid inflation models. F-termand D-term inflation are studied in the SUSY and minimal SUGRA framework. Theyare both found to agree with data but suffer from fine tuning of theirsuperpotential coupling (\lambda \lesssim 3\times 10^(-5) or less). Mass scalesof inflation are also constrained to be less than M \lesssim 3\times 10^(15)GeV.Comment: Based on talks given by J. Rocher at the "IAP Colloquium", Paris in  july 2004, at "COSMO 04", Toronto in September 2004, at the Workshop "Quest  For Unification", CERN in December 2004 and at the "Einstein's Century  Meeting", Paris in june 2005. To appear in the Proceedings of the "Einstein's  Century Meeting", Ed. J.-M. Alimi, A. Furzfa, AIP, Paris (2006

Constraining SUSY GUTs and Inflation with Cosmology