The recent discovery of the Higgs boson at the Large Hadron Collider (LHC) constitutes a milestone in a major work programme to test the Standard Model and search for new physics, in order to obtain a global picture of electroweak symmetry breaking and its possible connections to open questions in particle cosmology. A key question relating the high-energy, precision and cosmic frontiers in particle physics is the origin of the cosmic matter-antimatter asymmetry. The present proposal will combine for the first time experimental and theoretical inputs from all three frontiers in order to test one of the most compelling ways to explain the generation of this asymmetry in the early Universe: Electroweak Baryogenesis. Together with leading scientists from the Physics Department in the University of Sussex, which hold a unique expertise at the interface of these frontiers, I will design and develop a comprehensive strategy to search for viable Electroweak Baryogenesis scenarios at LHC, in combination with present and future experimental inputs from neutron/electron electric dipole moments (e.g. from Sussex/RAL Cryo-EDM experiment) and detection prospects from the foreseen gravitational wave mission eLISA/NGO from the ESA.A dedicated LHC search strategy aimed at probing new physics scenarios where the matter-antimatter asymmetry could be generated is at present essentially absent from the main LHC physics programme. The project will make this analysis available for the ATLAS and CMS experimental collaborations, and aims to trigger interest towards these searches in their community, taking advantage of the numerous high-quality national/international collaborations and networking opportunities (exemplified by SEPNet and NExT Institute consortiums) provided by the host. This will constitute a first step towards establishing the search for viable Electroweak Baryogenesis scenarios as an important part of the LHC physics programme, to be pursued in the coming years.