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We consider the construction of inverted hybrid inflation models in which thevacuum energy during inflation is at the TeV scale, and the inflaton couples tothe Higgs field. Such models are of interest in the context of some recentlyproposed models of electroweak baryogenesis. We demonstrate how constraints onthese models arise from quantum corrections, and how self-consistent examplesmay be constructed, albeit at the expense of fine-tuning. We discuss twopossible ways in which the baryon asymmetry of the universe may be produced inthese models. One of them is based on preheating and a consequent non-thermalelectroweak symmetry restoration and the other on the formation of Higgswinding configurations by the Kibble mechanism at the end of inflation.Comment: 21 pages, 5 figures. Minor changes, some references added. To appear  in PR

Hybrid inflation and baryogenesis at the TeV scale