  We consider the construction of inverted hybrid inflation models in which the
vacuum energy during inflation is at the TeV scale, and the inflaton couples to
the Higgs field. Such models are of interest in the context of some recently
proposed models of electroweak baryogenesis. We demonstrate how constraints on
these models arise from quantum corrections, and how self-consistent examples
may be constructed, albeit at the expense of fine-tuning. We discuss two
possible ways in which the baryon asymmetry of the universe may be produced in
these models. One of them is based on preheating and a consequent non-thermal
electroweak symmetry restoration and the other on the formation of Higgs
winding configurations by the Kibble mechanism at the end of inflation.
