We consider the construction of inverted hybrid inflation models in which t
he vacuum energy during inflation is on the TeV scale, and the inflaton cou
ples to the Higgs field. Such models are of interest in the context at some
recently proposed models of electroweak baryogenesis. We demonstrate how c
onstraints on these models arise from quantum corrections, and how self-con
sistent 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 c
onsequent nonthermal electroweak symmetry restoration, and the other on the
formation of Higgs winding configurations by the Kibble mechanism at the e
nd of inflation.