  Hybrid inflation, driven by a Fayet-Iliopoulos (FI) D term, is an intriguing
inflationary model. In its usual formulation, it however suffers from several
shortcomings. These pertain to the origin of the FI mass scale, the stability
of scalar fields during inflation, gravitational corrections in supergravity,
as well as to the latest constraints from the cosmic microwave background. We
demonstrate that these issues can be remedied if D-term inflation is realized
in the context of strongly coupled supersymmetric gauge theories. We suppose
that the D term is generated in consequence of dynamical supersymmetry
breaking. Moreover, we assume canonical kinetic terms in the Jordan frame as
well as an approximate shift symmetry along the inflaton direction. This
provides us with a unified picture of D-term inflation and high-scale
supersymmetry breaking. The D term may be associated with a gauged U(1)_B-L, so
that the end of inflation spontaneously breaks B-L in the visible sector.
