No-scale D-term inflation with stabilized moduli

We study the consistency of hybrid inflation and moduli stabilization, using the Kallosh--Linde model as an example for the latter. We find that F-term hybrid inflation is not viable since inflationary trajectories are destabilized by tachyonic modes. On the other hand, D-term hybrid inflation is naturally compatible with moduli stabilization due to the absence of a large superpotential term during the inflationary phase. Our model turns out to be equivalent to superconformal D-term inflation and it therefore successfully accounts for the CMB data in the large-field regime. Supersymmetry breaking can be incorporated via an O'Raifeartaigh model. For GUT-scale inflation one obtains stringent bounds on the gravitino mass. A rough estimate yields 10^5 GeV \lesssim m_3/2 \lesssim 10^10 GeV, contrary to naive expectation.