Moduli Corrections to D-term Inflation
  We present a D-term hybrid inflation model, embedded in supergravity with moduli stabilisation. Its novel features allow us to overcome the serious challenges of combining D-term inflation and moduli fields within the same string-motivated theory. One salient point of the model is the positive definite uplifting D-term arising from the moduli stabilisation sector. By coupling this D-term to the inflationary sector, we generate an effective Fayet-Iliopoulos term. Moduli corrections to the inflationary dynamics are also obtained. Successful inflation is achieved for a limited range of parameter values with spectral index compatible with the WMAP3 data. Cosmic D-term strings are also formed at the end of inflation; these are no longer Bogomol'nyi-Prasad-Sommerfeld (BPS) objects. The properties of the strings are studied. 
Ph. Brax, C. van de Bruck, A. C. Davis, Stephen C. Davis, R. Jeannerot   and M. Postma