A Next-to-Minimal Supersymmetric Model of Hybrid Inflation
  In this talk we discuss a model of inflation based on a simple variant of the NMSSM, called $\phi$NMSSM \cite{phiNMSSM}, where the additional singlet $\phi$ plays the role of the inflaton in hybrid (or inverted hybrid) type models. As in the original NMSSM, the $\phi$NMSSM solves the $\mu$ problem of the MSSM via the VEV of a gauge singlet $N$, but unlike the NMSSM does not suffer from domain wall problems since the offending $Z_3$ symmetry is replaced by an approximate Peccei-Quinn symmetry which also solves the strong CP problem, and leads to an invisible axion with interesting cosmological consequences. The model predicts a spectral index $n=1$ to one part in $10^{12}$. 
M. Bastero-Gil and S. F. King