F-Term Hybrid Inflation Followed by Modular Inflation

Abstract

We consider the well motivated model of the (standard) supersymmetric F-term hybrid inflation (FHI) which can be realized close to the grand unification scale. The predicted scalar spectral index $n_s$ cannot be smaller than 0.98 and can exceed unity including corrections from minimal supergravity, if the number of e-foldings corresponding to the pivot scale $k_*=0.002/{\rm Mpc}$ is around 50. These results are marginally consistent with the fitting of the Wilkinson microwave anisotropy probe data by the standard power-law cosmological model with cold dark matter and a cosmological constant. However, $n_s$ can be reduced by restricting the number of e-foldings that $k_*$ suffered during FHI. The additional e-foldings required for solving the horizon and flatness problems can be generated by a subsequent stage of fast-roll [slow-roll] modular inflation realized by a string modulus which does [does not] acquire effective mass before the onset of modular inflation.