F-Term Hybrid Inflation Followed by Modular Inflation

We consider the well motivated model of the (standard) supersymmetric (SUSY) Fterm hybrid inflation (FHI) which can be realized close to the grand unification (GUT) scale. The predicted scalar spectral index ns cannot be smaller than 0.98 and can exceed unity including corrections from minimal supergravity (SUGRA), if the number of e-foldings corresponding to the pivot scale k∗ = 0.002/Mpc is around 50. These results are marginally consistent with the fitting of the five-year Wilkinson microwave anisotropy probe (WMAP5) data by the standard power-law cosmological model with cold dark matter and a cosmological constant, ΛCDM. However, ns can be reduced by restricting the number of e-foldings that k∗ suffered during FHI. The additional efoldings required for solving the horizon and flatness problems can be generated by a subsequent stage of fast-roll [slow-roll] modular inflation (MI) realized by a string modulus which does [does not] acquire effective mass (ms|eff) before the onset of MI.