Reducing the Spectral Index in F-Term Hybrid Inflation

We consider a class of well motivated supersymmetric models of F-term hybrid inflation (FHI) which can be linked to the supersymmetric grand unification. The predicted scalar spectral index ns cannot be smaller than 0.97 and can exceed unity including corrections from minimal supergravity, 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 three-year Wilkinson microwave anisotropy probe data by the standard power-law cosmological model with cold dark matter and a cosmological constant. However, ns can be reduced by applying two mechanisms: (i) The utilization of a quasi-canonical Kähler potential with a convenient choice of a sign and (ii) the restriction of the number of e-foldings that k∗ suffered during FHI. In the case (i), we investigate the possible reduction of ns without generating maxima and minima of the potential on the inflationary path. In the case (ii), 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.