We consider the well motivated model of the ( standard ) supersymmetric ( SUSY ) F-term hybrid inflation ( FHI ) which can be realized close to the grand unification ( GUT ) scale .
The predicted scalar spectral index n _ { s } can not 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 , \Lambda CDM .
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 ( MI ) realized by a string modulus which does [ does not ] acquire effective mass ( m _ { s } | _ { eff } ) before the onset of MI .