Reducing the spectral index in F-term hybrid inflation through a complementary modular inflation

We consider two-stage inflationary models in which a superheavy scale F-term hybrid inflation is followed by an intermediate scale modular inflation. We confront these models with the restrictions on the power spectrum P-R of curvature perturbations and the spectral index n(s) implied by the recent data within the power-law cosmological model with cold dark matter and a cosmological constant. We show that these restrictions can be met provided that the number of e-foldings N-HI* suffered by the pivot scale k(*) = 0.002/Mpc during hybrid inflation is appropriately restricted. The additional e-foldings required for solving the horizon and flatness problems can be naturally generated by the subsequent modular inflation. For central values of P-R and n(s), we find that, in the case of standard hybrid inflation, the values obtained for the grand unification scale are close to its supersymmetric value M-GUT = 2.86 x 10(16) GeV, the relevant coupling constant is relatively large (approximate to 0.005-0.14), and 10 less than or similar to N-HI* less than or similar to 21.7. In the case of shifted [smooth] hybrid inflation, the grand unification scale can be identified with M-GUT provided that N-HI* similar or equal to 21 [N-HI* similar or equal to 18]. (c) 2007 Elsevier B.V. All rights reserved.