F-term hybrid inflation followed by 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 of density perturbations P_R and the spectral index n_s from 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* of 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 realized by a string axion.