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 _ { \cal 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 _ { \cal 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 \times 10 ^ { 16 } ~ { } { GeV } , the relevant coupling constant is relatively large ( \approx 0.005 - 0.14 ) , and 10 \lesssim N _ { HI* } \lesssim 21.7 .
In the case of shifted [ smooth ] hybrid inflation , the grand unification scale can be identified with M _ { GUT } provided that N _ { HI* } \simeq 21 [ N _ { HI* } \simeq 18 ] .