Inflationary models with a superheavy scale F-term hybrid inflation followed by an intermediate scale modular inflation are considered .
The restrictions on the power spectrum P _ { \cal R } of curvature perturbation and the spectral index n _ { s } from the recent data within the power-law cosmological model with cold dark matter and a cosmological constant 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 suitably restricted .
The additional e-foldings needed for solving the horizon and flatness problems are generated by modular inflation with a string axion as inflaton .
For central values of P _ { \cal R } and n _ { s } , the grand unification scale comes out , in the case of standard hybrid inflation , close to its supersymmetric value M _ { GUT } \simeq 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 shifted [ smooth ] hybrid inflation case , the grand unification scale can be identified with M _ { GUT } for N _ { HI* } \simeq 21 [ N _ { HI* } \simeq 18 ] .