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_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_R and n_s, the grand
unification scale comes out, in the case of standard hybrid inflation, close to
its supersymmetric value M_GUT=2.86 x 10^16 GeV, the relevant coupling constant
is relatively large (0.005-0.14), and N_HI* is between 10 and 21.7. In the
shifted [smooth] hybrid inflation case, the grand unification scale can be
identified with M_GUT for N_HI*=21 [N_HI*=18].Comment: 13 pages including 3 figures, uses ws-ijmpa.cls, minor corrections
included, talk given at the CTP Symposium on Supersymmetry at LHC:
Theoretical and Experimental Perspectives, British University in Egypt (BUE),
Cairo, 11-14 March 2007 (to appear in the proceedings