Realistic Hybrid Inflation in 5D Orbifold SO(10) GUT

We discuss the smooth hybrid inflation scenario in the context of a simple supersymmetric SO(10) GUT in 5D orbifold. In this GUT model, the SO(10) gauge symmetry is broken down to the Pati-Salam (PS) gauge group, SU(4)$_c \times$ SU(2)$_L \times$ SU(2)$_R$, by orbifold boundary conditions and all matter and Higgs multiplets are placed only on the brane (PS brane) where only the PS symmetry is manifest. Further breaking of the Pati-Salam group to the Standard Model one is realized by VEVs of the Higgs multiplets $({\bf 4},{\bf 1},{\bf 2}) \oplus (\overline{{\bf 4}},{\bf 1},{\bf 2})$. The gauge coupling unification is successfully realized at $M_{\rm GUT} =4.6 \times 10^{17}$ GeV after incorporating the threshold corrections of the Kaluza-Klein modes, with the compactification scale (assumed to be the same as the PS symmetry breaking scale) $M_c = v_{\rm PS}= 1.2 \times 10^{16}$ GeV. We show that this orbifold GUT model can naturally leads us to the smooth hybrid inflation, which tunes out to be consistent with the WMAP 5-year data with the predicted $M_{\rm GUT}$ and $v_{PS}$ in the model.