Inflationary cosmology with five dimensional SO(10)

We discuss inflationary cosmology in a five dimensional SO(10) model compactified on $S^1/(Z_2\times Z_2')$, which yields $SU(3)_c\times SU(2)_L\times U(1)_Y\times U(1)_X$ below the compactification scale. The gauge symmetry $SU(5)\times U(1)_X$ is preserved on one of the fixed points, while ``flipped'' $SU(5)'\times U(1)'_X$ is on the other fixed point. Inflation is associated with $U(1)_X$ breaking, and is implemented through $F$-term scalar potentials on the two fixed points. A brane-localized Einstein-Hilbert term allows both branes to have positive tensions during inflation. The scale of $U(1)_X$ breaking is fixed from $\delta T/T$ measurements to be around $10^{16}$ GeV, and the scalar spectral index $n=0.98-0.99$. The inflaton field decays into right-handed neutrinos whose subsequent out of equilibrium decay yield the observed baryon asymmetry via leptogenesis.