  In a class of realistic four and five dimensional supersymmetric grand
unified models, the scalar spectral index is found to be $n_s=0.98 (\pm 0.01)$,
in excellent agreement with the values determined by several previous
experiments and most recently by the Wilkinson Microwave Anisotropy Probe
(WMAP). The models predict $dn_s/d{\rm ln}k\sim 10^{-3}$ and a negligible
tensor-to-scalar ratio $r\sim 10^{-8}$. A new five dimensional supersymmetric
SO(10) model along these is presented in which inflation is associated with the
breaking of SO(10) to SU(5) at scale $M$, with $\delta T/T\propto (M/M_{\rm
Planck})^2$, so that $M\simeq 10^{16}$ GeV. The inflaton decay leads to the
observed baryon asymmetry via leptogenesis. We also discuss how the monopole
problem is solved without the use of non-renormalizable terms.
