Inflation with realistic supersymmetric SO(10)

We implement inflation within a realistic supersymmetric $SO(10)$ model in which the doublet-triplet splitting is realized through the Dimopoulos-Wilczek mechanism, the MSSM $\ensuremath{\mu}$ problem is resolved, and Higgsino mediated dimension five nucleon decay is heavily suppressed. The cosmologically unwanted topological defects are inflated away, and from $\ensuremath{\delta}T/T$, the $B\ensuremath{-}L$ breaking scale is estimated to be of order ${10}^{16}\char21{}{10}^{17}\text{ }\text{ }\mathrm{GeV}$. Including supergravity corrections, the scalar spectral index ${n}_{s}=0.99\ifmmode\pm\else\textpm\fi{}0.01$, with $|d{n}_{s}/d\mathrm{ln} k|\ensuremath{\lesssim}{10}^{\ensuremath{-}3}$.