Inflation, Proton Decay, and Higgs-Portal Dark Matter in $SO(10) \times
  U(1)_\psi$
  We propose a simple non-supersymmetric grand unified theory (GUT) based on
the gauge group $SO(10) \times U(1)_\psi$. The model includes 3 generations of
fermions in ${\bf 16}$ ($+1$), ${\bf 10}$ ($-2$) and ${\bf 1}$ ($+4$)
representations. The ${\bf 16}$-plets contain Standard Model (SM) fermions plus
right-handed neutrinos, and the ${\bf 10}$-plet and the singlet fermions are
introduced to make the model anomaly-free. Gauge coupling unification at
$M_{GUT} \simeq 5 \times 10^{15}-10^{16}$ GeV is achieved by including an
intermediate Pati-Salam breaking at $M_{I} \simeq 10^{12}-10^{11}$ GeV, which
is a natural scale for the seesaw mechanism. For $M_{I} \simeq
10^{12}-10^{11}$, proton decay will be tested by the Hyper-Kamiokande
experiment. The extra fermions acquire their masses from $U(1)_\psi$ symmetry
breaking, and a $U(1)_\psi$ Higgs field drives a successful inflection-point
inflation with a low Hubble parameter during inflation, $H_{inf} \ll M_{I}$.
Hence, cosmologically dangerous monopoles produced from $SO(10)$ and PS
breakings are diluted away. The reheating temperature after inflation can be
high enough for successful leptogenesis. With the Higgs field contents of our
model, a ${\bf Z}_2$ symmetry remains unbroken after GUT symmetry breaking, and
the lightest mass eigenstate among linear combinations of the ${\bf 10}$-plet
and the singlet fermions serves as a Higgs-portal dark matter (DM). We identify
the parameter regions to reproduce the observed DM relic density while
satisfying the current constraint from the direct DM detection experiments. The
present allowed region will be fully covered by the future direct detection
experiments such as LUX-ZEPLIN DM experiment. In the presence of the extra
fermions, the SM Higgs potential is stabilized up to $M_{I}$.
