Grand Unification, Axion, and Inflation in Intermediate Scale
  Supersymmetry
  A class of supersymmetric grand unified theories is introduced that has a
single scale below the cutoff, that of the supersymmetry breaking masses
$\tilde{m}$. For a wide range of the dimensionless parameters, agreement with
the observed mass of the Higgs boson determines $\tilde{m} \sim 10^9-10^{13}
{\rm GeV}$, yielding Intermediate Scale Supersymmetry. We show that within this
framework it is possible for seesaw neutrino masses, axions, and inflation to
be described by the scale $\tilde{m}$, offering the possibility of a unified
origin of disparate phenomena. Neutrino masses allowing for thermal
leptogenesis can be obtained, and the axion decay constant lies naturally in
the range $f_a \sim 10^9-10^{11} {\rm GeV}$, consistent with a recent
observational suggestion of high scale inflation. A minimal $SU(5)$ model is
presented that illustrates these features. In this model, the only states at
the grand unified scale are those of the heavy gauge supermultiplet. The grand
unified partners of the Higgs doublets have a mass of order $\tilde{m}$,
leading to the dominant proton decay mode $p \rightarrow \bar{\nu} K^+$, which
may be probed in upcoming experiments. Dark matter may be winos, with mass
environmentally selected to the TeV scale, and/or axions. Gauge coupling
unification is found to be successful, especially if the wino is at the TeV
scale.
