Axion Model with Intermediate Scale Fermionic Dark Matter
  We investigate a non-supersymmetric $SO(10)\times U(1)_{\rm PQ}$ axion model
in which the spontaneous breaking of $U(1)_{\rm PQ}$ occurs after inflation,
and the axion domain wall problem is resolved by employing the Lazarides-Shafi
mechanism. This requires the introduction of two fermion 10-plets, such that
the surviving discrete symmetry from the explicit $U(1)_{\rm PQ}$ breaking by
QCD instantons is reduced from $Z_{12}$ to $Z_4$, where $Z_4$ coincides with
the center of $SO(10)$ (more precisely $Spin(10)$). An unbroken $Z_2$ subgroup
of $Z_4$ yields intermediate scale topologically stable strings, as well as a
stable electroweak doublet non-thermal dark matter candidate from the fermion
10-plets with mass comparable to or somewhat smaller than the axion decay
constant $f_{\rm a}$. We present an explicit realization with inflation taken
into account and which also incorporates non-thermal leptogenesis. The fermion
dark matter mass lies in the $3\times 10^{8}-10^{10}~{\rm GeV}$ range and its
contribution to the relic dark matter abundance can be comparable to that from
the axion.
