Axion model with intermediate scale fermionic dark matter

We investigate a non-supersymmetric SO (10) × U(_1)PQ axion model in which the spontaneous breaking of U(_1)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)PQ breaking by QCD instantons is reduced from Z₁₂ to Z₄, where Z₄ coincides with the center of SO (10) (more precisely Spin (10)). An unbroken Z₂ subgroup of Z₄ 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_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 ×10⁸ -10¹⁰GeV range and its contribution to the relic dark matter abundance can be comparable to that from the axion.