SO(10) SUSY GUTs, the gravitino problem, non-thermal leptogenesis and   axino dark matter
  Simple SUSY GUT models based on the gauge group SO(10) require t-b-\tau Yukawa coupling unification, in addition to gauge coupling and matter unification. The Yukawa coupling unification places strong constraints on the expected superparticle mass spectrum, with scalar masses \sim 10 TeV while gaugino masses are quite light. A problem generic to all supergravity models comes from overproduction of gravitinos in the early universe: if gravitinos are unstable, then their late decays may destroy the predictions of Big Bang nucleosynthesis. We present a Yukawa-unified SO(10) SUSY GUT scenario which avoids the gravitino problem, gives rise to the correct matter-antimatter asymmetry via non-thermal leptogenesis, and is consistent with the WMAP-measured abundance of cold dark matter due to the presence of an axino LSP. To maintain a consistent cosmology for Yukawa-unified SUSY models, we require a re-heat temperature T_R\sim 10^6-10^7 GeV, an axino mass around \sim 0.1-10 MeV, and a PQ breaking scale f_a\sim 10^{12} GeV. 
Howard Baer and Heaya Summy