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Simple SUSY GUT models based on the gauge group SO(10) require t-b-t Yukawa coupling unification, in addition to gauge coupling and matter unification. The Yukawa coupling unification places a severe constraint on the expected spectrum of superpartners, with scalar masses ~ 10 TeV while gaugino masses are quite light. For Yukawa-unified models with μ > 0, the spectrum is characterized by three mass scales: i). first and second generation scalars in the multi-TeV range, ii). third generation scalars, μ and mA in the few-TeV range and iii). gluinos in the ~ 350−500 GeV range with chargino masses around 100−160 GeV. In such a scenario, gluino pair production should occur at large rates at the CERN LHC, followed by gluino three-body decays into neutralinos or charginos. Discovery of Yukawa-unified SUSY at the LHC should hence be possible with only 1 fb−1 of integrated luminosity, by tagging multi-jet events with 2–3 isolated leptons, without relying on missing ET . A characteristic dilepton mass edge should easily be apparent above Standard Model background. Combining dileptons with b-jets, along with the gluino pair production cross section information, should allow for gluino and neutralino mass reconstruction. A secondary corroborative signal should be visible at higher integrated luminosity in the X1±1X20 → 3l channel, and should exhibit the same dilepton mass edge as in the gluino cascade decay signal. 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 also 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 TR ~ 106−107 GeV, an axino mass around 0.1−10 MeV, and a Peccei-Quinn breaking scale fa ~ 1012 GeV.