Supersymmetric axion grand unified theories and their predictions

We introduce a class of unified supersymmetric axion theories with unified and Peccei-Quinn ( PQ) symmetries broken by the same set of fields at a scale similar to 2 x 10(16) GeV. Atypical domain wall number of order 30 leads to an axion decay constant f(a) of order 10(15) GeV. Inflation generates a large saxion condensate, giving a reheat temperature T-R below the QCD scale for supersymmetry breaking of order 1-10 TeV. Axion field oscillations commence in the saxion matter-dominated era near the QCD scale, and recent lattice computations of the temperature dependence of the axion mass in this era allow a controlled calculation of the axion dark matter abundance. The observed abundance can be successfully explained by an initial axion misalignment angle of order unity, theta(i) similar to 1. Ahighly correlated set of predictions is discussed for f(a), T-R, the supersymmetric Higgs mass parameter mu, the amount of dark radiation Delta N-eff, the proton decay rate Gamma(p -> e(+)pi(0)) isocurvature density perturbations and the B mode of the cosmic microwave background. The last two are particularly interesting when the energy scale of inflation is also of order 10(16) GeV.