Cosmological Problems of the String Axion Alleviated by High Scale SUSY of $m_{3/2}$ $\simeq$ 10-100 TeV

Abstract: The string axion may provide the most attractive solution to the strong CP problem in QCD. However, the axion energy density easily exceeds the dark matter density in the present universe due to a large decay constant around $10^{16}$ GeV, unless the initial value of the axion field is fine-tuned. We show that this problem is alleviated if and only if the SUSY particle mass scale is 10-100 TeV, since the decay of the saxion can produce a large enough amount of entropy after the QCD phase transition, not disturbing the BBN prediction. The saxion decay also produces a large number of the lightest SUSY particles (LSPs). As a consequence, R-parity needs to be violated to avoid the overproduction of the LSPs. The saxion field can be stabilized with relatively simple Kahler potentials, not inducing a too large axion dark radiation. Despite the large entropy production, the observed baryon number is explained by the Affleck-Dine mechanism. Furthermore, the constraint from isocurvature perturbations is relaxed, and the Hubble constant during inflation can be as large as several $\times$ $10^{10}$ GeV.