Moduli-induced axion problem

We point out that the cosmological moduli problem is not necessarily resolved even if the modulus mass is heavier than O(10) TeV, contrary to the common wisdom. The point is that, in many scenarios where the lightest moduli fields are stabilized by super-symmetry breaking effects, those moduli fields tend to mainly decay into almost massless axions, whose abundance is tightly constrained by the recent Planck results. We study the moduli-induced axion problem in concrete examples, and discuss possible solutions. The problem and its solutions are widely applicable to decays of heavy scalar fields which dominate the energy density of the Universe, for instance, the reheating of the inflaton.