Solving the Gravitino Problem by Axino

In a large class of supersymmetric (SUSY) axion model the mass of axino $\axino$ (a fermionic superpartner of the axion) is predicted as $m_{\axino} \lesssim {\cal O}(1)$ keV. Thus, the axino is the lightest SUSY particle (LSP). We pointed out that such a light axino provides a natural solution to the gravitino problem, if the gravitino is the next LSP. We derive a constraint on the reheating temperature $T_R$ of inflation, $T_R \lesssim 10^{15}$ GeV for the gravitino mass $m_{3/2} \simeq 100$ GeV, which is much weaker than that obtained in the minimal SUSY standard model.