Constraining Light Gravitino Mass from Cosmic Microwave Background

We investigate the possibilities of constraining the light gravitino mass m_{3/2} from future cosmic microwave background (CMB) surveys. A model with light gravitino with the mass m_{3/2}<O(10) eV is of great interest since it is free from the cosmological gravitino problem and, in addition, can be compatible with many baryogenesis/leptogenesis scenarios such as the thermal leptogenesis. We show that the lensing of CMB anisotropies can be a good probe for m_{3/2} and obtain an expected constraint on m_{3/2} from precise measurements of lensing potential in the future CMB surveys, such as the PolarBeaR and CMBpol experiments. If the gravitino mass is m_{3/2}=1 eV, we will obtain the constraint for the gravitino mass as m_{3/2} < 3.2 eV (95% C.L.) for the case with Planck+PolarBeaR combined and m_{3/2}=1.04^{+0.22}_{-0.26} eV (68% C.L.) for CMBpol. The issue of Bayesian model selection is also discussed.