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 = 1eV, we will obtain the constraint for the gravitino mass as m _3/23.2eV(95%C.L.) for the case with Planck+PolarBeaR combined and m _3/2 = 1.04 ^+0.22 _-0.26eV(68%C.L.) for CMBpol. The issue of Bayesian model selection is also discussed.