Cosmological Constraint on the Light Gravitino Mass from CMB Lensing and
  Cosmic Shear
  Light gravitinos of mass $\lesssim \mathcal{O} (10)$ eV are of particular
interest in cosmology, offering various baryogenesis scenarios without
suffering from the cosmological gravitino problem. The gravitino may contribute
considerably to the total matter content of the Universe and affect structure
formation from early to present epochs. After the gravitinos decouple from
other particles in the early Universe, they free-stream and consequently
suppress density fluctuations of (sub-)galactic length scales. Observations of
structure at the relevant length-scales can be used to infer or constrain the
mass and the abundance of light gravitinos. We derive constraints on the light
gravitino mass using the data of cosmic microwave background (CMB) lensing from
Planck and of cosmic shear from the Canada France Hawaii Lensing Survey,
combined with analyses of the primary CMB anisotropies and the signature of
baryon acoustic oscillations in galaxy distributions. The obtained constraint
on the gravitino mass is $m_{3/2} < 4.7$ eV (95% C.L.), which is substantially
tighter than the previous constraint from clustering analysis of Ly-$\alpha$
forests.
