  We investigate how well we can constrain the mass of light gravitino m_3/2 by
using future observations of 21 cm line fluctuations such as Square Kilometre
Array (SKA) and Omniscope. Models with light gravitino with the mass m_3/2 <
O(10) eV are quite interesting because they are free from the cosmological
gravitino problem and consistent with many baryogenesis/leptogenesis scenarios.
We evaluate expected constraints on the mass of light gravitino from the
observations of 21 cm line, and show that the observations are quite useful to
prove the mass. If the gravitino mass is m_3/2 = 1 eV, we found expected 1
sigma errors on m_3/2 are sigma(m_3/2) = 0.25 eV (SKA phase 1), 0.16 eV (SKA
phase 2) and 0.067 eV (Omniscope) in combination with Planck + Simons Array +
DESI (BAO) + H_0. Additionally, we also discuss detectability of the effective
number of neutrino species by varying the effective number of neutrino species
for light gravitino N_3/2 and constraints on the mass of light gravitino in the
presence of massive neutrinos. We show that 21 cm line observations can detect
the nonzero value of N_3/2, and allow us to distinguish the effects of the
light gravitino from those of massive neutrino.
