  The heavy gravitinos in minimal supergravity (mSUGRA) models couple
gravitionally and can naturally be the Superweakly Interacting Massive Particle
(SuperWIMP). As plausible candidates for the cold dark matter in the universe,
such gravitino SuperWIMPs can naturally evade the current dark matter detection
experiments due to their superweak couplings. However, this scenario must
subject to the constraints from the Big Bang nucleosynthesis (BBN) predictions
for light element abundances as well as the Wilkinson Mircrowave Anisotropy
Probe (WMAP) data for the relic density. Our study shows that requiring BBN
predictions to agree with the WMAP data of light element abundances can impose
upper and lower mass bounds for both the gravitino and the next-to-lightest
supersymmetric particle (NLSP). From a scan over the mSUGRA parameter space
subjected to the BBN constraints and the WMAP data, we find that in the
neutralino NLSP case, the low tan-beta (< 40) region as well as the region
accessible at CERN Large Hadron Colldier (LHC) will be severely restrained.
