  In this work, we explore the "degenerate gravitino" scenario where the mass
difference between the gravitino and the lightest MSSM particle is much smaller
than the gravitino mass itself. In this case, the energy released in the decay
of the next to lightest sypersymmetric particle (NLSP) is reduced. Consequently
the cosmological and astrophysical constraints on the gravitino abundance, and
hence on the reheating temperature, become softer than in the usual case. On
the other hand, such small mass splittings generically imply a much longer
lifetime for the NLSP. We find that, in the constrained MSSM (CMSSM), for
neutralino LSP or NLSP, reheating temperatures compatible with thermal
leptogenesis are reached for small splittings of order 10^{-2} GeV. While for
stau NLSP, temperatures of 4x10^9 GeV can be obtained even for splittings of
order of tens of GeVs. This "degenerate gravitino" scenario offers a possible
way out to the gravitino problem for thermal leptogenesis in supersymmetric
theories.
