Nucleosynthesis Constraints on a Massive Gravitino in Neutralino Dark
  Matter Scenarios
  The decays of massive gravitinos into neutralino dark matter particles and
Standard Model secondaries during or after Big-Bang nucleosynthesis (BBN) may
alter the primordial light-element abundances. We present here details of a new
suite of codes for evaluating such effects, including a new treatment based on
PYTHIA of the evolution of showers induced by hadronic decays of massive,
unstable particles such as a gravitino. We also develop an analytical treatment
of non-thermal hadron propagation in the early universe, and use this to derive
analytical estimates for light-element production and in turn on decaying
particle lifetimes and abundances. We then consider specifically the case of an
unstable massive gravitino within the constrained minimal supersymmetric
extension of the Standard Model (CMSSM). We present upper limits on its
possible primordial abundance before decay for different possible gravitino
masses, with CMSSM parameters along strips where the lightest neutralino
provides all the astrophysical cold dark matter density. We do not find any
CMSSM solution to the cosmological Li7 problem for small m_{3/2}. Discounting
this, for m_{1/2} ~ 500 GeV and tan beta = 10 the other light-element
abundances impose an upper limit m_{3/2} n_{3/2}/n_\gamma < 3 \times 10^{-12}
GeV to < 2 \times 10^{-13} GeV for m_{3/2} = 250 GeV to 1 TeV, which is similar
in both the coannihilation and focus-point strips and somewhat weaker for tan
beta = 50, particularly for larger m_{1/2}. The constraints also weaken in
general for larger m_{3/2}, and for m_{3/2} > 3 TeV we find a narrow range of
m_{3/2} n_{3/2}/n_\gamma, at values which increase with m_{3/2}, where the Li7
abundance is marginally compatible with the other light-element abundances.
