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 present several sets of results obtained using these codes, including general constraints on the possible lifetime and abundance of an unstable particle decaying into neutralino dark matter under various hypotheses for its decay mechanism. 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, which confirm our numerical results and illuminate the underlying physics. 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 ⁷Li problem for small m _3/2. Discounting this, for m _1/2 ∼ 500 GeV and tanβ = 10 the other light-element abundances impose an upper limit m _3/2n _3/2/n _γ3 × 10 ^-12GeV to 2 × 10 ^-13GeV for m _3/2 = 250 GeV to 1 TeV, which is similar in both the coannihilation and focus-point strips and somewhat weaker for tanβ = 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 _3/2n _3/2/n _γ, at values which increase with m _3/2, where the ⁷Li abundance is marginally compatible with the other light-element abundances.