Big-bang nucleosynthesis with unstable gravitino and upper bound on the reheating temperature

We study the effects of unstable gravitino on big-bang nucleosynthesis. If the gravitino mass is smaller than $\sim 10\mathrm{TeV}$, primordial gravitinos produced after inflation are likely to decay after big-bang nucleosynthesis starts, and light-element abundances may be significantly affected by hadro and photodissociation processes as well as by $p\leftrightarrow n$ conversion process. We calculate the light-element abundances and derive upper bounds on the reheating temperature after inflation. In our analysis, we calculate decay parameters of the gravitino (i.e. lifetime and branching ratios) in detail. In addition, we perform a systematic study of the hadron spectrum produced by the gravitino decay, taking account of all the hadrons produced by the decay products of the gravitino (including the daughter superparticles). We discuss model dependence of the upper bound on the reheating temperature.