Big-Bang Nucleosynthesis and Gravitino

TL;DR

This work analyzes big-bang nucleosynthesis (BBN) constraints on both unstable and stable gravitinos in supersymmetric models. It advances prior studies by incorporating the longitudinal component of gravitino production, updating light-element observational constraints, and solving the Boltzmann equations for bound-state formation (notably for stau NLSPs), thereby tightening bounds on the reheating temperature $T_R$ and on NLSP properties. For unstable gravitinos, the longitudinal mode yields stricter upper limits on $T_R$, especially at lighter gravitino masses, while very heavy gravitinos allow higher $T_R$ and relax constraints. When the gravitino is the LSP, BBN bounds depend strongly on the NLSP identity (neutralino, stau, or sneutrino); in particular, Bino- and stau-NLSP scenarios face stringent limits (often excluding $m_{3/2}\gtrsim$ a few GeV for sub-TeV NLSPs) due to hadro- and catalyzed Li-6 production, whereas sneutrino-NLSP effects are comparatively weak. The results imply that gravitino dark matter is unlikely to be produced predominantly from MSSM-LSP decays and instead requires alternative sources (e.g., thermal scattering at reheating or scalar condensate decays), with important consequences for early-universe cosmology and leptogenesis.

Abstract

We derive big-bang nucleosynthesis (BBN) constraints on both unstable and stable gravitino taking account of recent progresses in theoretical study of the BBN processes as well as observations of primordial light-element abundances. In the case of unstable gravitino, we set the upper limit on the reheating temperature assuming that the primordial gravitinos are mainly produced by the scattering processes of thermal particles. For stable gravitino, we consider Bino, stau and sneutrino as the next-to-the-lightest supersymmetric particle and obtain constraints on their properties. Compared with the previous works, we improved the following points: (i) we use the most recent observational data, (ii) for gravitino production, we include contribution of the longitudinal component, and (iii) for the case with unstable long-lived stau, we estimate the bound-state effect of stau accurately by solving the Boltzmann equation.

Figures (16)

• Figure 1: Lifetime of gravitino for Cases 1 $-$ 4. The horizontal axis is the gravitino mass.
• Figure 2: BBN constraints for the Case 1 at 95 % C.L. Each solid line shows upper bound on the reheating temperature from ${\rm D}$, ${\rm ^3He}$, ${\rm ^4He}$, ${\rm ^6Li}$, or ${\rm ^7Li}$. The dotted line is the upper bound on the reheating temperature from the overclosure of the universe.
• Figure 3: BBN constraints for the Case 2.
• Figure 4: BBN constraints for the Case 3.
• Figure 5: BBN constraints for the Case 4.