Big-Bang Nucleosynthesis and Gravitino

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.

• The paper refines Big-Bang Nucleosynthesis constraints by incorporating updated light-element observations and longitudinal gravitino production effects.
• It establishes stringent upper limits on reheating temperatures for unstable gravitinos, preventing disruptive photo- and hadro-dissociation processes.
• The study accurately assesses bound-state effects in long-lived stau scenarios by solving the Boltzmann equation, impacting primordial element abundances.

Big-Bang Nucleosynthesis and Gravitino: Constraints and Implications

This paper investigates the implications of gravitinos, both stable and unstable, on Big-Bang Nucleosynthesis (BBN) by incorporating recent advancements in theoretical understanding and observational data of light-element abundances. Gravitinos, as the superpartners of gravitons in supersymmetric models, play a potentially significant role in cosmology, particularly during the BBN epoch.

Main Contributions

The study makes substantial improvements over previous works by:

1. Utilizing the most updated observational constraints on the primordial abundances of light elements.
2. Including contributions from the longitudinal component in the production of gravitinos, providing a more stringent upper bound on the reheating temperature, especially for light gravitino masses.
3. Accurately estimating the bound-state effects in scenarios involving long-lived stau particles by solving the Boltzmann equation, thereby refining the constraints on these scenarios.

Key Findings

Unstable Gravitino Scenario

For unstable gravitinos, the research derives upper limits on the reheating temperature after inflation to prevent BBN disruption. This constraint is primarily due to energetic decay products causing photo- and hadro-dissociation processes and $p \leftrightarrow n$ conversion, which alter the abundances of light elements such as D, $^3$He, $^4$He, $^6$Li, and $^7$Li. Notably, the constraints vary with gravitino mass; severe constraints are placed when the gravitino mass is comparable to the LSP mass, addressing overproduction issues of $^3$He. When gravitino masses exceed 30 TeV, the reheating temperature constraints relax, allowing values up to $10^{10}$ GeV.

Stable Gravitino Scenario

When gravitino is stable and the LSP, the decay of the MSSM-NLSP into gravitino and standard-model particles can similarly affect BBN. The paper evaluates different MSSM-NLSP configurations, focusing on scenarios where the NLSP is either a Bino, stau, or sneutrino. Each scenario presents unique BBN constraints due to variations in decay processes and resultant particle spectrums:

• Bino-like Neutralino NLSP: Sizable hadronic interactions lead to significant constraints from both hadro-dissociation and photo-dissociation processes.
• Stau NLSP: The bound-state effects, especially the catalyzed $^6$Li production, pose tight constraints, although overall hadronic branching ratios are minimal.
• Sneutrino NLSP: Exhibits the weakest constraints due to predominant decay into weakly interacting particles.

Implications and Future Directions

This comprehensive analysis underscores the sensitivity of BBN constraints to particular supersymmetric model parameters and scenarios, with potential implications for models of reheating and dark matter production. These findings necessitate precision in model building to accommodate these stringent astrophysical constraints. As observational data on primordial element abundances and our understanding of supersymmetric models evolve, these constraints may guide future model specifications and inflationary scenarios.

The improvements in bound-state treatment and inclusion of new mechanisms provide a refined framework for assessing the cosmological viability of models involving gravitinos. Continued progress in this field may necessitate integrating more complex decay channels or considering the effects of non-standard cosmological evolution, enhancing our comprehension of the early universe's particle dynamics.