Insights into Gravitinos Abundance, Cosmic Strings and Stochastic Gravitational Wave Background

In this paper, we investigate D-term inflation within the framework of supergravity, employing the minimal K\"{a}hler potential. Following previous studies that revealed that this model can overcome the $\eta$-problem found in F-term models, we explore reheating dynamics and gravitino production, emphasizing the interplay between reheating temperature, spectral index, and gravitino abundance. Our analysis indicates that gravitino production is sensitive to the equation of state during reheating, affecting the reheating temperature and subsequent dark matter relic density. Furthermore, we analyze gravitational waves generated by cosmic strings, providing critical constraints on early Universe dynamics and cosmic string properties, the energy scales of both inflation and string formation influence the stochastic gravitational wave background (SGWB) generated by these cosmic strings.