Jing-Zhi Zhou, Zhi-Chao Li, Di Wu

In contrast to the large-scale primordial power spectrum $\mathcal{P}_{\zeta}(k)$ and primordial non-Gaussianity $f_{\mathrm{NL}}$, which are strictly constrained, the small-scale $\mathcal{P}_{\zeta}(k)$ and $f_{\mathrm{NL}}$ remain less restricted. Considering local-type primordial non-Gaussianity, we study the PBH and SIGW caused by large-amplitude small-scale primordial power spectrum. By analyzing current observational data from PTA, CMB, BAO, and abundance of PBH, and combining them with the SNR analysis of LISA, we rigorously constrain the parameter space of $\mathcal{P}_{\zeta}(k)$ and $f_{\mathrm{NL}}$. Furthermore, we examine the effects of different shapes of the primordial power spectrum on these constraints and comprehensively calculate the Bayes factors for various models. Our results indicate that SIGW generated by a monochromatic primordial power spectrum are more likely to dominate current PTA observations, with the corresponding constraint on the primordial non-Gaussian parameter being $-10.0<f_{\mathrm{NL}}<1.2$.