Cosmological constraints on small-scale primordial non-Gaussianity

In contrast to the large-scale primordial power spectrum ${\mathcal{P}}_{\ensuremath{\zeta}}(k)$ and primordial non-Gaussianity ${f}_{\mathrm{NL}}$, which are strictly constrained, the small-scale ${\mathcal{P}}_{\ensuremath{\zeta}}(k)$ and ${f}_{\mathrm{NL}}$ are not as limited. Considering local-type primordial non-Gaussianity, we study the primordial black holes (PBHs) and scalar induced gravitational waves (SIGWs) caused by large-amplitude small-scale primordial power spectrum. By analyzing current observational data from pulsar timing array (PTA), cosmic microwave background (CMB), baryon acoustic oscillations (BAO), and abundance of PBHs, and combining it with the signal-to-noise ratio (SNR) analysis of Laser Interferometer Space Antenna (LISA), we rigorously constrain the parameter space of ${\mathcal{P}}_{\ensuremath{\zeta}}(k)$ and ${f}_{\mathrm{NL}}$. Furthermore, we examine the effects of different shapes of the primordial power spectrum on these constraints and comprehensively calculate the Bayesian factors for various models. Our results indicate that SIGWs 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 $\ensuremath{-}10.0<{f}_{\mathrm{NL}}<1.2$.