Exploring the Implications of 2023 Pular Timing Array Datasets for Scalar-Induced Gravitational Waves and Primordial Black Holes

摘要: Significant evidence for a gravitational-wave background was reported by several pulsar-timing-array collaborations. By assuming that this signal is interpreted by the scalar-induced gravitational waves, we study physical implications of the observed signal for the nature of primordial curvature perturbations and primordial black holes. In particular, we explore the effects of primordial non-Gaussianity on the inferences of model parameters, and obtain the parameter region allowed by the observed signal, i.e., the primordial scalar spectral amplitude $A_S\sim10^{-2}-1$, the primordial non-Gaussian parameter $-10\lesssim f_{\mathrm{NL}} \lesssim 10$, and the mass of primordial black holes $m_{\mathrm{pbh}}\sim10^{-3}-0.1M_{\odot}$. We find that the non-Gaussianity suppressing the abundance of primordial black holes is preferred by the observed signal. We show that the anisotropies of scalar-induced gravitational waves are a powerful probe for measurements of the non-Gaussian parameter $f_{\mathrm{NL}}$, and conduct a complete analysis of the angular power spectrum in the nano-Hertz band. We expect that the Square Kilometre Array project has potentials to measure such anisotropies.