Bayesian Implications for the Primordial Black Holes from NANOGrav's Pulsar-Timing Data Using the Scalar-Induced Gravitational Waves

Understand

Assuming that the common-spectrum process in the NANOGrav 12.5-year dataset has an origin of scalar-induced gravitational waves, we study the enhancement of primordial curvature perturbations and the mass function of primordial black holes, by performing the Bayesian parameter inference for the first time.

• We obtain lower limits on the spectral amplitude, i.e., $\mathcal{A}\gtrsim10^{-2}$ at 95\% confidence level, when assuming the power spectrum of primordial curvature perturbations to follow a log-normal distribution function with width $\sigma$.
• In the case of $\sigma\rightarrow0$, we find that the primordial black holes with $2\times10^{-4}-10^{-2}$ solar mass are allowed to compose at least a fraction $10^{-6}$ of dark matter.
• Such a mass range is shifted to more massive regimes for larger values of $\sigma$, e.g., to a regime of $4\times10^{-3}-0.2$ solar mass in the case of $\sigma=1$.