Primordial black holes and scalar-induced gravitational waves from the polynomial attractor model

Primordial black holes (PBHs) generated in the early Universe are considered as one of the candidates for dark matter. To produce PBHs with sufficient abundance, the primordial scalar power spectrum needs to be enhanced to the order of 0.01. Considering the third-order polynomial potential with polynomial attractors, we show that PBHs with a mass of about 10¹⁷ g can be produced while satisfying the constraints from the cosmic microwave background observations at the 2σ confidence level. The mass of PBHs produced in the polynomial attractors can be much bigger than that in the exponential α attractors. By adding a negative power-law term to the polynomials, abundant PBHs with different masses and the accompanying scalar-induced gravitational waves (SIGWs) with different peak frequencies are easily generated. The PBHs with masses around 10^-15--10^-12M_ can account for almost all dark matter. The SIGWs generated in the nanohertz band can explain the recent detection of stochastic gravitational-wave background by the pulsar timing array observations. The non-Gaussianities of the primordial curvature perturbations in the squeezed and equilateral limits are calculated numerically. We find that the non-Gaussianity correction enhances the PBH abundance which makes the production of PBHs much easier, but the effect of non-Gaussianity on the generation of SIGWs is negligible.