Results for the monochromatic curvature perturbations described by Eq. (24). Left panel: recovered slopes γ of a simple power-law model as a function of characteristic scale k^* of the injected GWB generated by the monochromatic curvature perturbations. The horizontal lines show the theoretical value of γ from a population of circular, GW-driven SMBHBs (grey) and the one obtained in Paper III (orange). Right panel: 1σ and 2σ contours of the posterior distributions on the amplitude A_ζ and characteristic scale of fluctuations k^* for DR2new (orange colour). The posterior distribution is overlaid with the current constraints on the primordial power spectrum using Planck data (CMB). The grey colour depicts the 2-σ-confidence intervals. The purple shaded area represents the bounds from spectral distortions (Chluba et al. 2012). For comparison in green we place the prediction of the primordial spectrum of scalar perturbations in the two-field model of inflation described in Braglia et al. (2020) for a range of the model parameters. All three models result in PBH mass functions peaked at ∼35 M_⊙ with the brightest line corresponding to the dark matter fraction of PBHs of ∼0.01.