Double peaks of gravitational wave spectrum induced from inflection point inflation

We investigate the possibility of inducing the gravitational waves (GWs) with double peak energy spectrum from primordial scalar perturbations in inflationary models with three inflection points. Here the inflection points can be generated from a polynomial potential or generated from a Higgs-like $$\phi ^4$$ potential with the running of quartic coupling. In such models, the inflection point at large scales predicts the scalar spectral index and tensor-to-scalar ratio to be consistent with current CMB constraints, and the other two inflection points generate two large peaks in the scalar power spectrum at small scales, which can induce GWs with a double peak energy spectrum. We find that for some choices of the parameters the double peak spectrum can be detected by future GW detectors, and one of the peaks around $$f\simeq 10^{-9}{-}10^{-8}$$ Hz can also explain the recent NANOGrav signal. Moreover, the peaks of the power spectrum allow for the generation of primordial black holes, which accounts for a significant fraction of dark matter