Constraints on primordial curvature spectrum from primordial black holes and scalar-induced gravitational waves

The observational data of primordial black holes and scalar-induced gravitational waves can constrain the primordial curvature perturbation at small scales. We parameterize the primordial curvature perturbation by a broken power law form and find that it is consistent with many inflation models that can produce primordial black holes, such as nonminimal derivative coupling inflation, scalar–tensor inflation, Gauss–Bonnet inflation, and K/G inflation. The constraints from primordial black holes on the primordial curvature power spectrum with the broken power law form are obtained, where the fraction of primordial black holes in dark matter is calculated by the peak theory. Both the real-space top-hat and the Gaussian window functions are considered. The constraints on the amplitude of primordial curvature perturbation with Gaussian window function are around three times larger than those with real-space top-hat window function. The constraints on the primordial curvature perturbation from the NANOGrav 12.5 years data sets are displayed, where the NANOGrav signals are assumed as the scalar-induced gravitational waves, and only the first five frequency bins are used.