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

TL;DR

This paper uses observational data of primordial black holes and scalar-induced gravitational waves to constrain the primordial curvature spectrum at small scales, exploring various inflation models and analyzing different window functions.

Contribution

It introduces a broken power law parameterization of the primordial curvature perturbation and derives constraints from PBH and GW data, considering multiple inflation scenarios and window functions.

Findings

Constraints on primordial curvature perturbation amplitude vary with window function.

NANOGrav data constrains the curvature spectrum assuming scalar-induced gravitational waves.

The broken power law form is consistent with several inflation models.

Abstract

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 Gauss window functions are considered. The constraints on the amplitude of primordial curvature perturbation with Gauss 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 12.5yrs 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.