Testing primordial black hole and measuring the Hubble constant with multiband gravitational-wave observations

TL;DR

This paper proposes a method to detect primordial black holes and measure the Hubble constant using multiband gravitational-wave observations of two stochastic backgrounds linked to primordial curvature perturbations.

Contribution

It establishes a relation between the peak frequencies of two gravitational-wave backgrounds, enabling primordial black hole detection and Hubble constant measurement.

Findings

Derived a relation for the peak frequencies of gravitational-wave backgrounds.

Proposed a method for measuring Hubble constant with multiband GW observations.

Provided a criterion for the existence of primordial black holes.

Abstract

There exist two kinds of stochastic gravitational-wave backgrounds associated with the primordial curvature perturbations. One is called induced gravitational wave due to the nonlinear coupling of curvature perturbations to tensor perturbations, while the other is produced by coalescences of binary primordial black holes formed when the large amplitude curvature perturbations reenter the horizon in the radiation dominant era. In this paper we find a quite useful relation for the peak frequencies of these two stochastic gravitational-wave backgrounds. This relation can not only offer a smoking-gun criterion for the existence of primordial black holes, but also provide a method for measuring the Hubble constant $H_0$ by multiband observations of the stochastic gravitational-wave backgrounds.