摘要: 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.