Primordial Black Holes as a Novel Probe of Primordial Gravitational Waves

Abstract

We propose a novel method to probe primordial gravitational waves by means of primordial black holes (PBHs). When the amplitude of primordial tensor perturbations on comoving scales much smaller than those relevant to Cosmic Microwave Background is very large, it induces scalar perturbations due to second-order effects substantially. If the amplitude of resultant scalar perturbations becomes too large, then PBHs are overproduced to a level that is inconsistent with a variety of existing observations constraining their abundance. This leads to upper bounds on the amplitude of initial tensor perturbations on super-horizon scales. These upper bounds from PBHs are compared with other existing bounds. PACS numbers:Introduction.-Stochastic gravitational wave background (SGWB) on a wide range of scales is thought to have been generated in the early universe. SGWB on the largest observable scales have been investigated by Planck [1] and BICEP2 [2]. SGWB on smaller scales can be constrained by inferring the value of N eff , the effective number of extra degrees of freedom of relativistic species, at Big Bang Nucleosynthesis (BBN) through the current abundance of light elements [3], or at photon decoupling through the anisotropy of Cosmic Microwave Background (CMB) [4,5]. More recently SGWB on small scales has been constrained by CMB spectral distortions as well [6,7]. SGWB can also be directly constrained by gravitational wave detectors (see e.g. [8]). BBN and CMB have played a major role in constraining SGWB since they are applicable on a wide range of scales, noting ground-based laser interferometers tend to target gravitational waves (GWs) on a relatively limited frequency range with high sensitivity. However, it would be worthwhile to note that upper bounds obtained through N eff need an assumption about the number of relativistic species in the early universe, as is discussed later. In addition, in obtaining BBN or CMB bounds we implicitly assume that any physical mechanisms, both known and unknown, increase N eff , making N eff larger than the standard value N eff = 3.046 [9]. However, in principle it is possible to decrease N eff (see e.g. [10][11][12]). Therefore, it would be desirable to have another independent cosmological method to probe SGWB on a wide range of scales, which does not much depend on the assumptions mentioned above.