Primordial black holes and secondary gravitational waves from natural inflation

Qing Gao,Yungui Gong,Zhu Yi

doi:10.1016/j.nuclphysb.2021.115480

Abstract

The production of primordial black hole (PBH) dark matter (DM) and the generation of scalar induced secondary gravitational waves by using the enhancement mechanism with a peak function in the non-canonical kinetic term in natural inflation is discussed. We show explicitly that the power spectrum for the primordial curvature perturbation can be enhanced at 1012Mpc−1, 108Mpc−1 and 105Mpc−1 by adjusting the model parameters. With the enhanced primordial curvature perturbations, we show the production of PBH DM with peak masses around 10−13M⊙, the Earth's mass and the stellar mass, and the generation of scalar induced gravitational waves (SIGWs) with peak frequencies around mHz, 10−6Hz and nHz, respectively. The PBHs with the mass scale 10−13M⊙ can make up almost all the DM and the associated SIGWs is testable by spaced-based gravitational wave observatory.

Highlights

If the density contrast of overdense regions at the horizon reentry exceeds the threshold value during radiation domination, the overdense regions gravitationally collapse to form primordial black holes (PBHs) [1, 2]
The stellar mass PBHs may explain BHs observed by Laser Interferometer Gravitational Wave Observatory (LIGO)/Virgo collaboration
The amplitude of primordial curvature perturbations at small scales can become large by the enhancement mechanism with a peak function in the non-canonical kinetic term [59,60,61]

Summary

INTRODUCTION

If the density contrast of overdense regions at the horizon reentry exceeds the threshold value during radiation domination, the overdense regions gravitationally collapse to form primordial black holes (PBHs) [1, 2]. To the second order of perturbations, the first order perturbations are the sources of the second order tensor perturbation, so associated with the formation of PBHs the large curvature perturbations at small scales induce secondary GWs after the horizon reentry during the radiation dominated epoch [62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86] These scalar induced GWs (SIGWs) consist of the stochastic background and they can detected by Pulsar Timing Arrays (PTA) [87,88,89,90,91] and the space based GW observatories like Laser Interferometer Space Antenna (LISA) [92, 93], Taiji [94] and TianQin [95].

NATURAL INFLATION

The enhancement of the scalar power spectrum

Primordial Black hole dark matter

Scalar Induced secondary Gravitational Waves

CONCLUSION