Primordial black holes and secondary gravitational waves from k/G inflation
Abstract
The possibility that in the mass range around $10^{-12}\ M_\odot$ most of dark matter constitutes of primordial black holes (PBHs) is a very interesting topic. To produce PBHs with this mass, the primordial scalar power spectrum needs to be enhanced to the order of 0.01 at the scale $k\sim 10^{12}\ \text{Mpc}^{-1}$. The enhanced power spectrum also produces large secondary gravitational waves at the mHz band. A phenomenological delta function power spectrum is usually used to discuss the production of PBHs and secondary gravitational waves. Based on G and k inflations, we propose a new mechanism to enhance the power spectrum at small scales by introducing a non-canonical kinetic term $[1-2G(\phi)]X$ with the function $G(\phi)$ having a peak. Away from the peak, $G(\phi)$ is negligible and we recover the usual slow-roll inflation which is constrained by the cosmic microwave background anisotrpy observations. Around the peak, the slow-roll inflation transiently turns to ultra slow-roll inflation. The enhancement of the power spectrum can be obtained with generic potentials, and there is no need to fine tune the parameters in $G(\phi)$. The energy spectrum $\Omega_{GW}(f)$ of secondary gravitational waves have the characteristic power law behaviour $\Omega_{GW}(f)\sim f^{n}$ and is testable by pulsar timing array and space based gravitational wave detectors.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2020
- DOI:
- 10.48550/arXiv.2001.05909
- arXiv:
- arXiv:2001.05909
- Bibcode:
- 2020arXiv200105909L
- Keywords:
-
- General Relativity and Quantum Cosmology;
- Astrophysics - Cosmology and Nongalactic Astrophysics
- E-Print:
- Phys. Rev. D 101, 103515 (2020)