Primordial black holes and induced gravitational waves in $k$-inflation

Milad Solbi; Kayoomars Karami

doi:10.1088/1475-7516/2021/08/056

paper

Primordial black holes and induced gravitational waves in $k$ -inflation

arXiv:2102.05651 · doi:10.1088/1475-7516/2021/08/056

Abstract

Recent observational constraints indicate that primordial black holes (PBHs) with the mass scale $\sim 1 0^{- 12} M_{⊙}$ can explain most of dark matter in the Universe. To produce this kind of PBHs, we need an enhance in the primordial scalar curvature perturbations to the order of $O (1 0^{- 2})$ at the scale $k \sim 1 0^{12} Mp c^{- 1}$ . Here, we investigate the production of PBHs and induced gravitational waves (GWs) in the framework of \textbf{ $k$ -inflation}. We solve numerically the Mukhanov-Sasaki equation to obtain the primordial scalar power spectrum. In addition, we estimate the PBHs abundance $f_{PBH}^{peak}$ as well as the energy density parameter $Ω_{GW, 0}$ of induced GWs. Interestingly enough is that for a special set of model parameters, we estimate the mass scale and the abundance of PBHs as $\sim O (1 0^{- 13}) M_{⊙}$ and $f_{PBH}^{peak} = 0.96$ , respectively. This confirms that the mechanism of PBHs production in our inflationary model can justify most of dark matter. Furthermore, we evaluate the GWs energy density parameter and conclude that it behaves like a power-law function $Ω_{GW} \sim (f / f_{c})^{n}$ where in the infrared limit $f ≪ f_{c}$ , the power index reads $n = 3 - 2/ ln (f_{c} / f)$ .

17 pages, 4 figures, 2 tables

Primordial black holes and induced gravitational waves in $k$ -inflation

Abstract

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Cited by in corpus (36)

Primordial black holes and induced gravitational waves in k-inflation

Abstract

References in corpus (29)

Cited by in corpus (36)

Primordial black holes and induced gravitational waves in $k$ -inflation