Abstract
Within the framework of inflationary model with field-dependent kinetic term for quartic and natural potentials, we investigate generation of the primordial black holes (PBHs) and induced gravitational waves (GWs). In this setup, we consider a kinetic function as G(phi )=g_I(phi )big (1+g_{II}(phi )big ) and show that in the presence of first term g_I(phi ) both quartic and natural potentials, in contrast to the standard model of inflation, can be consistent, with the 68% CL of Planck observations. Besides, the second term g_{II}(phi ) can cause a significant enhancement in the primordial curvature perturbations at the small scales which results the PBHs formation. For the both potentials, we obtain an enhancement in the scalar power spectrum at the scales ksim 10^{12}~{mathrm{Mpc}}^{-1}, 10^{8}~{mathrm{Mpc}}^{-1}, and 10^{5}~{mathrm{Mpc}}^{-1}, which causes PBHs production in mass scales around 10^{-13}M_{odot }, 10^{-5}M_{odot }, and 10 M_{odot }, respectively. Observational constraints confirm that PBHs with a mass scale of 10^{-13}M_{odot } can constitute the total of dark matter in the universe. Furthermore, we estimate the energy density parameter of induced GWs which can be examined by the observation. Also we conclude that it can be parametrized as a power-law function Omega _{mathrm{GW}}sim (f/f_c)^n, where the power index equals n=3-2/ln (f_c/f) in the infrared limit fll f_{c}.
Highlights
Of around 12 − 213 Gpc−3year−1 and a mass scale of about 10M can make up roughly O(1)% of the total dark matter (DM)
Observational constraints confirm that primordial black holes (PBHs) with a mass scale of 10−13 M can constitute the total of dark matter in the universe
The PBHs formation is followed by the generation of the induced gravitational waves (GWs), when the primordial curvature perturbations enhance significantly
Summary
The ultra-short timescale microlensing events were detected in the OGLE data and they prepare an allowed region for PBHs formation. The production of PBHs by the collapse of the overdense regions demands an amplitude of the primordial curvature perturbation As in order of ∼ O(10−2) at small scales [28]. The PBHs formation is followed by the generation of the induced gravitational waves (GWs), when the primordial curvature perturbations enhance significantly [59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74]. In the Galileon inflation models, the CMB anomalies and the decaying of the CMB power spectrum at the largest scales can be explained when inflaton undergoes the ultra slow-roll phase [83].
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