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Register a new userReconstruction of potentials of the hybrid inflation in the light of primordial black hole formation
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Added by
Rathul Nath Raveendran
Publication date
2021
fields
Physics
and research's language is
English
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The large enhancement of the primordial power spectrum of the curvature perturbation can seed the formation of primordial black hole, that can play as a dark matter component in the Universe. In multi-filed inflation models, the curved trajectory of the scalar fields in the field space can generate a peak in the power spectrum on small scales due to the existence of the isocurvature perturbation. Here we show that a potential can be reconstructed from a given power spectrum, which is made of a scale-invariant one on large scales and the other function with a peak on small scales. In multi-field inflation models the reconstructed potential may not be unique and we can find different potentials from a given power spectrum.
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Within the framework of Galileon inflation with quartic and natural potentials, we investigate generation of the primordial black holes (PBHs) and induced gravitational waves (GWs). In this setup, we consider a Galileon 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 $ksim10^{12}~rm Mpc^{-1}$, $10^{8}~rm Mpc^{-1}$, and $10^{5}~rm Mpc^{-1}$, 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 $Omega_{rm GW}sim (f/f_c)^n$, where the power index equals $n=3-2/ln(f_c/f)$ in the infrared limit $fll f_{c}$.
We study the parameter space of the effective (with two scalars) models of cosmological inflation and primordial black hole (PBH) formation in the modified $(R+R^2)$ supergravity. Our models describe double inflation, whose first stage is driven by Starobinskys scalaron coming from the $R^2$ gravity, and whose second stage is driven by another scalar belonging to the supergravity multiplet. The ultra-slow-roll regime between the two stages leads a large peak (enhancement) in the power spectrum of scalar perturbations, which results in efficient PBH formation. Both inflation and PBH formation are generic in our models, while those PBH can account for a significant part or the whole of dark matter. Some of the earlier proposed models in the same class are in tension (over $3sigma$) with the observed value of the scalar tilt $n_s$, so that we study more general models with more parameters, and investigate the dependence of the cosmological tilts $(n_s,r)$ and the scalar power spectrum enhancement upon the parameters. The PBH masses and their density fraction (as part of dark matter) are also calculated. A good agreement (between $2sigma$ and $3sigma$) with the observed value of $n_s$ requires fine tuning of the parameters, and it is only realized in the so-called $delta$-models. Our models offer the (super)gravitational origin of inflation, PBH and dark matter together, and may be confirmed or falsified by future precision measurements of the cosmic microwave background radiation and PBH-induced gravitational waves.
We re-analyse current single-field inflationary models related to primordial black holes formation. We do so by taking into account recent developments on the estimations of their abundances and the influence of non-gaussianities. We show that, for all of them, the gaussian approximation, which is typically used to estimate the primordial black holes abundances, fails. However, in the case in which the inflaton potential has an inflection point, the contribution of non-gaussianities is only perturbative. Finally, we infer that only models featuring an inflection point in the inflationary potential, might predict, with a very good approximation, the desired abundances by the sole use of the gaussian statistics.
We investigate primordial black hole formation in the matter-dominated phase of the Universe, where nonspherical effects in gravitational collapse play a crucial role. This is in contrast to the black hole formation in a radiation-dominated era. We apply the Zeldovich approximation, Thornes hoop conjecture, and Doroshkevichs probability distribution and subsequently derive the production probability $beta_{0}$ of primordial black holes. The numerical result obtained is applicable even if the density fluctuation $sigma$ at horizon entry is of the order of unity. For $sigmall 1$, we find a semi-analytic formula $beta_{0}simeq 0.05556 sigma^{5}$, which is comparable with the Khlopov-Polnarev formula. We find that the production probability in the matter-dominated era is much larger than that in the radiation-dominated era for $sigmalesssim 0.05$, while they are comparable with each other for $sigmagtrsim 0.05$. We also discuss how $sigma$ can be written in terms of primordial curvature perturbations.
The properties of primordial curvature perturbations on small scales are still unknown while those on large scales have been well probed by the observations of the cosmic microwave background anisotropies and the large scale structure. In this paper, we propose the reconstruction method of primordial curvature perturbations on small scales through the merger rate of binary primordial black holes, which could form from large primordial curvature perturbation on small scales.
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