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Register a new userIdentifying the most crucial parameters of the initial curvature profile for primordial black hole formation
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Primordial black holes (PBHs) are an important tool in cosmology to probe the primordial spectrum of small-scale curvature perturbations that reenter the cosmological horizon during radiation domination epoch. We numerically solve the evolution of spherically symmetric highly perturbed configurations to clarify the criteria of PBHs formation using an extremely wide class of curvature profiles characterized by five parameters, (in contrast to only two parameters used in all previous papers) which specify the curvature profiles not only at the central region but also at the outer boundary of configurations. It is shown that formation or non-formation of PBHs is determined entirely by only two master parameters one of which can be presented as an integral of curvature over initial configurations and the other is presented in terms of the position of the boundary and the edge of the core.
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For an arbitrary strong, spherically symmetric super-horizon curvature perturbation, we present analytical solutions of the Einstein equations in terms of asymptotic expansion over the ratio of the Hubble radius to the length-scale of the curvature perturbation under consideration. To obtain this solution we develop a recursive method of quasi-linearization which reduces the problem to a system of coupled ordinary differential equations for the $N$-th order terms in the asymptotic expansion with sources consisting of a non-linear combination of the lower order terms. We use this solution for setting initial conditions for subsequent numerical computations. For an arbitrary precision requirement predetermined by the intended accuracy and stability of the computer code, our analytical solution yields optimal truncated asymptotic expansion which can be used to find the upper limit on the moment of time when the initial conditions expressed in terms of such truncated expansion should be set. Examples of how these truncated (up to eighth order) solutions provide initial conditions with given accuracy for different radial profiles of curvature perturbations are presented.
We perform (3+1)-dimensional simulations of primordial black hole (PBH) formation starting from the spheroidal super-horizon perturbations. We investigate how the ellipticity (prolateness or oblateness) affects the threshold of PBH formation in terms of the peak amplitude of curvature perturbation. We find that, in the case of the radiation-dominated universe, the effect of ellipticity on the threshold is negligibly small for large amplitude of perturbations expected for PBH formation.
Primordial black holes (PBHs) are an important tool in cosmology to probe the primordial spectrum of small-scale curvature perturbations that reenter the cosmological horizon during radiation domination epoch. We numerically solve the evolution of spherically symmetric highly perturbed configurations to clarify the criteria of PBHs formation using a wide class of curvature profiles characterized by five parameters. It is shown that formation or non-formation of PBHs is determined essentialy by only two master parameters.
In this paper we derive the probability of the radial profiles of spherically symmetric inhomogeneities in order to provide an improved estimation of the number density of primordial black holes (PBHs). We demonstrate that the probability of PBH formation depends sensitively on the radial profile of the initial configuration. We do this by characterising this profile with two parameters chosen heuristically: the amplitude of the inhomogeneity and the second radial derivative, both evaluated at the centre of the configuration. We calculate the joint probability of initial cosmological inhomogeneities as a function of these two parameters and then find a correspondence between these parameters and those used in numerical computations of PBH formation. Finally, we extend our heuristic study to evaluate the probability of PBH formation taking into account for the first time the radial profile of curvature inhomogeneities.
In the context of transient constant-roll inflation near a local maximum, we derive the non-perturbative field redefinition that relates a Gaussian random field with the true non-Gaussian curvature perturbation. Our analysis shows the emergence of a new critical amplitude $zeta_*$, corresponding to perturbations that prevent the inflaton from overshooting the local maximum, thus becoming trapped in the false minimum of the potential. For potentials with a mild curvature at the local maximum (and thus small non-Gaussianity), we recover the known perturbative field redefinition. We apply these results to the formation of primordial black holes, and discuss the cases for which $zeta_*$ is smaller or of the same order than the critical value for collapse of spherically symmetric overdensities. In the latter case, we present a simple potential for which the power spectrum needs an amplitude 10 times smaller that in the Gaussian case for producing a sizeable amount of primordial black holes.
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