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Register a new userPrimordial black holes from metric preheating: mass fraction in the excursion-set approach
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We calculate the mass distribution of Primordial Black Holes (PBHs) produced during metric preheating. After inflation, the oscillations of the inflaton at the bottom of its potential source a parametric resonant instability for small-scale scalar perturbations, that may collapse into black holes. After reviewing in a pedagogical way different techniques that have been developed in the literature to compute mass distributions of PBHs, we focus on the excursion-set approach. We derive a Volterra integral equation that is free of a singularity sometimes encountered, and apply it to the case of metric preheating. We find that if the energy density at which the instability stops, $rho_Gamma$, is sufficiently smaller than the one at which inflation ends, $rho_mathrm{end}$, namely if $rho_Gamma^{1/4}/rho_mathrm{end}^{1/4}< 10^{-5}(rho_mathrm{end}^{1/4}/10^{16}mathrm{GeV})^{3/2}$, then PBHs dominate the universe content at the end of the oscillatory phase. This confirms the previous analysis of arXiv:1907.04236 . By properly accounting for the cloud-in-cloud mechanism, we find that the mass distribution is more suppressed at low masses than previously thought, and peaks several orders of magnitude above the Hubble mass at the end of inflation. The peak mass ranges from $10$ g to stellar masses, giving rise to different possible cosmological effects that we discuss.
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Evidences for the primordial black holes (PBH) presence in the early Universe renew permanently. New limits on their mass spectrum challenge existing models of PBH formation. One of the known model is based on the closed walls collapse after the inflationary epoch. Its intrinsic feature is multiple production of small mass PBH which might contradict observations in the nearest future. We show that the mechanism of walls collapse can be applied to produce substantially different PBH mass spectra if one takes into account the classical motion of scalar fields together with their quantum fluctuations at the inflationary stage.
Primordial black holes (PBHs) are a viable candidate for dark matter if the PBH masses are in the currently unconstrained sublunar mass range. We revisit the possibility that PBHs were produced by nucleation of false vacuum bubbles during inflation. We show that this scenario can produce a population of PBHs that simultaneously accounts for all dark matter, explains the candidate event in Subaru Hyper Suprime-Cam (HSC) data, and contains both heavy black holes as observed by LIGO and very heavy seeds of supermassive black holes. We demonstrate with numerical studies that future observations of HSC, as well as other optical surveys, such as LSST, will be able to provide a definitive test for this generic PBH formation mechanism if it is the dominant source of dark matter.
In excursion set theory the computation of the halo mass function is mapped into a first-passage time process in the presence of a barrier, which in the spherical collapse model is a constant and in the ellipsoidal collapse model is a fixed function of the variance of the smoothed density field. However, N-body simulations show that dark matter halos grow through a mixture of smooth accretion, violent encounters and fragmentations, and modeling halo collapse as spherical, or even as ellipsoidal, is a significant oversimplification. We propose that some of the physical complications inherent to a realistic description of halo formation can be included in the excursion set theory framework, at least at an effective level, by taking into account that the critical value for collapse is not a fixed constant $delta_c$, as in the spherical collapse model, nor a fixed function of the variance $sigma$ of the smoothed density field, as in the ellipsoidal collapse model, but rather is itself a stochastic variable, whose scatter reflects a number of complicated aspects of the underlying dynamics. Solving the first-passage time problem in the presence of a diffusing barrier we find that the exponential factor in the Press-Schechter mass function changes from $exp{-delta_c^2/2sigma^2}$ to $exp{-adelta_c^2/2sigma^2}$, where $a=1/(1+D_B)$ and $D_B$ is the diffusion coefficient of the barrier. The numerical value of $D_B$, and therefore the corresponding value of $a$, depends among other things on the algorithm used for identifying halos. We discuss the physical origin of the stochasticity of the barrier and we compare with the mass function found in N-body simulations, for the same halo definition.[Abridged]
We compute the effect of primordial non-Gaussianity on the halo mass function, using excursion set theory. In the presence of non-Gaussianity the stochastic evolution of the smoothed density field, as a function of the smoothing scale, is non-markovian and beside local terms that generalize Press-Schechter (PS) theory, there are also memory terms, whose effect on the mass function can be computed using the formalism developed in the first paper of this series. We find that, when computing the effect of the three-point correlator on the mass function, a PS-like approach which consists in neglecting the cloud-in-cloud problem and in multiplying the final result by a fudge factor close to 2, is in principle not justified. When computed correctly in the framework of excursion set theory, in fact, the local contribution vanishes (for all odd-point correlators the contribution of the image gaussian cancels the Press-Schechter contribution rather than adding up), and the result comes entirely from non-trivial memory terms which are absent in PS theory. However it turns out that, in the limit of large halo masses, where the effect of non-Gaussianity is more relevant, these memory terms give a contribution which is the the same as that computed naively with PS theory, plus subleading terms depending on derivatives of the three-point correlator. We finally combine these results with the diffusive barrier model developed in the second paper of this series, and we find that the resulting mass function reproduces recent N-body simulations with non-Gaussian initial conditions, without the introduction of any ad hoc parameter.
An observable stochastic background of gravitational waves is generated whenever primordial black holes are created in the early universe thanks to a small-scale enhancement of the curvature perturbation. We calculate the anisotropies and non-Gaussianity of such stochastic gravitational waves background which receive two contributions, the first at formation time and the second due to propagation effects. The former contribution can be generated if the distribution of the curvature perturbation is characterized by a local and scale-invariant shape of non-Gaussianity. Under such an assumption, we conclude that a sizeable magnitude of anisotropy and non-Gaussianity in the gravitational waves would suggest that primordial black holes may not comply the totality of the dark matter.
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