Primordial black hole formation in the early universe: critical behaviour and self-similarity
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Following on after three previous papers discussing the formation of primordial black holes during the radiative era of the early universe, we present here a further investigation of the critical nature of the process involved, aimed at making contact with some of the basic underlying ideas from the literature on critical collapse. We focus on the intermediate state, which we have found appearing in cases with perturbations close to the critical limit, and examine the connection between this and the similarity solutions which play a fundamental role in the standard picture of critical collapse. We have derived a set of self-similar equations for the null-slicing form of the metric which we are using for our numerical calculations, and have then compared the results obtained by integrating these with the ones coming from our simulations for the collapse of cosmological perturbations within an expanding universe. We find that the similarity solution is asymptotically approached in a region which grows to cover both the contracting matter and part of the semi-void which forms outside it. Our main interest is in the situation relevant for primordial black hole formation in the radiative era of the early universe, where the relation between the pressure p and the energy density e can be reasonably approximated by an expression of the form p = we with w = 1/3. However, we have also looked at other values of w, both because these have been considered in the previous literature and also because they can be helpful for giving further insight into situations relevant for primordial black hole formation. As in our previous work, we have started our simulations with initial supra-horizon scale perturbations of a type which could have come from inflation.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/0a1d3d4b4007ec6faa1edf114d7e17b54eeb5ab2
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Citations in the corpus
- Primordial black holes and gravitational waves from parametric amplification of curvature perturbations (2019, background): “To get more accurate results, one needs to consider more details of PBH formation, such as the critical collapse [81–86], and the nonlinearity of the transfer function [57].”
- Primordial Black Holes as Dark Matter: Recent Developments (2020, background): “The gravitational collapse of the mass within the QCD Hubble horizon can be extremely violent [52] with particles being driven out as a relativistically expanding shock-wave and acquiring energies a thousand times their rest mass from the gravitational potential energy released by the collapse.”
- PRIMORDIAL BLACK HOLE FORMATION IN THE MATTER-DOMINATED PHASE OF THE UNIVERSE (2016, background): “01 0.6 (Musco & Miller 2013).”
- Primordial black holes as generators of cosmic structures (2018, background): “A simple analytic argument suggest δc ≈ γ but more precise arguments – both numerical (Musco & Miller 2013) and analytical (Harada, Yoo & Kohri 2013) – suggest a somewhat larger value.”
- Solar-mass primordial black holes explain NANOGrav hint of gravitational waves (2020, background): “where we have assumed that the primordial curvature perturbations have the Gaussian statistics, δc is the critical value of the coarse-grained density perturbations that produces a PBH [58–64], for which we take δc = 0.”
- Primordial black hole formation and abundance: contribution from the non-linear relation between the density and curvature perturbation (2019, result): “As has been shown in previous works [20, 21, 31, 33, 39] the mass spectrum of PBHs follows the critical collapse, characterized by a scaling law relation”