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Recently, Hutsi et al.[arXiv:2105.09328] critiqued our work that reconsidered the mathematical description of cosmological black holes. In this short comment, we highlight some of the conceptual issues with this criticism in relation to the interpretation of the quasi-local Misner-Sharp mass, and the fact that our description of cosmological black holes does not impose any assumptions about matter accretion.
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Recently, the Thakurta metric has been adopted as a model of primordial black holes by several authors. We show that the spacetime described by this metric has neither black-hole event horizon nor black-hole trapping horizon and involves the violation of the null energy condition as a solution of the Einstein equation. Therefore, this metric does not describe a cosmological black hole in the early universe.
Considerable attention has recently focused on gravity theories obtained by extending general relativity with additional scalar, vector, or tensor degrees of freedom. In this paper, we show that the black-hole solutions of these theories are essentially indistinguishable from those of general relativity. Thus, we conclude that a potential observational verification of the Kerr metric around an astrophysical black hole cannot, in and of itself, be used to distinguish between these theories. On the other hand, it remains true that detection of deviations from the Kerr metric will signify the need for a major change in our understanding of gravitational physics.
We investigate Hawking evaporation of a population of primordial black holes (PBHs) prior to Big Bang Nucleosynthesis (BBN) as a mechanism to achieve asymmetric reheating of two sectors coupled solely by gravity. While the visible sector is reheated by the inflaton or a modulus, the dark sector is reheated by PBHs. Compared to inflationary or modular reheating of both sectors, there are two advantages: $(i)$ inflaton or moduli mediated operators that can subsequently thermalize the dark sector with the visible sector are not relevant to the asymmetric reheating process; $(ii)$ the mass and abundance of the PBHs provide parametric control of the thermal history of the dark sector, and in particular the ratio of the temperatures of the two sectors. Asymmetric reheating with PBHs turns out to have a particularly rich dark sector phenomenology, which we explore using a single self-interacting real scalar field in the dark sector as a template. Four thermal histories, involving non-relativistic and relativistic dark matter (DM) at chemical equilibrium, followed by the presence or absence of cannibalism, are explored. These histories are then constrained by the observed relic abundance in the current Universe and the Bullet Cluster. The case where PBHs dominate the energy density of the Universe, and reheat both the visible as well as the dark sectors, is also treated in detail.
It is remarkable that the primordial fluctuations as revealed by the CMB coincide with what quantum fluctuations would look like if they were stretched across the sky by accelerated cosmic expansion. It has been observed that this same stretching also brings very small -- even trans-Planckian -- length scales up to observable sizes if extrapolated far enough into the past. This potentially jeopardizes later descriptions of late-time cosmology by introducing uncontrolled trans-Planckian theoretical errors into all calculations. Recent speculations, such as the Trans-Planckian Censorship Conjecture (TCC), have been developed to avoid this problem. We revisit old arguments why the consistency of (and control over) the Effective Field Theory (EFT) governing late-time cosmology is not necessarily threatened by the descent of modes due to universal expansion, even if EFT methods may break down at much earlier times. Failure of EFT methods only poses a problem if late-time predictions rely on non-adiabatic behaviour at these early times (such as is often true for bouncing cosmologies, for example). We illustrate our arguments using simple non-gravitational examples such as slowly rolling scalar fields and the spacing between Landau levels for charged particles in slowly varying magnetic fields, for which similar issues arise and are easier to understand. We comment on issues associated with UV completions. Our arguments need not invalidate speculative ideas like the TCC but suggest they are not required by the present evidence.
We update the constraints on the fraction of the Universe that may have gone into primordial black holes (PBHs) over the mass range $10^{-5}text{--}10^{50}$ g. Those smaller than $sim 10^{15}$ g would have evaporated by now due to Hawking radiation, so their abundance at formation is constrained by the effects of evaporated particles on big bang nucleosynthesis, the cosmic microwave background (CMB), the Galactic and extragalactic $gamma$-ray and cosmic ray backgrounds and the possible generation of stable Planck mass relics. PBHs larger than $sim 10^{15}$ g are subject to a variety of constraints associated with gravitational lensing, dynamical effects, influence on large-scale structure, accretion and gravitational waves. We discuss the constraints on both the initial collapse fraction and the current fraction of the CDM in PBHs at each mass scale but stress that many of the constraints are associated with observational or theoretical uncertainties. We also consider indirect constraints associated with the amplitude of the primordial density fluctuations, such as second-order tensor perturbations and $mu$-distortions arising from the effect of acoustic reheating on the CMB, if PBHs are created from the high-$sigma$ peaks of nearly Gaussian fluctuations. Finally we discuss how the constraints are modified if the PBHs have an extended mass function, this being relevant if PBHs provide some combination of the dark matter, the LIGO/Virgo coalescences and the seeds for cosmic structure. Even if PBHs make a small contribution to the dark matter, they could play an important cosmological role and provide a unique probe of the early Universe.
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