PBHEMF.bib

@article{PhysRevD.105.103508,
  title = {Primordial black hole dark matter in the context of extra dimensions},
  author = {Friedlander, Avi and Mack, Katherine J. and Schon, Sarah and Song, Ningqiang and Vincent, Aaron C.},
  journal = {Phys. Rev. D},
  volume = {105},
  issue = {10},
  pages = {103508},
  numpages = {39},
  year = {2022},
  month = {May},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.105.103508},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.105.103508}
}

@article{Bellomo_2018,
doi = {10.1088/1475-7516/2018/01/004},
url = {https://dx.doi.org/10.1088/1475-7516/2018/01/004},
year = {2018},
month = {jan},
publisher = {},
volume = {2018},
number = {01},
pages = {004},
author = {Nicola Bellomo and José Luis Bernal and Alvise Raccanelli and Licia Verde},
title = {Primordial black holes as dark matter: converting constraints from monochromatic to extended mass distributions},
journal = {Journal of Cosmology and Astroparticle Physics},
abstract = {The model in which Primordial Black Holes (PBHs) constitute a non-negligible fraction of the dark matter has (re)gained popularity after the first detections of binary black hole mergers. Most of the observational constraints to date have been derived assuming a single mass for all the PBHs, although some more recent works tried to generalize constraints to the case of extended mass functions. Here we derive a general methodology to obtain constraints for any PBH Extended Mass Distribution (EMD) and any observables in the desired mass range. Starting from those obtained for a monochromatic distribution, we convert them into constraints for EMDs by using an equivalent, effective mass Meq that depends on the specific observable. We highlight how limits of validity of the PBH modelling affect the EMD parameter space. Finally, we present converted constraints on the total abundance of PBH from microlensing, stellar distribution in ultra-faint dwarf galaxies and CMB accretion for Lognormal and Power Law mass distributions, finding that EMD constraints are generally stronger than monochromatic ones.}
}

@article{PhysRevD.94.083504,
  title = {Primordial black holes as dark matter},
  author = {Carr, Bernard and K\"uhnel, Florian and Sandstad, Marit},
  journal = {Phys. Rev. D},
  volume = {94},
  issue = {8},
  pages = {083504},
  numpages = {28},
  year = {2016},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.94.083504},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.94.083504}
}

@article{Green_2021,
doi = {10.1088/1361-6471/abc534},
url = {https://dx.doi.org/10.1088/1361-6471/abc534},
year = {2021},
month = {feb},
publisher = {IOP Publishing},
volume = {48},
number = {4},
pages = {043001},
author = {Anne M Green and Bradley J Kavanagh},
title = {Primordial black holes as a dark matter candidate},
journal = {Journal of Physics G: Nuclear and Particle Physics},
abstract = {The detection of gravitational waves from mergers of tens of Solar mass black hole binaries has led to a surge in interest in primordial black holes (PBHs) as a dark matter candidate. We aim to provide a (relatively) concise overview of the status of PBHs as a dark matter candidate, circa Summer 2020. First we review the formation of PBHs in the early Universe, focussing mainly on PBHs formed via the collapse of large density perturbations generated by inflation. Then we review the various current and future constraints on the present day abundance of PBHs. We conclude with a discussion of the key open questions in this field.}
}

@article{PhysRevD.96.123523,
  title = {Merger rate of primordial black-hole binaries},
  author = {Ali-Ha\"{\i}moud, Yacine and Kovetz, Ely D. and Kamionkowski, Marc},
  journal = {Phys. Rev. D},
  volume = {96},
  issue = {12},
  pages = {123523},
  numpages = {18},
  year = {2017},
  month = {Dec},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.96.123523},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.96.123523}
}

@article{PhysRevD.87.123524,
  title = {Constraints on primordial black holes as dark matter candidates from capture by neutron stars},
  author = {Capela, Fabio and Pshirkov, Maxim and Tinyakov, Peter},
  journal = {Phys. Rev. D},
  volume = {87},
  issue = {12},
  pages = {123524},
  numpages = {7},
  year = {2013},
  month = {Jun},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.87.123524},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.87.123524}
}

@article{PhysRevD.96.043504,
  title = {Inflationary primordial black holes as all dark matter},
  author = {Inomata, Keisuke and Kawasaki, Masahiro and Mukaida, Kyohei and Tada, Yuichiro and Yanagida, Tsutomu T.},
  journal = {Phys. Rev. D},
  volume = {96},
  issue = {4},
  pages = {043504},
  numpages = {7},
  year = {2017},
  month = {Aug},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.96.043504},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.96.043504}
}

@article{PhysRevLett.111.181302,
  title = {New limits on primordial black hole dark matter from an analysis of kepler source microlensing data},
  author = {Griest, Kim and Cieplak, Agnieszka M. and Lehner, Matthew J.},
  journal = {Phys. Rev. Lett.},
  volume = {111},
  issue = {18},
  pages = {181302},
  numpages = {5},
  year = {2013},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.111.181302},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.111.181302}
}

@article{PhysRevD.101.123514,
  title = {$INTEGRAL$ constraints on primordial black holes and particle dark matter},
  author = {Laha, Ranjan and Mu\~noz, Julian B. and Slatyer, Tracy R.},
  journal = {Phys. Rev. D},
  volume = {101},
  issue = {12},
  pages = {123514},
  numpages = {9},
  year = {2020},
  month = {Jun},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.101.123514},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.101.123514}
}

@article{10.1093/mnras/stac2705,
    author = {Ziparo, F and Gallerani, S and Ferrara, A and Vito, F},
    title = "{Cosmic radiation backgrounds from primordial black holes}",
    journal = {Monthly Notices of the Royal Astronomical Society},
    volume = {517},
    number = {1},
    pages = {1086-1097},
    year = {2022},
    month = {09},
    abstract = "{Recent measurements of the cosmic X-ray background (CXB) and cosmic radio background (CRB) obtained with Chandra and ARCADE2 (Absolute Radiometer for Cosmology, Astrophysics, and Diffuse Emission) report signals in excess of those expected from known sources, suggesting the presence of a yet undiscovered population of emitters. We investigate the hypothesis that such excesses are due to primordial black holes (PBHs) that may constitute a substantial fraction of dark matter (DM). We present a novel semi-analytical model that predicts X-ray and radio emission due to gas accretion on to PBHs, assuming that they are distributed both inside DM haloes and in the intergalactic medium (IGM). Our model includes a self-consistent treatment of heating/ionization feedback on the surrounding environment. We find that (i) the emission from PBHs accreting in the IGM is subdominant at all times (\\$1\\{\\{\\ \\rm per\\ cent\\}\\} \\le I\_\\{\\rm IGM\\}/I\_\\{\\rm tot\\} \\le 40\\{\\{\\ \\rm per\\ cent\\}\\}\\$); (ii) most of the CXB/CRB emission comes from PBHs in DM mini-haloes (Mh ≤ 106 M⊙) at early epochs (\\$z\\$ \\> 6). While a small fraction (\\$f\_\\{\\rm PBH\\} \\simeq 0.3\\{\\{\\ \\rm per\\ cent\\}\\}\\$) of DM in the form of PBHs can account for the total observed CXB excess, the CRB one cannot be explained by PBHs. Our results set the strongest existing constraint on fPBH ≤ 3 × 10−4 (30/MPBH) in the mass range of \\$1 \\!-\\! 1000 \\, \\mathrm\\{M\\}\_\\odot\\$. Finally, we comment on the implications of our results on the global H i 21 cm signal.}",
    issn = {0035-8711},
    doi = {10.1093/mnras/stac2705},
    url = {https://doi.org/10.1093/mnras/stac2705},
    eprint = {https://academic.oup.com/mnras/article-pdf/517/1/1086/46395703/stac2705.pdf},
}

@article{PhysRevD.96.023514,
  title = {Primordial black hole constraints for extended mass functions},
  author = {Carr, Bernard and Raidal, Martti and Tenkanen, Tommi and Vaskonen, Ville and Veerm\"ae, Hardi},
  journal = {Phys. Rev. D},
  volume = {96},
  issue = {2},
  pages = {023514},
  numpages = {10},
  year = {2017},
  month = {Jul},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.96.023514},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.96.023514}
}

@article{CYBURT2003227,
title = {Primordial nucleosynthesis in light of WMAP},
journal = {Physics Letters B},
volume = {567},
number = {3},
pages = {227-234},
year = {2003},
issn = {0370-2693},
doi = {https://doi.org/10.1016/j.physletb.2003.06.026},
url = {https://www.sciencedirect.com/science/article/pii/S037026930300916X},
author = {Richard H Cyburt and Brian D Fields and Keith A Olive},
abstract = {Big bang nucleosynthesis has long provided the primary determination of the cosmic baryon density ΩBh2, or equivalently the baryon-to-photon ratio, η. Recently, data on CMB anisotropies have become increasingly sensitive to η. The comparison of these two independent measures provides a key test for big bang cosmology. The first release of results from the Wilkinson Microwave Anisotropy Probe (WMAP) marks a milestone in this test. With the precision of WMAP, the CMB now offers a significantly stronger constraint on η. We discuss the current state of BBN theory and light element observations (including their possible lingering systematic errors). The resulting BBN baryon density prediction is in overall agreement with the WMAP prediction, an important and non-trivial confirmation of hot big bang cosmology. Going beyond this, the powerful CMB baryometer can be used as an input to BBN and one can accurately predict the primordial light element abundances. By comparing these with observations one can obtain new insight into post-BBN nucleosynthesis processes and associated astrophysics. Finally, one can test the possibility of nonstandard physics at the time of BBN, now with all light elements available as probes. Indeed, with the WMAP precision η, deuterium is already beginning to rival 4He's sensitivity to nonstandard physics, and additional D/H measurements can improve this further.}
}

@ARTICLE{1976ApJ...206....1P,
       author = {Page, D.~N. and Hawking, S.~W.},
        title = "{Gamma rays from primordial black holes.}",
      journal = {Astrophysical Journal},
     keywords = {Black Holes (Astronomy), Gamma Rays, High Energy Interactions, Particle Emission, Radiant Flux Density, Diffuse Radiation, Quantum Theory, Relativistic Theory, Stellar Mass, Universe, Space Radiation},
         year = 1976,
        month = may,
       volume = {206},
        pages = {1-7},
          doi = {10.1086/154350},
       url = {https://ui.adsabs.harvard.edu/abs/1976ApJ...206....1P}
}

@ARTICLE{2009A&A...502...37L,
       author = {Lehoucq, R. and Cass{\'e}, M. and Casandjian, J. -M. and Grenier, I.},
        title = "{New constraints on the primordial black hole number density from Galactic {\ensuremath{\gamma}}-ray astronomy}",
      journal = {Astronomy and Astrophysics},
     keywords = {gamma rays: observations, Galaxy: center, cosmology: dark matter, gamma rays: theory, black hole physics, Astrophysics - High Energy Astrophysical Phenomena},
         year = 2009,
        month = jul,
       volume = {502},
       number = {1},
        pages = {37-43},
          doi = {10.1051/0004-6361/200911961},
archivePrefix = {arXiv},
       eprint = {0906.1648},
 primaryClass = {astro-ph.HE},
       url = {https://www.aanda.org/component/article?access=bibcode&bibcode=&bibcode=2009A%2526A...502...37LFUL}
}

@article{BARRAU2000269,
title = {Primordial black holes as a source of extremely high energy cosmic rays},
journal = {Astroparticle Physics},
volume = {12},
number = {4},
pages = {269-275},
year = {2000},
issn = {0927-6505},
doi = {https://doi.org/10.1016/S0927-6505(99)00103-6},
url = {https://www.sciencedirect.com/science/article/pii/S0927650599001036},
author = {Aurélien Barrau},
keywords = {Extremely-high energy cosmic rays, Primordial black holes},
abstract = {The origin of observed extremely high energy cosmic rays remains an astrophysical enigma. We show that a single evaporating primordial black hole should produce 8.5·1014 particles over a 1020 eV threshold. This emission results from direct production of fundamental constituents and from hadronization of quarks and gluons. The induced flux on the Earth is studied as a function of the local density of exploding black holes and compared with experimental data. The discovery potential of future detectors is finally reviewed.}
}

@ARTICLE{1980A&A....81..263O,
       author = {Okele, P.~N. and Rees, M.~J.},
        title = "{Observational consequences of positron production by evaporating black holes}",
      journal = {Astronomy and Astrophysics},
     keywords = {Black Holes (Astronomy), Pair Production, Positrons, Annihilation Reactions, Electron-Positron Pairs, Electrons, Gravitons, Mass Spectra, Neutrinos, Photons, Astrophysics},
         year = 1980,
        month = jan,
       volume = {81},
       number = {1-2},
        pages = {263},
       url = {https://ui.adsabs.harvard.edu/abs/1980A&A....81..263O}
}

@article{Belotsky_2015,
doi = {10.1088/1475-7516/2015/01/041},
url = {https://dx.doi.org/10.1088/1475-7516/2015/01/041},
year = {2015},
month = {jan},
publisher = {},
volume = {2015},
number = {01},
pages = {041},
author = {K.M. Belotsky and A.A. Kirillov},
title = {Primordial black holes with mass 1016−1017 g and reionization of the Universe},
journal = {Journal of Cosmology and Astroparticle Physics},
abstract = {Primordial black holes (PBHs) with mass 1016−1017 g almost escape constraints from observations so could essentially contribute to dark matter density.  Hawking evaporation of such PBHs produces with a steady rate γ- and e±-radiations in MeV energy range, which can be absorbed by ordinary matter. Simplified estimates show that a small fraction of evaporated energy had to be absorbed by baryonic matter what can turn out to be enough to heat the matter so it is fully ionized at the redshift z∼ 5… 10. The result is found to be close to a borderline case where the effect appears, what makes it sensitive to the approximation used. In our approximation, degree of gas ionization reaches 50-100% by z∼ 5 for PBH mass (3…7)× 1016 g with their abundance corresponding to the upper limit.}
}

@ARTICLE{1993Natur.366..242H,
       author = {Hawkins, M.~R.~S.},
        title = "{Gravitational microlensing, quasar variability and missing matter}",
      journal = {Nature},
         year = 1993,
        month = nov,
       volume = {366},
       number = {6452},
        pages = {242-245},
          doi = {10.1038/366242a0},
       url = {https://www.nature.com/articles/366242a0}
}

@ARTICLE{1985ApJ...299..633L,
       author = {Lacey, C.~G. and Ostriker, J.~P.},
        title = "{Massive black holes in galactic halos ?}",
      journal = {Astrophysical Journal},
     keywords = {Black Holes (Astronomy), Galactic Structure, Star Distribution, Brightness Distribution, Chronology, Dark Matter, Dwarf Galaxies, Ellipsoids, Gravitational Lenses, Radii, Stellar Motions, Velocity Distribution, Astrophysics},
         year = 1985,
        month = dec,
       volume = {299},
        pages = {633-652},
          doi = {10.1086/163729},
       url = {https://ui.adsabs.harvard.edu/link_gateway/1985ApJ...299..633L/doi:10.1086/163729}
}

@article{PhysRevLett.116.201301,
  title = {Did LIGO detect dark matter?},
  author = {Bird, Simeon and Cholis, Ilias and Mu\~noz, Julian B. and Ali-Ha\"{\i}moud, Yacine and Kamionkowski, Marc and Kovetz, Ely D. and Raccanelli, Alvise and Riess, Adam G.},
  journal = {Phys. Rev. Lett.},
  volume = {116},
  issue = {20},
  pages = {201301},
  numpages = {6},
  year = {2016},
  month = {May},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.116.201301},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.116.201301}
}

@article{https://doi.org/10.1002/andp.20045160301,
author = {Barrau, A. and Blais, D. and Boudoul, G. and Polarski, D.},
title = {Peculiar relics from Primordial Black Holes in the inflationary paradigm},
journal = {Annalen der Physik},
volume = {516},
number = {3},
pages = {115-123},
keywords = {Primordial black holes, inflation, relics},
doi = {https://doi.org/10.1002/andp.20045160301},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/andp.20045160301},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/andp.20045160301},
abstract = {Abstract Depending on various assumptions on the energy scale of inflation and assuming a primordial power spectrum of a step-like structure, we explore new possibilities for Primordial Black Holes (PBH) and Planck relics to contribute substantially to Cold Dark Matter in the Universe. A recently proposed possibility to produce Planck relics in four-dimensional string gravity is considered in this framework. Possible experimental detection of PBHs through gravitational waves is also explored. We stress that inflation with a low energy scale, and also possibly when Planck relics are produced, leads unavoidably to relics originating from PBHs that are not effectively classical during their formation, rendering the usual formalism inadequate for them.},
year = {2004}
}

@article{10.1093/mnras/152.1.75,
    author = {Hawking, Stephen},
    title = "{Gravitationally collapsed objects of very low mass}",
    journal = {Monthly Notices of the Royal Astronomical Society},
    volume = {152},
    number = {1},
    pages = {75-78},
    year = {1971},
    month = {04},
    abstract = "{It is suggested that there may be a large number of gravitationally collapsed objects of mass 10–5 g upwards which were formed as a result of fluctuations in the early Universe. They could carry an electric charge of up to ± 30 electron units. Such objects would produce distinctive tracks in bubble chambers and could form atoms with orbiting electrons or protons. A mass of 1017 g of such objects could have accumulated at the centre of a star like the Sun. If such a star later became a neutron star there would be a steady accretion of matter by a central collapsed object which could eventually swallow up the whole star in about ten million years.}",
    issn = {0035-8711},
    doi = {10.1093/mnras/152.1.75},
    url = {https://doi.org/10.1093/mnras/152.1.75},
    eprint = {https://academic.oup.com/mnras/article-pdf/152/1/75/9360899/mnras152-0075.pdf},
}

@article{10.1093/mnras/168.2.399,
    author = {Carr, B. J. and Hawking, S. W.},
    title = "{Black holes in the early universe}",
    journal = {Monthly Notices of the Royal Astronomical Society},
    volume = {168},
    number = {2},
    pages = {399-415},
    year = {1974},
    month = {08},
    abstract = "{ The existence of galaxies today implies that the early Universe must have been inhomogeneous. Some regions might have got so compressed that they underwent gravitational collapse to produce black holes. Once formed, black holes in the early Universe would grow by accreting nearby matter. A first estimate suggests that they might grow at the same rate as the Universe during the radiation era and be of the order of 10 15 to 10 17 solar masses now. The observational evidence however is against the existence of such giant black holes. This motivates a more detailed study of the rate of accretion which shows that black holes will not in fact substantially increase their original mass by accretion. There could thus be primordial black holes around now with masses from 10 −5 g upwards. }",
    issn = {0035-8711},
    doi = {10.1093/mnras/168.2.399},
    url = {https://doi.org/10.1093/mnras/168.2.399},
    eprint = {https://academic.oup.com/mnras/article-pdf/168/2/399/8079885/mnras168-0399.pdf},
}

@ARTICLE{1975ApJ...201....1C,
       author = {Carr, B.~J.},
        title = "{The primordial black hole mass spectrum.}",
      journal = {Astrophysical Journal},
     keywords = {Astronomical Models, Black Holes (Astronomy), Cosmology, Mass Spectra, Density (Mass/Volume), Galactic Clusters, Perturbation Theory, Universe, Astrophysics},
         year = 1975,
        month = oct,
       volume = {201},
        pages = {1-19},
          doi = {10.1086/153853},
       url = {https://ui.adsabs.harvard.edu/abs/1975ApJ...201....1C}
}

@article{PhysRevD.60.084002,
  title = {Black hole formation in the Friedmann universe: Formulation and computation in numerical relativity},
  author = {Shibata, Masaru and Sasaki, Misao},
  journal = {Phys. Rev. D},
  volume = {60},
  issue = {8},
  pages = {084002},
  numpages = {11},
  year = {1999},
  month = {Sep},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.60.084002},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.60.084002}
}

@article{PhysRevD.70.041502,
  title = {New calculation of the mass fraction of primordial black holes},
  author = {Green, Anne M. and Liddle, Andrew R. and Malik, Karim A. and Sasaki, Misao},
  journal = {Phys. Rev. D},
  volume = {70},
  issue = {4},
  pages = {041502},
  numpages = {5},
  year = {2004},
  month = {Aug},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.70.041502},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.70.041502}
}

@article{PhysRevD.88.084051,
  title = {Threshold of primordial black hole formation},
  author = {Harada, Tomohiro and Yoo, Chul-Moon and Kohri, Kazunori},
  journal = {Phys. Rev. D},
  volume = {88},
  issue = {8},
  pages = {084051},
  numpages = {10},
  year = {2013},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.88.084051},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.88.084051}
}

@article{PhysRevD.89.029903,
  title = {Erratum: Threshold of primordial black hole formation [Phys. Rev. D 88, 084051 (2013)]},
  author = {Harada, Tomohiro and Yoo, Chul-Moon and Kohri, Kazunori},
  journal = {Phys. Rev. D},
  volume = {89},
  issue = {2},
  pages = {029903},
  numpages = {1},
  year = {2014},
  month = {Jan},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.89.029903},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.89.029903}
}

@ARTICLE{1978SvA....22..129N,
       author = {Nadezhin, D.~K. and Novikov, I.~D. and Polnarev, A.~G.},
        title = "{The hydrodynamics of primordial black hole formation}",
      journal = {Soviet Astronomy},
     keywords = {Big Bang Cosmology, Black Holes (Astronomy), Hydrodynamics, Astronomical Models, Numerical Analysis, Universe, Astrophysics},
         year = 1978,
        month = apr,
       volume = {22},
        pages = {129-138},
       url = {https://ui.adsabs.harvard.edu/abs/1978SvA....22..129N}
}

@ARTICLE{1979ApJ...232..670B,
       author = {Bicknell, G.~V. and Henriksen, R.~N.},
        title = "{Formation of primordial black holes.}",
      journal = {Astrophysical Journal},
     keywords = {Astronomical Models, Big Bang Cosmology, Black Holes (Astronomy), Gravitational Collapse, Astronomical Coordinates, Baryons, Inhomogeneity, Relativity, Astrophysics, Black Holes:Formation},
         year = 1979,
        month = sep,
       volume = {232},
        pages = {670-682},
          doi = {10.1086/157325},
       url = {https://ui.adsabs.harvard.edu/abs/1979ApJ...232..670B}
}

@article{PhysRevLett.80.5481,
  title = {Near-critical gravitational collapse and the initial mass function of primordial black holes},
  author = {Niemeyer, J. C. and Jedamzik, K.},
  journal = {Phys. Rev. Lett.},
  volume = {80},
  issue = {25},
  pages = {5481--5484},
  numpages = {0},
  year = {1998},
  month = {Jun},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.80.5481},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.80.5481}
}

@article{PhysRevD.59.124013,
  title = {Dynamics of primordial black hole formation},
  author = {Niemeyer, J. C. and Jedamzik, K.},
  journal = {Phys. Rev. D},
  volume = {59},
  issue = {12},
  pages = {124013},
  numpages = {8},
  year = {1999},
  month = {May},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.59.124013},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.59.124013}
}

@article{Musco_2005,
doi = {10.1088/0264-9381/22/7/013},
url = {https://dx.doi.org/10.1088/0264-9381/22/7/013},
year = {2005},
month = {mar},
publisher = {},
volume = {22},
number = {7},
pages = {1405},
author = {Ilia Musco and John C Miller and Luciano Rezzolla},
title = {Computations of primordial black-hole formation},
journal = {Classical and Quantum Gravity},
abstract = {Results are presented from general relativistic numerical computations of primordial black-hole formation during the radiation-dominated era of the universe. Growing-mode perturbations are specified within the linear regime and their subsequent evolution is followed as they become nonlinear. We use a spherically symmetric Lagrangian code and study both super-critical perturbations, which go on to produce black holes, and sub-critical perturbations, for which the overdensity eventually disperses into the background medium. For super-critical perturbations, we confirm the results of previous work concerning scaling laws but note that the threshold amplitude for a perturbation to lead to black-hole formation is substantially reduced when the initial conditions are taken to represent purely growing modes. For sub-critical cases, where an initial collapse is followed by a subsequent re-expansion, strong compressions and rarefactions are seen for perturbation amplitudes near to the threshold. We have also investigated the effect of including a significant component of vacuum energy and have calculated the resulting changes in the threshold and in the slope of the scaling law.}
}

@article{Musco_2009,
doi = {10.1088/0264-9381/26/23/235001},
url = {https://dx.doi.org/10.1088/0264-9381/26/23/235001},
year = {2009},
month = {oct},
publisher = {},
volume = {26},
number = {23},
pages = {235001},
author = {Ilia Musco and John C Miller and Alexander G Polnarev},
title = {Primordial black hole formation in the radiative era: investigation of the critical nature of the collapse},
journal = {Classical and Quantum Gravity},
abstract = {Following on after two previous papers discussing the formation of primordial black holes in the early universe, we present here results from an in-depth investigation of the extent to which primordial black hole formation in the radiative era can be considered as an example of the critical collapse phenomenon. We focus on initial supra-horizon-scale perturbations of a type which could have come from inflation, with only a growing component and no decaying component. In order to study perturbations with amplitudes extremely close to the supposed critical limit, we have modified our previous computer code with the introduction of an adaptive mesh refinement scheme. This has allowed us to follow black hole formation from perturbations whose amplitudes are up to eight orders of magnitude closer to the threshold than we could do before. We find that scaling-law behaviour continues down to the smallest black hole masses that we are able to follow and we see no evidence of shock production such as has been reported in some previous studies and which led there to a breaking of the scaling-law behaviour at small black hole masses. We attribute this difference to the different initial conditions used. In addition to the scaling law, we also present other features of the results which are characteristic of critical collapse in this context.}
}

@article{Polnarev_2007,
doi = {10.1088/0264-9381/24/6/003},
url = {https://dx.doi.org/10.1088/0264-9381/24/6/003},
year = {2007},
month = {mar},
publisher = {},
volume = {24},
number = {6},
pages = {1405},
author = {Alexander G Polnarev and Ilia Musco},
title = {Curvature profiles as initial conditions for primordial black hole formation},
journal = {Classical and Quantum Gravity},
abstract = {This work is part of an ongoing research programme to study possible primordial black hole (PBH) formation during the radiation-dominated era of the early universe. Working within spherical symmetry, we specify an initial configuration in terms of a curvature profile, which represents initial conditions for the large amplitude metric perturbations, away from the homogeneous Friedmann–Robertson–Walker model, which are required for PBH formation. Using an asymptotic quasi-homogeneous solution, we relate the curvature profile with the density and velocity fields, which at an early enough time, when the length scale of the configuration is much larger than the cosmological horizon, can be treated as small perturbations of the background values. We present general analytic solutions for the density and velocity profiles. These solutions enable us to consider in a self-consistent way the formation of PBHs in a wide variety of cosmological situations with the cosmological fluid being treated as an arbitrary mixture of different components with different equations of state. We obtain the analytical solutions for the density and velocity profiles as functions of the initial time. We then use two different parametrizations for the curvature profile and follow numerically the evolution of initial configurations.}
}

@article{Nakama_2014,
doi = {10.1088/1475-7516/2014/01/037},
url = {https://dx.doi.org/10.1088/1475-7516/2014/01/037},
year = {2014},
month = {jan},
publisher = {},
volume = {2014},
number = {01},
pages = {037},
author = {Tomohiro Nakama and Tomohiro Harada and A.G. Polnarev and Jun'ichi Yokoyama},
title = {Identifying the most crucial parameters of the initial curvature profile for primordial black hole formation},
journal = {Journal of Cosmology and Astroparticle Physics},
abstract = {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 essentialy 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.}
}

@article{PhysRevD.100.123524,
  title = {Threshold for primordial black holes: Dependence on the shape of the cosmological perturbations},
  author = {Musco, Ilia},
  journal = {Phys. Rev. D},
  volume = {100},
  issue = {12},
  pages = {123524},
  numpages = {18},
  year = {2019},
  month = {Dec},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.100.123524},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.100.123524}
}

@article{PhysRevD.101.044022,
  title = {Universal threshold for primordial black hole formation},
  author = {Escriv\`a, Albert and Germani, Cristiano and Sheth, Ravi K.},
  journal = {Phys. Rev. D},
  volume = {101},
  issue = {4},
  pages = {044022},
  numpages = {5},
  year = {2020},
  month = {Feb},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.101.044022},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.101.044022}
}

@article{PhysRevLett.122.141302,
  title = {Abundance of Primordial Black Holes Depends on the Shape of the Inflationary Power Spectrum},
  author = {Germani, Cristiano and Musco, Ilia},
  journal = {Phys. Rev. Lett.},
  volume = {122},
  issue = {14},
  pages = {141302},
  numpages = {6},
  year = {2019},
  month = {Apr},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.122.141302},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.122.141302}
}

@article{PhysRevD.103.063538,
  title = {Threshold for primordial black holes. II. A simple analytic prescription},
  author = {Musco, Ilia and De Luca, Valerio and Franciolini, Gabriele and Riotto, Antonio},
  journal = {Phys. Rev. D},
  volume = {103},
  issue = {6},
  pages = {063538},
  numpages = {15},
  year = {2021},
  month = {Mar},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.103.063538},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.103.063538}
}

@article{Saito_2008,
doi = {10.1088/1475-7516/2008/06/024},
url = {https://dx.doi.org/10.1088/1475-7516/2008/06/024},
year = {2008},
month = {jun},
publisher = {},
volume = {2008},
number = {06},
pages = {024},
author = {Ryo Saito and Jun’ichi Yokoyama and Ryo Nagata},
title = {Single-field inflation, anomalous enhancement of superhorizon fluctuations and
non-Gaussianity in primordial black hole formation},
journal = {Journal of Cosmology and Astroparticle Physics},
abstract = {We show a textbook potential for single-field inflation, namely the Coleman–Weinberg model can induce double inflation and formation of primordial black holes (PBHs), because fluctuations that leave the horizon near the end of first inflation are anomalously enhanced at the onset of second inflation when the time-dependent mode turns into a growing mode rather than a decaying mode. The mass of PBHs produced in this mechanism with an appreciable density are distributed at certain intervals depending on the model parameters. We also calculate the effects of non-Gaussian statistics due to higher-order interactions on the abundance of PBHs, which turns out to be small.}
}

@article{Kehagias_2019,
doi = {10.1088/1475-7516/2019/12/029},
url = {https://dx.doi.org/10.1088/1475-7516/2019/12/029},
year = {2019},
month = {dec},
publisher = {},
volume = {2019},
number = {12},
pages = {029},
author = {A. Kehagias and I. Musco and A. Riotto},
title = {Non-Gaussian formation of primordial black holes:  effects on the threshold},
journal = {Journal of Cosmology and Astroparticle Physics},
abstract = {Primordial black holes could have been formed in the early universe from sufficiently large cosmological perturbations re-entering the horizon when the Universe is still radiation dominated. These originate from the spectrum of curvature perturbations generated during inflation at small-scales. Because of the non-linear relation between the curvature perturbation ζ and the overdensity δρ, the formation of the primordial black holes is affected by intrinsic non-Gaussianity even if the curvature perturbation is Gaussian. We investigate the impact of this non-Gaussianity on the critical threshold δc which measures the excess of mass of the perturbation, finding a relative change with respect to the value obtained using a linear relation between ζ and δρ, of a few percent  suggesting that the value of the critical threshold is rather robust against non-linearities. The same holds also when local primordial non-Gaussianity, with fNL≳−3/2, are added to the curvature perturbation.}
}

@article{PhysRevD.58.107502,
  title = {Cosmological constraints on primordial black holes produced in the near-critical gravitational collapse},
  author = {Yokoyama, Jun'ichi},
  journal = {Phys. Rev. D},
  volume = {58},
  issue = {10},
  pages = {107502},
  numpages = {4},
  year = {1998},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.58.107502},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.58.107502}
}

@article{PhysRevD.60.103510,
  title = {Bounds from primordial black holes with a near critical collapse initial mass function},
  author = {Kribs, Graham D. and Leibovich, Adam K. and Rothstein, I. Z.},
  journal = {Phys. Rev. D},
  volume = {60},
  issue = {10},
  pages = {103510},
  numpages = {9},
  year = {1999},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.60.103510},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.60.103510}
}

@article{Harada_2021,
doi = {10.3847/1538-4357/abd9b9},
url = {https://dx.doi.org/10.3847/1538-4357/abd9b9},
year = {2021},
month = {feb},
publisher = {The American Astronomical Society},
volume = {908},
number = {2},
pages = {140},
author = {Tomohiro Harada and Chul-Moon Yoo and Kazunori Kohri and Yasutaka Koga and Takeru Monobe},
title = {Spins of primordial black holes formed in the radiation-dominated phase of the universe: first-order effect},
journal = {The Astrophysical Journal},
abstract = {The standard deviation of the initial values of the nondimensional Kerr parameter a* of primordial black holes (PBHs) that formed in the radiation-dominated phase of the universe is estimated to the first order of perturbation for the narrow power spectrum. Evaluating the angular momentum at turnaround based on linearly extrapolated transfer functions and peak theory, we obtain the expression  , where MH, β0(MH), and γ are the mass within the Hubble horizon at the horizon entry of the overdense region, the fraction of the universe which collapsed to PBHs at the scale of MH, and a quantity that characterizes the width of the power spectrum, respectively. This implies that for M ≃ MH, the higher the probability of the PBH formation, the larger the standard deviation of the spins, while PBHs of M ≪ MH that formed through near-critical collapse may have larger spins than those of M ≃ MH. In comparison to the previous estimate, the new estimate has an explicit dependence on the ratio M/MH and no direct dependence on the current dark matter density. On the other hand, it suggests that the first-order effect can be numerically comparable to the second-order one.}
}

@article{PhysRevD.55.R5871,
  title = {Primordial black hole formation during the QCD epoch},
  author = {Jedamzik, Karsten},
  journal = {Phys. Rev. D},
  volume = {55},
  issue = {10},
  pages = {R5871--R5875},
  numpages = {0},
  year = {1997},
  month = {May},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.55.R5871},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.55.R5871}
}

@ARTICLE{1998astro.ph..8142W,
       author = {Widerin, Peter and Schmid, Christoph},
        title = "{Primordial black holes from the QCD transition?}",
      journal = {arXiv e-prints},
     keywords = {Astrophysics, General Relativity and Quantum Cosmology, High Energy Physics - Phenomenology},
         year = 1998,
        month = aug,
          eid = {astro-ph/9808142},
        pages = {astro-ph/9808142},
          doi = {10.48550/arXiv.astro-ph/9808142},
archivePrefix = {arXiv},
       eprint = {astro-ph/9808142},
 primaryClass = {astro-ph},
       url = {https://ui.adsabs.harvard.edu/abs/1998astro.ph..8142W}
}

@article{PhysRevD.59.124014,
  title = {Primordial black hole formation during first-order phase transitions},
  author = {Jedamzik, K. and Niemeyer, J. C.},
  journal = {Phys. Rev. D},
  volume = {59},
  issue = {12},
  pages = {124014},
  numpages = {7},
  year = {1999},
  month = {May},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.59.124014},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.59.124014}
}

@article{Byrnes_2018,
doi = {10.1088/1475-7516/2018/08/041},
url = {https://dx.doi.org/10.1088/1475-7516/2018/08/041},
year = {2018},
month = {aug},
publisher = {},
volume = {2018},
number = {08},
pages = {041},
author = {Christian T. Byrnes and Mark Hindmarsh and Sam Young and Michael R.S. Hawkins},
title = {Primordial black holes with an accurate QCD equation of state},
journal = {Journal of Cosmology and Astroparticle Physics},
abstract = {Making use of definitive new lattice computations of the Standard Model thermodynamics during the quantum chromodynamic (QCD) phase transition, we calculate the enhancement in the mass distribution of primordial black holes (PBHs) due to the softening of the equation of state. We find that the enhancement peaks at approximately 0.7M⊙, with the formation rate increasing by at least two orders of magnitude due to the softening of the equation of state at this time, with a range of approximately 0.3M⊙<M<1.4M⊙ at full width half-maximum. PBH formation is increased by a smaller amount for PBHs with masses spanning a large range, 10−3M⊙<MPBH<103M⊙, which includes the masses of the BHs that LIGO detected. The most significant source of uncertainty in the number of PBHs formed is now due to unknowns in the formation process, rather than from the phase transition. A near scale-invariant density power spectrum tuned to generate a population with mass and merger rate consistent with that detected by LIGO should also produce a much larger energy density of PBHs with solar mass. The existence of  BHs below the Chandresekhar mass limit would be a smoking gun for a primordial origin and they could arguably constitute a significant fraction of the cold dark matter density.  They also pose a challenge to inflationary model building which seek to produce the LIGO BHs without overproducing lighter PBHs.}
}

@article{PhysRevD.48.543,
  title = {Primordial black holes and generalized constraints on chaotic inflation},
  author = {Carr, B. J. and Lidsey, James E.},
  journal = {Phys. Rev. D},
  volume = {48},
  issue = {2},
  pages = {543--553},
  numpages = {0},
  year = {1993},
  month = {Jul},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.48.543},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.48.543}
}

@article{PhysRevD.50.7173,
  title = {Inflation and primordial black holes as dark matter},
  author = {Ivanov, P. and Naselsky, P. and Novikov, I.},
  journal = {Phys. Rev. D},
  volume = {50},
  issue = {12},
  pages = {7173--7178},
  numpages = {0},
  year = {1994},
  month = {Dec},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.50.7173},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.50.7173}
}

@article{PhysRevD.58.083510,
  title = {Chaotic new inflation and formation of primordial black holes},
  author = {Yokoyama, Jun'ichi},
  journal = {Phys. Rev. D},
  volume = {58},
  issue = {8},
  pages = {083510},
  numpages = {9},
  year = {1998},
  month = {Sep},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.58.083510},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.58.083510}
}

@article{GARCIABELLIDO201747,
title = {Primordial black holes from single field models of inflation},
journal = {Physics of the Dark Universe},
volume = {18},
pages = {47-54},
year = {2017},
issn = {2212-6864},
doi = {https://doi.org/10.1016/j.dark.2017.09.007},
url = {https://www.sciencedirect.com/science/article/pii/S2212686417300493},
author = {Juan García-Bellido and Ester Ruiz Morales},
keywords = {Inflation, Primordial black holes, Dark matter},
abstract = {Primordial black holes (PBH) have been shown to arise from high peaks in the matter power spectra of multi-field models of inflation. Here we show, with a simple toy model, that it is also possible to generate a peak in the curvature power spectrum of single-field inflation. We assume that the effective dynamics of the inflaton field presents a near-inflection point which slows down the field right before the end of inflation and gives rise to a prominent spike in the fluctuation power spectrum at scales much smaller than those probed by Cosmic Microwave Background (CMB) and Large Scale Structure (LSS) observations. This peak will give rise, upon reentry during the radiation era, to PBH via gravitational collapse. The mass and abundance of these PBH is such that they could constitute the totality of the Dark Matter today. We satisfy all CMB and LSS constraints and predict a very broad range of PBH masses. Some of these PBH are light enough that they will evaporate before structure formation, leaving behind a large curvature fluctuation on small scales. This broad mass distribution of PBH as Dark Matter will be tested in the future by AdvLIGO and LISA interferometers.}
}

@article{PhysRevD.97.023501,
  title = {Primordial black hole dark matter from single field inflation},
  author = {Ballesteros, Guillermo and Taoso, Marco},
  journal = {Phys. Rev. D},
  volume = {97},
  issue = {2},
  pages = {023501},
  numpages = {17},
  year = {2018},
  month = {Jan},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.97.023501},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.97.023501}
}

@article{PhysRevD.97.083509,
  title = {Primordial black holes from polynomial potentials in single field inflation},
  author = {Hertzberg, Mark P. and Yamada, Masaki},
  journal = {Phys. Rev. D},
  volume = {97},
  issue = {8},
  pages = {083509},
  numpages = {14},
  year = {2018},
  month = {Apr},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.97.083509},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.97.083509}
}

@article{PhysRevD.72.023515,
  title = {Horizon crossing and inflation with large $\ensuremath{\eta}$},
  author = {Kinney, William H.},
  journal = {Phys. Rev. D},
  volume = {72},
  issue = {2},
  pages = {023515},
  numpages = {12},
  year = {2005},
  month = {Jul},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.72.023515},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.72.023515}
}

@article{GERMANI20176,
title = {On primordial black holes from an inflection point},
journal = {Physics of the Dark Universe},
volume = {18},
pages = {6-10},
year = {2017},
issn = {2212-6864},
doi = {https://doi.org/10.1016/j.dark.2017.09.001},
url = {https://www.sciencedirect.com/science/article/pii/S2212686417300432},
author = {Cristiano Germani and Tomislav Prokopec},
keywords = {Inflation, Primordial black holes, Dark matter},
abstract = {Recently, it has been claimed that inflationary models with an inflection point in the scalar potential can produce a large resonance in the power spectrum of curvature perturbation. In this paper however we show that the previous analyses are incorrect. The reason is twofold: firstly, the inflaton is over-shot from a stage of standard inflation and so deviates from the slow-roll attractor before reaching the inflection. Secondly, on the (or close to) the inflection point, the ultra-slow-roll trajectory supersede the slow-roll one and thus, the slow-roll approximations used in the literature cannot be used. We then reconsider the model and provide a recipe for how to produce nevertheless a large peak in the matter power spectrum via fine-tuning of parameters.}
}

@article{LYTH20025,
title = {Generating the curvature perturbation without an inflaton},
journal = {Physics Letters B},
volume = {524},
number = {1},
pages = {5-14},
year = {2002},
issn = {0370-2693},
doi = {https://doi.org/10.1016/S0370-2693(01)01366-1},
url = {https://www.sciencedirect.com/science/article/pii/S0370269301013661},
author = {David H Lyth and David Wands},
abstract = {We present a mechanism for the origin of the large-scale curvature perturbation in our Universe by the late decay of a massive scalar field, the curvaton. The curvaton is light during a period of cosmological inflation, when it acquires a perturbation with an almost scale-invariant spectrum. This corresponds initially to an isocurvature density perturbation, which generates the curvature perturbation after inflation when the curvaton density becomes a significant fraction of the total. The isocurvature density perturbation disappears if the curvaton completely decays into thermalised radiation. Any residual isocurvature perturbation is 100% correlated with the curvature. The same mechanism can also generate the curvature perturbation in pre-big bang/ekpyrotic models, provided that the curvaton has a suitable non-canonical kinetic term so as to generate a flat spectrum.}
}

@article{KHLOPOV1980383,
title = {Primordial black holes as a cosmological test of grand unification},
journal = {Physics Letters B},
volume = {97},
number = {3},
pages = {383-387},
year = {1980},
issn = {0370-2693},
doi = {https://doi.org/10.1016/0370-2693(80)90624-3},
url = {https://www.sciencedirect.com/science/article/pii/0370269380906243},
author = {M.Yu. Khlopov and A.G. Polnarev},
abstract = {The stage of nonrelativistic superheavy particle dominance in the early Universe is predicted within the frame of grand unified theories. The minimal probability of primordial black hole formation at this stage is estimated. Astrophysical restrictions on grand unified models are obtained.}
}

@ARTICLE{1981SvA....25..406P,
       author = {Polnarev, A.~G. and Khlopov, M.~Y.},
        title = "{Primordial black holes and the ERA of superheavy particle dominance in the early universe}",
      journal = {Soviet Astronomy},
         year = 1981,
        month = aug,
       volume = {25},
        pages = {406},
       url = {https://ui.adsabs.harvard.edu/abs/1981SvA....25..406P}
}

@ARTICLE{1982SvA....26..391P,
       author = {Polnarev, A.~G. and Khlopov, M.~Y.},
        title = "{Dustlike stages in the early universe and constraints on the primordial black-hole spectrum}",
      journal = {Soviet Astronomy},
         year = 1982,
        month = aug,
       volume = {26},
        pages = {391-395},
       url = {https://ui.adsabs.harvard.edu/abs/1982SvA....26..391P}
}

@article{10.1093/mnras/215.4.575,
    author = {Khlopov, M. Yu. and Malomed, B. A. and Zeldovich, Ya. B.},
    title = "{Gravitational instability of scalar fields and formation of primordial black holes}",
    journal = {Monthly Notices of the Royal Astronomical Society},
    volume = {215},
    number = {4},
    pages = {575-589},
    year = {1985},
    month = {08},
    abstract = "{The gravitational instability of a spatially uniform state of a relativistic scalar field on a time-independent background is considered.The instability is demonstrated to be similar to the well-known Jeans instability of dust-like non-relativistic matter. The consideration is generalized to incorporate ‘hydrodynamics’, i.e. self-interaction of the field. It is demonstrated that ‘hydrodynamic’ effects may drastically alter the character of the instability; in particular, the dependence of the instability growth rate on perturbation wavenumber may become non-monotone. The non-linear stage of instability development is analysed half-quantitatively. It is demonstrated that, the ‘hydrodynamics’ being stabilizing, the instability growth may result in establishing stable spatially periodic structures in the one-dimensional situation. The results obtained are applied to estimating the probability of primordial black hole formation from perturbations growing due to gravitational instability in a universe dominated by a scalar axion field.}",
    issn = {0035-8711},
    doi = {10.1093/mnras/215.4.575},
    url = {https://doi.org/10.1093/mnras/215.4.575},
    eprint = {https://academic.oup.com/mnras/article-pdf/215/4/575/4082842/mnras215-0575.pdf},
}

@article{PhysRevD.50.4853,
  title = {Black hole relics and inflation: Limits on blue perturbation spectra},
  author = {Carr, B. J. and Gilbert, J. H. and Lidsey, James E.},
  journal = {Phys. Rev. D},
  volume = {50},
  issue = {8},
  pages = {4853--4867},
  numpages = {0},
  year = {1994},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.50.4853},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.50.4853}
}

@article{PhysRevD.97.123535,
  title = {Primordial black hole formation during slow reheating after inflation},
  author = {Carr, Bernard and Dimopoulos, Konstantinos and Owen, Charlotte and Tenkanen, Tommi},
  journal = {Phys. Rev. D},
  volume = {97},
  issue = {12},
  pages = {123535},
  numpages = {7},
  year = {2018},
  month = {Jun},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.97.123535},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.97.123535}
}

@article{Allahverdi2021first,
	journal={The Open Journal of Astrophysics},
	doi={10.21105/astro.2006.16182},
	publisher={Maynooth Academic Publishing},
	title={The first three seconds: A Review of Possible Expansion Histories of the early Universe},
	volume={4},
	author={Allahverdi, Rouzbeh and Amin, Mustafa A. and Berlin, Asher and Bernal, Nicolas and Byrnes, Christian T. and Delos, M. Sten and Erickcek, Adrienne L. and Escudero, Miguel and Figueroa, Daniel G. and Freese, Katherine and Harada, Tomohiro and Hooper, Dan and Kaiser, David I. and Karwal, Tanvi and Kohri, Kazunori and Krnjaic, Gordan and Lewicki, Marek and Lozanov, Kaloian D. and Poulin, Vivian and Sinha, Kuver and Smith, Tristan L. and Takahashi, Tomo and Tenkanen, Tommi and Unwin, James and Vaskonen, Ville and Watson, Scott},
	date={2021-01-29},
	year={2021},
	month={1},
	day={29}
}

@article{refId2014,
	author = {Planck Collaboration and Ade, P. A. R. and Aghanim, N. and Armitage-Caplan, C. and Arnaud, M. and Ashdown, M. and Atrio-Barandela, F. and Aumont, J. and Baccigalupi, C. and Banday, A. J. and Barreiro, R. B. and Bartlett, J. G. and Bartolo, N. and Battaner, E. and Battye, R. and Benabed, K. and Benoît, A. and Benoit-Lévy, A. and Bernard, J.-P. and Bersanelli, M. and Bielewicz, P. and Bobin, J. and Bock, J. J. and Bonaldi, A. and Bonavera, L. and Bond, J. R. and Borrill, J. and Bouchet, F. R. and Bridges, M. and Bucher, M. and Burigana, C. and Butler, R. C. and Cardoso, J.-F. and Catalano, A. and Challinor, A. and Chamballu, A. and Chiang, L.-Y and Chiang, H. C. and Christensen, P. R. and Church, S. and Clements, D. L. and Colombi, S. and Colombo, L. P. L. and Couchot, F. and Coulais, A. and Crill, B. P. and Curto, A. and Cuttaia, F. and Danese, L. and Davies, R. D. and Davis, R. J. and de Bernardis, P. and de Rosa, A. and de Zotti, G. and Delabrouille, J. and Delouis, J.-M. and Désert, F.-X. and Diego, J. M. and Dole, H. and Donzelli, S. and Doré, O. and Douspis, M. and Ducout, A. and Dunkley, J. and Dupac, X. and Efstathiou, G. and Enßlin, T. A. and Eriksen, H. K. and Fergusson, J. and Finelli, F. and Forni, O. and Frailis, M. and Franceschi, E. and Galeotta, S. and Ganga, K. and Giard, M. and Giardino, G. and Giraud-Héraud, Y. and González-Nuevo, J. and Górski, K. M. and Gratton, S. and Gregorio, A. and Gruppuso, A. and Hansen, F. K. and Hanson, D. and Harrison, D. and Henrot-Versillé, S. and Hernández-Monteagudo, C. and Herranz, D. and Hildebrandt, S. R. and Hivon, E. and Hobson, M. and Holmes, W. A. and Hornstrup, A. and Hovest, W. and Huffenberger, K. M. and Jaffe, T. R. and Jaffe, A. H. and Jones, W. C. and Juvela, M. and Keihänen, E. and Keskitalo, R. and Kisner, T. S. and Knoche, J. and Knox, L. and Kunz, M. and Kurki-Suonio, H. and Lagache, G. and Lähteenmäki, A. and Lamarre, J.-M. and Lasenby, A. and Laureijs, R. J. and Lawrence, C. R. and Leahy, J. P. and Leonardi, R. and Lesgourgues, J. and Liguori, M. and Lilje, P. B. and Linden-Vørnle, M. and López-Caniego, M. and Lubin, P. M. and Macías-Pérez, J. F. and Maffei, B. and Maino, D. and Mandolesi, N. and Maris, M. and Marshall, D. J. and Martin, P. G. and Martínez-González, E. and Masi, S. and Matarrese, S. and Matthai, F. and Mazzotta, P. and McEwen, J. D. and Melchiorri, A. and Mendes, L. and Mennella, A. and Migliaccio, M. and Mitra, S. and Miville-Deschênes, M.-A. and Moneti, A. and Montier, L. and Morgante, G. and Mortlock, D. and Moss, A. and Munshi, D. and Naselsky, P. and Natoli, P. and Netterfield, C. B. and Nørgaard-Nielsen, H. U. and Noviello, F. and Novikov, D. and Novikov, I. and Osborne, S. and Oxborrow, C. A. and Paci, F. and Pagano, L. and Pajot, F. and Paoletti, D. and Pasian, F. and Patanchon, G. and Peiris, H. V. and Perdereau, O. and Perotto, L. and Perrotta, F. and Piacentini, F. and Piat, M. and Pierpaoli, E. and Pietrobon, D. and Plaszczynski, S. and Pointecouteau, E. and Polenta, G. and Ponthieu, N. and Popa, L. and Poutanen, T. and Pratt, G. W. and Prézeau, G. and Prunet, S. and Puget, J.-L. and Rachen, J. P. and Räth, C. and Rebolo, R. and Remazeilles, M. and Renault, C. and Ricciardi, S. and Riller, T. and Ringeval, C. and Ristorcelli, I. and Rocha, G. and Rosset, C. and Roudier, G. and Rowan-Robinson, M. and Rusholme, B. and Sandri, M. and Santos, D. and Savini, G. and Scott, D. and Seiffert, M. D. and Shellard, E. P. S. and Spencer, L. D. and Starck, J.-L. and Stolyarov, V. and Stompor, R. and Sudiwala, R. and Sureau, F. and Sutton, D. and Suur-Uski, A.-S. and Sygnet, J.-F. and Tauber, J. A. and Tavagnacco, D. and Terenzi, L. and Toffolatti, L. and Tomasi, M. and Tristram, M. and Tucci, M. and Tuovinen, J. and Valenziano, L. and Valiviita, J. and Van Tent, B. and Varis, J. and Vielva, P. and Villa, F. and Vittorio, N. and Wade, L. A. and Wandelt, B. D. and Yvon, D. and Zacchei, A. and Zonca, A.},
	title = {Planck 2013 results. XXV. Searches for cosmic strings and other topological defects},
	DOI= "10.1051/0004-6361/201321621",
	url= "https://doi.org/10.1051/0004-6361/201321621",
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}

@article{BLANCOPILLADO2018392,
title = {New limits on cosmic strings from gravitational wave observation},
journal = {Physics Letters B},
volume = {778},
pages = {392-396},
year = {2018},
issn = {0370-2693},
doi = {https://doi.org/10.1016/j.physletb.2018.01.050},
url = {https://www.sciencedirect.com/science/article/pii/S0370269318300583},
author = {Jose J. Blanco-Pillado and Ken D. Olum and Xavier Siemens},
keywords = {Cosmic strings, Gravitational waves},
abstract = {We combine new analysis of the stochastic gravitational wave background to be expected from cosmic strings with the latest pulsar timing array (PTA) limits to give an upper bound on the energy scale of the possible cosmic string network, Gμ<1.5×10−11 at the 95% confidence level. We also show bounds from LIGO and to be expected from LISA and BBO. Current estimates for the gravitational wave background from supermassive black hole binaries are at the level where a PTA detection is expected. But if PTAs do observe a background soon, it will be difficult in the short term to distinguish black holes from cosmic strings as the source, because the spectral indices from the two sources happen to be quite similar. If PTAs do not observe a background, then the limits on Gμ will improve somewhat, but a string network with Gμ substantially below 10−11 will produce gravitational waves primarily at frequencies too high for PTA observation, so significant further progress will depend on intermediate-frequency observatories such as LISA, DECIGO and BBO.}
}

@article{HAWKING1989237,
title = {Black holes from cosmic strings},
journal = {Physics Letters B},
volume = {231},
number = {3},
pages = {237-239},
year = {1989},
issn = {0370-2693},
doi = {https://doi.org/10.1016/0370-2693(89)90206-2},
url = {https://www.sciencedirect.com/science/article/pii/0370269389902062},
author = {S.W. Hawking},
abstract = {Cosmic string loops that shrink by a factor of order 1/Gμ will form black holes. I estimate that a fraction of order (Gμ)2x−4 of loops will form black holes, where x=L/s, and s is the correlation length of the string. Although this fraction is very low, the emission of γ-rays from these little black holes could be significant. Observations of the γ-ray background indicate the Gμ must be less than 10−7 if x=3, or that x must be less than 3.5 if Gμ=10−6.}
}

@article{PhysRevD.43.1106,
  title = {Formation of primordial black holes by cosmic strings},
  author = {Polnarev, Alexander and Zembowicz, Robert},
  journal = {Phys. Rev. D},
  volume = {43},
  issue = {4},
  pages = {1106--1109},
  numpages = {0},
  year = {1991},
  month = {Feb},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.43.1106},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.43.1106}
}

@article{doi:10.1142/S0217751X00001452,
author = {HANSEN, R. N. and CHRISTENSEN, M. and LARSEN, A. L.},
title = {Cosmic string loops collapsing to black holes},
journal = {International Journal of Modern Physics A},
volume = {15},
number = {28},
pages = {4433-4445},
year = {2000},
doi = {10.1142/S0217751X00001452},
URL = {https://doi.org/10.1142/S0217751X00001452},
eprint = {https://doi.org/10.1142/S0217751X00001452},
abstract = { We examine the question of collapse of Turok's two-parameter family of cosmic strings. We first perform a classification of the strings according to the specific time(s) at which the minimal string size is reached during one period. We then obtain an exact analytical expression for the probability of collapse to black holes for the Turok strings. Our result has the same general behavior as previously obtained in the literature but we find, in addition, a numerical prefactor that changes the result by three orders of magnitude. Finally we show that our careful computation of the prefactor helps us to understand the discrepancy between previously obtained results and, in particular, that for "large" values of Gμ, there may not even be a discrepancy. We also give a simple physical argument that can immediately rule out some of the previously obtained results. }
}

@article{HOGAN198487,
title = {Massive black holes generated by cosmic strings},
journal = {Physics Letters B},
volume = {143},
number = {1},
pages = {87-91},
year = {1984},
issn = {0370-2693},
doi = {https://doi.org/10.1016/0370-2693(84)90810-4},
url = {https://www.sciencedirect.com/science/article/pii/0370269384908104},
author = {Craig J. Hogan},
abstract = {Zel'dovich and Vilenkin have suggested that topological strings associated with symmetry breaking in a unified Yang-Mills theory might be responsible for the formation of galaxies and clusters. It is shown in this letter that the same strings would probably also lead to the occurrence of massive black holes in galactic nuclei.}
}

@ARTICLE{2005GReGr..37.1635N,
  author = {Nagasawa, Michiyasu},
  title = "{Primordial black hole formation by stabilized embedded strings in the early universe}",
  journal = {General Relativity and Gravitation},
  keywords = {Primordial black holes, Cosmic strings, Multiple winding number, Embedded defects},
  year = 2005,
  month = sep,
  volume = {37},
  number = {9},
  pages = {1635-1649},
  doi = {10.1007/s10714-005-0141-9},
  url = {https://doi.org/10.1007/s10714-005-0141-9}
}

@article{PhysRevD.101.123526,
  title = {Constraints on the cosmic string loop collapse fraction from primordial black holes},
  author = {James-Turner, Chloe and Weil, Danton P. B. and Green, Anne M. and Copeland, Edmund J.},
  journal = {Phys. Rev. D},
  volume = {101},
  issue = {12},
  pages = {123526},
  numpages = {5},
  year = {2020},
  month = {Jun},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.101.123526},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.101.123526}
}

@article{PhysRevD.45.3447,
  title = {Cosmological constraints on cosmic-string gravitational radiation},
  author = {Caldwell, R. R. and Allen, B.},
  journal = {Phys. Rev. D},
  volume = {45},
  issue = {10},
  pages = {3447--3468},
  numpages = {0},
  year = {1992},
  month = {May},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.45.3447},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.45.3447}
}

@article{PhysRevD.57.2158,
  title = {Limits on black hole formation from cosmic string loops},
  author = {MacGibbon, Jane H. and Brandenberger, Robert H. and Wichoski, U. F.},
  journal = {Phys. Rev. D},
  volume = {57},
  issue = {4},
  pages = {2158--2165},
  numpages = {0},
  year = {1998},
  month = {Feb},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.57.2158},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.57.2158}
}

@article{PhysRevD.99.104028,
  title = {Cosmic string loop collapse in full general relativity},
  author = {Helfer, Thomas and Aurrekoetxea, Josu C. and Lim, Eugene A.},
  journal = {Phys. Rev. D},
  volume = {99},
  issue = {10},
  pages = {104028},
  numpages = {10},
  year = {2019},
  month = {May},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.99.104028},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.99.104028}
}

@article{TomohiroMatsuda_2006,
doi = {10.1088/1126-6708/2006/04/017},
url = {https://dx.doi.org/10.1088/1126-6708/2006/04/017},
year = {2006},
month = {apr},
publisher = {},
volume = {2006},
number = {04},
pages = {017},
author = {Tomohiro Matsuda},
title = {Primordial black holes from cosmic necklaces},
journal = {Journal of High Energy Physics},
abstract = {Cosmic necklaces are hybrid topological defects consisting of monopoles and strings.  We argue that primordial black holes (PBHs) may have formed from loops of the necklaces, if there exist stable winding states, such as coils and cycloops.  Unlike the standard scenario of PBH formation from string loops, in which the kinetic energy play important role when strings collapse into black holes, the PBH formation may occur in our scenario after necklaces have dissipated their kinetic energy.  Then, the significant difference appears in the production ratio.  In the standard scenario, the production ratio f becomes a tiny fraction  f ∼ 10−20 , however it becomes  f ∼ 1 in our case.  On the other hand, the typical mass of the PBHs is much smaller than the standard scenario, if they are produced in the same epoch.  As the two mechanisms may work at the same time, the necklaces may have more than one channel of the gravitational collapse.  Although the result obtained in this paper depends on the evolution of the dimensionless parameter r, the existence of the winding state could be a serious problem in some cases.  Since the existence of the winding state in brane models is due to the existence of a non-tivial circle in the compactified space, the PBH formation can be used to probe the structure of the compactified space.  Black holes produced by this mechanism may have peculiar properties.}
}

@article{MatthewLake_2009,
doi = {10.1088/1126-6708/2009/12/033},
url = {https://dx.doi.org/10.1088/1126-6708/2009/12/033},
year = {2009},
month = {dec},
publisher = {},
volume = {2009},
number = {12},
pages = {033},
author = {Matthew Lake and  Steve Thomas and  John Ward},
title = {String necklaces and primordial black holes from type IIB strings},
journal = {Journal of High Energy Physics},
abstract = {We consider a model of static cosmic string loops in type IIB string theory, where the strings wrap cycles within the internal space. The strings are not topologically stabilised, however the presence of a lifting potential traps the windings giving rise to kinky cycloops.  We find that PBH formation occurs at early times in a small window, whilst at late times we observe the formation of dark matter relics in the scaling regime.  This is in stark contrast to previous predictions based on field theoretic models.  We also consider the PBH contribution to the mass density of the universe, and use the experimental data to impose bounds on the string theory parameters.}
}

@article{PhysRevLett.119.031103,
  title = {Primordial black holes from supersymmetry in the early universe},
  author = {Cotner, Eric and Kusenko, Alexander},
  journal = {Phys. Rev. Lett.},
  volume = {119},
  issue = {3},
  pages = {031103},
  numpages = {5},
  year = {2017},
  month = {Jul},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.119.031103},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.119.031103}
}

@article{PhysRevD.96.103002,
  title = {Primordial black holes from scalar field evolution in the early universe},
  author = {Cotner, Eric and Kusenko, Alexander},
  journal = {Phys. Rev. D},
  volume = {96},
  issue = {10},
  pages = {103002},
  numpages = {13},
  year = {2017},
  month = {Nov},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.96.103002},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.96.103002}
}

@article{PhysRevD.98.083513,
  title = {Primordial black holes from inflaton fragmentation into oscillons},
  author = {Cotner, Eric and Kusenko, Alexander and Takhistov, Volodymyr},
  journal = {Phys. Rev. D},
  volume = {98},
  issue = {8},
  pages = {083513},
  numpages = {7},
  year = {2018},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.98.083513},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.98.083513}
}

@article{Cotner_2019,
doi = {10.1088/1475-7516/2019/10/077},
url = {https://dx.doi.org/10.1088/1475-7516/2019/10/077},
year = {2019},
month = {oct},
publisher = {},
volume = {2019},
number = {10},
pages = {077},
author = {Eric Cotner and Alexander Kusenko and Misao Sasaki and Volodymyr Takhistov},
title = {Analytic description of primordial black hole formation from scalar field fragmentation},
journal = {Journal of Cosmology and Astroparticle Physics},
abstract = {Primordial black hole (PBH) formation is a more generic phenomenon than was once thought.  The dynamics of a scalar field in inflationary universe can produce PBHs under mild assumptions regarding the scalar potential. In the early universe, light scalar fields develop large expectation values during inflation and subsequently relax to the minimum of the effective potential at a later time. During the relaxation process, an initially homogeneous scalar condensate can fragment into lumps via an instability similar to the gravitational (Jeans) instability, where the scalar self-interactions, rather than gravity, play the leading role.  The fragmentation of the scalar field into lumps (e.g. Q-balls or oscillons) creates matter composed of relatively few heavy “particles”, whose distribution is subject to significant fluctuations unconstrained by comic microwave background (CMB) observations and unrelated to the large-scale structure.  If this matter component comes to temporarily dominate the energy density before the scalar lumps decay, PBHs can be efficiently produced during the temporary matter-dominated era. We develop a general analytic framework for description of PBH formation in this class of models. We highlight the differences between the scalar fragmentation scenario and other  commonly considered PBH formation models. Given the existence of the Higgs field and the preponderance of scalar fields within supersymmetric and other models of new physics, PBHs constitute an appealing and plausible candidate for dark matter.}
}

@article{PhysRevD.81.104019,
  title = {New cosmological constraints on primordial black holes},
  author = {Carr, B. J. and Kohri, Kazunori and Sendouda, Yuuiti and Yokoyama, Jun'ichi},
  journal = {Phys. Rev. D},
  volume = {81},
  issue = {10},
  pages = {104019},
  numpages = {33},
  year = {2010},
  month = {May},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.81.104019},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.81.104019}
}

@article{LEMOINE2000333,
title = {Moduli constraints on primordial black holes},
journal = {Physics Letters B},
volume = {481},
number = {2},
pages = {333-338},
year = {2000},
issn = {0370-2693},
doi = {https://doi.org/10.1016/S0370-2693(00)00469-X},
url = {https://www.sciencedirect.com/science/article/pii/S037026930000469X},
author = {Martin Lemoine},
abstract = {The amount of late decaying massive particles (e.g., gravitinos, moduli) produced in the evaporation of primordial black holes (PBHs) of mass MBH≲109g is calculated. Limits imposed by big-bang nucleosynthesis on the abundance of these particles are used to constrain the initial PBH mass fraction β (ratio of PBH energy density to critical energy density at formation), as: β≲5×10−19(xφ/6·10−3)−1(MBH/109g)−1/2(Yφ/10−14); xφ is the fraction of PBH luminosity going into gravitinos or moduli, Yφ is the upper bound imposed by nucleosynthesis on the number density to entropy density ratio of gravitinos or moduli. This notably implies that such PBHs should never come to dominate the cosmic energy density.}
}

@article{Acharya_2020,
doi = {10.1088/1475-7516/2020/06/018},
url = {https://dx.doi.org/10.1088/1475-7516/2020/06/018},
year = {2020},
month = {jun},
publisher = {},
volume = {2020},
number = {06},
pages = {018},
author = {Sandeep Kumar Acharya and Rishi Khatri},
title = {CMB and BBN constraints on evaporating primordial black holes revisited},
journal = {Journal of Cosmology and Astroparticle Physics},
abstract = {We derive new CMB anisotropy power spectrum and BBN   constraints for evaporating primordial black holes with mass between   1011 g and 1016 g by explicitly solving the   electromagnetic particle cascades of emitted particles and the   deposition of this emitted energy to the background baryon-photon   plasma. We show that the CMB anisotropies can provide stronger   constraints compared to BBN and CMB spectral distortions on black   holes with masses as small as MBH=1.1× 1013 g, a   slightly smaller mass than what has been considered in literature   until now. We also show that, with more up-to-date data on   abundances of deuterium and helium-3, BBN constraints are   strengthened significantly. The abundance of these primordial black   holes constrains the epoch of inflation 0∼ 4 e-folds after the   epoch constrained by the CMB observations.}
}

@article{10.1093/mnras/staa2131,
    author = {Chluba, Jens and Ravenni, Andrea and Acharya, Sandeep Kumar},
    title = "{Thermalization of large energy release in the early Universe}",
    journal = {Monthly Notices of the Royal Astronomical Society},
    volume = {498},
    number = {1},
    pages = {959-980},
    year = {2020},
    month = {07},
    abstract = "{Spectral distortions of the cosmic microwave background (CMB) provide a unique tool for learning about the early phases of cosmic history, reaching deep into the primordial Universe. At redshifts z ≲ 106, thermalization processes become inefficient and existing limits from COBE/FIRAS imply that no more than Δρ/ρ ≲ 6 × 10−5 (\\$95\\{\\{\\ \\rm per\\ cent\\}\\}\\$ c.l.) of energy could have been injected into the CMB. However, at higher redshifts, when thermalization is efficient, the constraint weakens and Δρ/ρ ≃ 0.01−0.1 could in principle have occurred. Existing computations for the evolution of distortions commonly assume Δρ/ρ ≪ 1 and thus become inaccurate in this case. Similarly, relativistic temperature corrections become relevant for large energy release, but have previously not been modelled as carefully. Here, we study the evolution of distortions and the thermalization process after single large energy release at z ≳ 105. We show that for large distortions the thermalization efficiency is significantly reduced and that the distortion visibility is sizeable to much earlier times. This tightens spectral distortions constraints on low-mass primordial black holes with masses \\$M\_\\{\\rm PBH\\}\\lesssim 2 \\times 10^\\{11\\}\\, \\{\\rm g\\}\\$. Similarly, distortion limits on the amplitude of the small-scale curvature power spectrum at wavenumbers \\$k\\gtrsim 10^4\\, \\{\\rm Mpc\\}^\\{-1\\}\\$ and short-lived decaying particles with lifetimes \\$t\_X\\lesssim 10^7\\, \\{\\rm s\\}\\$ are tightened, however, these still require a more detailed time-dependent treatment. We also briefly discuss the constraints from measurements of the effective number of relativistic degrees of freedom and light element abundances and how these complement spectral distortion limits.}",
    issn = {0035-8711},
    doi = {10.1093/mnras/staa2131},
    url = {https://doi.org/10.1093/mnras/staa2131},
    eprint = {https://academic.oup.com/mnras/article-pdf/498/1/959/33718749/staa2131.pdf},
}

@article{PhysRevLett.125.101101,
  title = {Neutrino and positron constraints on spinning primordial black hole dark matter},
  author = {Dasgupta, Basudeb and Laha, Ranjan and Ray, Anupam},
  journal = {Phys. Rev. Lett.},
  volume = {125},
  issue = {10},
  pages = {101101},
  numpages = {6},
  year = {2020},
  month = {Aug},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.125.101101},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.125.101101}
}

@article{PhysRevD.94.044029,
  title = {Constraints on primordial black holes from the Galactic gamma-ray background},
  author = {Carr, B. J. and Kohri, Kazunori and Sendouda, Yuuiti and Yokoyama, Jun'ichi},
  journal = {Phys. Rev. D},
  volume = {94},
  issue = {4},
  pages = {044029},
  numpages = {24},
  year = {2016},
  month = {Aug},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.94.044029},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.94.044029}
}

@article{PhysRevLett.122.041104,
  title = {Voyager 1 ${e}^{\ifmmode\pm\else\textpm\fi{}}$ further constrain primordial black holes as dark matter},
  author = {Boudaud, Mathieu and Cirelli, Marco},
  journal = {Phys. Rev. Lett.},
  volume = {122},
  issue = {4},
  pages = {041104},
  numpages = {6},
  year = {2019},
  month = {Jan},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.122.041104},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.122.041104}
}

@article{PhysRevLett.126.171101,
  title = {Direct detection of Hawking radiation from asteroid-mass primordial black holes},
  author = {Coogan, Adam and Morrison, Logan and Profumo, Stefano},
  journal = {Phys. Rev. Lett.},
  volume = {126},
  issue = {17},
  pages = {171101},
  numpages = {8},
  year = {2021},
  month = {Apr},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.126.171101},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.126.171101}
}

@article{PhysRevLett.123.251102,
  title = {Constraining primordial black hole abundance with the galactic 511 keV line},
  author = {DeRocco, William and Graham, Peter W.},
  journal = {Phys. Rev. Lett.},
  volume = {123},
  issue = {25},
  pages = {251102},
  numpages = {5},
  year = {2019},
  month = {Dec},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.123.251102},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.123.251102}
}

@article{PhysRevLett.123.251101,
  title = {Primordial black holes as a dark matter candidate are severely constrained by the galactic center 511 keV $\gamma$-ray line},
  author = {Laha, Ranjan},
  journal = {Phys. Rev. Lett.},
  volume = {123},
  issue = {25},
  pages = {251101},
  numpages = {8},
  year = {2019},
  month = {Dec},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.123.251101},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.123.251101}
}

@article{10.1093/mnras/staa1966,
    author = {Chan, Man Ho and Lee, Chak Man},
    title = "{Constraining primordial black hole fraction at the galactic centre using radio observational data}",
    journal = {Monthly Notices of the Royal Astronomical Society},
    volume = {497},
    number = {1},
    pages = {1212-1216},
    year = {2020},
    month = {07},
    abstract = "{Recent gamma-ray and cosmic-ray observations have put strong constraints on the amount of primordial black holes (PBHs) in our universe. In this paper, we use the archival radio data of the inner Galactic Centre to constrain the PBH to dark matter ratio for three different PBH mass distributions including monochromatic, lognormal, and power law. We show that the amount of PBHs only constitutes a very minor component of dark matter at the Galactic Centre for a large parameter space.}",
    issn = {0035-8711},
    doi = {10.1093/mnras/staa1966},
    url = {https://doi.org/10.1093/mnras/staa1966},
    eprint = {https://academic.oup.com/mnras/article-pdf/497/1/1212/33549993/staa1966.pdf},
}

@article{10.1093/mnras/stab1222,
    author = {Kim, Hyungjin},
    title = "{A constraint on light primordial black holes from the interstellar medium temperature}",
    journal = {Monthly Notices of the Royal Astronomical Society},
    volume = {504},
    number = {4},
    pages = {5475-5484},
    year = {2021},
    month = {04},
    abstract = "{Primordial black holes are a viable dark matter candidate. They decay via Hawking evaporation. Energetic particles from the Hawking radiation interact with interstellar gas, depositing their energy as heat and ionization. For a sufficiently high Hawking temperature, fast electrons produced by black holes deposit a substantial fraction of energy as heat through the Coulomb interaction. Using the dwarf galaxy Leo T, we place an upper bound on the fraction of primordial black hole dark matter. For \\$M \\lt 5 \\times 10^\\{-17\\}\\, \\mathrm\\{M\\}\_\\odot\\$, our bound is competitive with or stronger than other bounds.}",
    issn = {0035-8711},
    doi = {10.1093/mnras/stab1222},
    url = {https://doi.org/10.1093/mnras/stab1222},
    eprint = {https://academic.oup.com/mnras/article-pdf/504/4/5475/37975323/stab1222.pdf},
}