References.bib

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 ISSN = {09501207},
 URL = {http://www.jstor.org/stable/95639},
 author = {P. A. M. Dirac},
 journal = {Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character},
 number = {821},
 pages = {60--72},
 publisher = {The Royal Society},
 title = {Quantised singularities in the electromagnetic field},
 urldate = {2024-04-04},
 volume = {133},
 year = {1931}
}

@article{HOOFT1974276,
title = {Magnetic monopoles in unified gauge theories},
journal = {Nuclear Physics B},
volume = {79},
number = {2},
pages = {276-284},
year = {1974},
issn = {0550-3213},
doi = {https://doi.org/10.1016/0550-3213(74)90486-6},
url = {https://www.sciencedirect.com/science/article/pii/0550321374904866},
author = {G.'t Hooft},
abstract = {It is shown that in all those gauge theories in which the electromagnetic group U(1) is taken to be a subgroup of a larger group with a compact covering group, like SU(2) or SU(3), genuine magnetic monopoles can be created as regular solutions of the field equations. Their mass is calculable and of order 137 MW, where MW is a typical vector boson mass.}
}

@article{PhysRevLett.33.451,
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@article{PhysRevLett.43.1365,
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}

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}

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}

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}

@book{clxjch,
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}

@article{TWBKibble_1976,
doi = {10.1088/0305-4470/9/8/029},
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year = {1976},
month = {aug},
publisher = {},
volume = {9},
number = {8},
pages = {1387},
author = {T W B Kibble},
title = {Topology of cosmic domains and strings},
journal = {Journal of Physics A: Mathematical and General},
abstract = {The possible domain structures which can arise in the universe in a spontaneously broken gauge theory are studied. It is shown that the formation of domain wall, strings or monopoles depends on the homotopy groups of the manifold of degenerate vacua. The subsequent evolution of these structures is investigated. It is argued that while theories generating domain walls can probably be eliminated (because of their unacceptable gravitational effects), a cosmic network of strings may well have been formed and may have had important cosmological effects.}
}

@article{PhysRevD.14.870,
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}

@article{VILENKIN1985263,
title = {Cosmic strings and domain walls},
journal = {Physics Reports},
volume = {121},
number = {5},
pages = {263-315},
year = {1985},
issn = {0370-1573},
doi = {https://doi.org/10.1016/0370-1573(85)90033-X},
url = {https://www.sciencedirect.com/science/article/pii/037015738590033X},
author = {Alexander Vilenkin},
abstract = {Phase transitions in the early universe can give rise to microscopic topological defects: vacuum domain walls, strings, walls bounded by strings, and monopoles connected by strings. This article reviews the formation, physical properties and the cosmological evolution of various defects. A particular attention is paid to strings and their cosmological consequences, including the string scenario of galaxy formation and possible observational effects of strings.}
}

@article{PhysRevD.72.045012,
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@article{ZELDOVICH1978239,
title = {On the concentration of relic magnetic monopoles in the universe},
journal = {Physics Letters B},
volume = {79},
number = {3},
pages = {239-241},
year = {1978},
issn = {0370-2693},
doi = {https://doi.org/10.1016/0370-2693(78)90232-0},
url = {https://www.sciencedirect.com/science/article/pii/0370269378902320},
author = {Ya.B. Zeldovich and M.Yu. Khlopov},
abstract = {The modern concentration of relic 't Hooft-Polyakov monopoles is shown to amount to ∼ 10−19 cm−3, being determined by the diffusion annihilation rate at t<10−5 s. To eliminate the contradiction with experimental upper limits some mechanism similar to quark confinement should forbid free monopole existence.}
}

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}

@article{PhysRevD.68.123512,
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}

@article{NOJIRI20171,
title = {Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution},
journal = {Physics Reports},
volume = {692},
pages = {1-104},
year = {2017},
note = {Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution},
issn = {0370-1573},
doi = {https://doi.org/10.1016/j.physrep.2017.06.001},
url = {https://www.sciencedirect.com/science/article/pii/S0370157317301527},
author = {S. Nojiri and S.D. Odintsov and V.K. Oikonomou},
abstract = {We systematically review some standard issues and also the latest developments of modified gravity in cosmology, emphasizing on inflation, bouncing cosmology and late-time acceleration era. Particularly, we present the formalism of standard modified gravity theory representatives, like F(R), F(G) and F(T) gravity theories, but also several alternative theoretical proposals which appeared in the literature during the last decade. We emphasize on the formalism developed for these theories and we explain how these theories can be considered as viable descriptions for our Universe. Using these theories, we present how a viable inflationary era can be produced in the context of these theories, with the viability being justified if compatibility with the latest observational data is achieved. Also we demonstrate how bouncing cosmologies can actually be described by these theories. Moreover, we systematically discuss several qualitative features of the dark energy era by using the modified gravity formalism, and also we critically discuss how a unified description of inflation with dark energy era can be described by solely using the modified gravity framework. Finally, we also discuss some astrophysical solutions in the context of modified gravity, and several qualitative features of these solutions. The aim of this review is to gather the different modified gravity techniques and form a virtual modified gravity “toolbox”, which will contain all the necessary information on inflation, dark energy and bouncing cosmologies in the context of the various forms of modified gravity.}
}

@article{DeFelice:2010aj,
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}

@article{STOJKOVIC2005251,
title = {A black hole solution to the cosmological monopole problem},
journal = {Physics Letters B},
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year = {2005},
issn = {0370-2693},
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url = {https://www.sciencedirect.com/science/article/pii/S0370269304016752},
author = {Dejan Stojkovic and Katherine Freese},
abstract = {We propose a solution to the cosmological monopole problem: primordial black holes, produced in the early universe, can accrete magnetic monopoles before the relics dominate the energy density of the universe. These small black holes quickly evaporate and thereby convert most of the monopole energy density into radiation. We estimate the range of parameters for which this solution is possible: under very conservative assumptions we find that the black hole mass must be less than 109 g.}
}

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}

@article{10.1093/mnras/177.1.51,
    author = {Lin, D. N. C. and Carr, B. J. and Fall, S. M.},
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    abstract = "{It is shown that the Einstein equations permit solutions in which pressure effects cause a black hole to grow as fast as the universe if the equation of state is ‘ stiff ’ (p = µ). This is in contrast to the situation with any softer equation of state \\$(p=\\alpha \\mu ,\\,0\\leqslant\\alpha \\lt \\text\\{I\\})\\$, when a black hole cannot grow very much. If the universe is stiff until some time t*, this means that any primordial black holes either formed before then or fed into the universe ab initio will just grow to the horizon size at t*. This implies a lower limit on the mass of a primordial black hole of \\$\\{10\\}^\\{15\\}\\times (\\{t\\}\_\\{*\\}/\\{10\\}^\\{-23\\}\\,\\text\\{s\\})\\, \\text\\{g\\}.\\$ If t* exceeds 10-23s, no primordial black holes could have evaporated by now through the Hawking process. Thus the strong observational limits on the number of 1015 g black holes would no longer exclude the possibility that primordial black holes have a critical density. If the stiff era is extended for as long as possible \\$(\\{t\\}\_\\{*\\}\\,\\sim \\,\\{10\\}^\\{-4\\}\\text\\{s\\})\\$, there could be a concentration of primordial black holes with mass around 1 M⊙. This would favour Meszaros' model of galaxy formation, in which galaxies form from the overdensities associated with the statistical excess of 1 M⊙ black holes in some regions.}",
    issn = {0035-8711},
    doi = {10.1093/mnras/177.1.51},
    url = {https://doi.org/10.1093/mnras/177.1.51},
    eprint = {https://academic.oup.com/mnras/article-pdf/177/1/51/9333365/mnras177-0051.pdf},
}

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        title = "{On the growth of primordial black holes}",
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     keywords = {Astrophysics, Black Holes (Astronomy), Stellar Evolution, Equations Of State, Mass Spectra, Stellar Mass Accretion, Universe, Astrophysics},
         year = 1981,
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       adsurl = {https://ui.adsabs.harvard.edu/abs/1981A&A....94..306B},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{PhysRevD.58.023504,
  title = {Evolution of a primordial black hole population},
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  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.58.023504},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.58.023504}
}

@article{PhysRevD.66.063505,
  title = {Could supermassive black holes be quintessential primordial black holes?},
  author = {Bean, Rachel and Magueijo, Jo\~ao},
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  issue = {6},
  pages = {063505},
  numpages = {11},
  year = {2002},
  month = {Sep},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.66.063505},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.66.063505}
}

@article{PhysRevD.71.104009,
  title = {Upper limits on the size of a primordial black hole},
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  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.71.104009},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.71.104009}
}

@article{PhysRevD.71.104010,
  title = {Growth of primordial black holes in a universe containing a massless scalar field},
  author = {Harada, Tomohiro and Carr, B. J.},
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  year = {2005},
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  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.71.104010},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.71.104010}
}

@book{ryden2017introduction,
  title={Introduction to cosmology},
  author={Ryden, Barbara},
  year={2017},
  publisher={Cambridge University Press}
}

@article{PhysRevD.13.198,
  title = {Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole},
  author = {Page, Don N.},
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  doi = {10.1103/PhysRevD.13.198},
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}

@article{PhysRevD.60.063509,
  title = {Critical collapse and the primordial black hole initial mass function},
  author = {Green, Anne M. and Liddle, Andrew R.},
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  doi = {10.1103/PhysRevD.60.063509},
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}

@misc{poulter2019cmb,
      title={CMB constraints on ultra-light primordial black holes with extended mass distributions}, 
      author={Harry Poulter and Yacine Ali-Haïmoud and Jan Hamann and Martin White and Anthony G. Williams},
      year={2019},
      eprint={1907.06485},
      archivePrefix={arXiv},
      primaryClass={astro-ph.CO}
}
@ARTICLE{2019arXiv190706485P,
    author = {Poulter, Harry and Ali-Ha{\"\i}imoud, Yacine and Hamann, Jan and White, Martin and Williams, Anthony G.},
    title = "{CMB constraints on ultra-light primordial black holes with extended mass distributions}",
    journal = {arXiv e-prints},
    keywords = {Astrophysics - Cosmology and Nongalactic Astrophysics, High Energy Physics - Phenomenology},
    year = 2019,
    month = jul,
    eid = {arXiv:1907.06485},
    pages = {arXiv:1907.06485},
    doi = {10.48550/arXiv.1907.06485},
    archivePrefix = {arXiv},
    eprint = {1907.06485},
    primaryClass = {astro-ph.CO},
    url = {https://arxiv.org/abs/1907.06485}
}



@article{PhysRevLett.121.081306,
  title = {Primordial black holes from sound speed resonance during inflation},
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  year = {2018},
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  doi = {10.1103/PhysRevLett.121.081306},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.121.081306}
}

@article{PismaZhETF.20.430,
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    year = {1974},
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} 

@incollection{hawking1975particle,
  title={Particle creation by black holes},
  author={Hawking, Stephen W},
  booktitle={Euclidean quantum gravity},
  pages={167--188},
  year={1975},
  publisher={World Scientific},
  doi={10.1142/9789814539395_0011},
  url={https://doi.org/10.1142/9789814539395_0011}
}

@ARTICLE{1974Natur.248...30H,
  author = {Hawking, S.~W.},
  title = "{Black hole explosions?}",
  journal = {Nature},
  year = 1974,
  month = mar,
  volume = {248},
  number = {5443},
  pages = {30-31},
  doi = {10.1038/248030a0},
  url = {https://www.nature.com/articles/248030a0}
}

@article{Carr_2021,
doi = {10.1088/1361-6633/ac1e31},
url = {https://dx.doi.org/10.1088/1361-6633/ac1e31},
year = {2021},
month = {dec},
publisher = {IOP Publishing},
volume = {84},
number = {11},
pages = {116902},
author = {Bernard Carr and Kazunori Kohri and Yuuiti Sendouda and Jun’ichi Yokoyama},
title = {Constraints on primordial black holes},
journal = {Reports on Progress in Physics},
abstract = {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 to 1050 g. Those smaller than ∼1015 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 γ-ray and cosmic ray backgrounds and the possible generation of stable Planck mass relics. PBHs larger than ∼1015 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 dark matter (DM) 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 μ-distortions arising from the effect of acoustic reheating on the CMB, if PBHs are created from the high-σ 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 DM, the LIGO/Virgo coalescences and the seeds for cosmic structure. Even if PBHs make a small contribution to the DM, they could play an important cosmological role and provide a unique probe of the early Universe.}
}

@article{PhysRev.119.1743,
  title = {Maximal extension of schwarzschild metric},
  author = {Kruskal, M. D.},
  journal = {Phys. Rev.},
  volume = {119},
  issue = {5},
  pages = {1743--1745},
  numpages = {0},
  year = {1960},
  month = {Sep},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRev.119.1743},
  url = {https://link.aps.org/doi/10.1103/PhysRev.119.1743}
}

@ARTICLE{1973CMaPh..31..161B,
       author = {Bardeen, J.~M. and Carter, B. and Hawking, S.~W.},
        title = "{The four laws of black hole mechanics}",
      journal = {Communications in Mathematical Physics},
         year = 1973,
        month = jun,
       volume = {31},
       number = {2},
        pages = {161-170},
          doi = {10.1007/BF01645742},
       url = {https://doi.org/10.1007/BF01645742}
}

@ARTICLE{1975CMaPh..43..199H,
       author = {Hawking, S.~W.},
        title = "{Particle creation by black holes}",
      journal = {Communications in Mathematical Physics},
         year = 1975,
        month = aug,
       volume = {43},
       number = {3},
        pages = {199-220},
          doi = {10.1007/BF02345020},
       adsurl = {https://doi.org/10.1007/BF02345020}
}

@BOOK{1995iqft.book.....P,
  author = {Peskin, Michael E. and Schroeder, Daniel V.},
  title = "{An introduction to quantum field theory}",
  year = 1995,
  publisher = {Westview Press},
  url = {https://ui.adsabs.harvard.edu/abs/1995iqft.book.....P}
}


@book{QFTN2022,
    author = {徐一鸿},
    translator={超理汉化组},
    title = {果壳中的量子场论},
    isbn = {9787312051890},
    publisher = {中国科学技术大学出版社},
    month = {2月},
    year = {2022},
    language={zh}
}

@book{ZJYQM,
    author = {{曾谨言}},
    title = {量子力学(卷1)(第五版)},
    isbn = {9787030387226},
    publisher = {科学出版社},
    month = {10月},
    year = {2013},
    language={zh}
}

@ARTICLE{1970A&A.....5..184H,
       author = {Hagedorn, R.},
        title = "{Thermodynamics of strong interactions at high energy and its consequences for astrophysics}",
      journal = {Astronomy and Astrophysics},
         year = 1970,
        month = apr,
       volume = {5},
        pages = {184},
       adsurl = {https://ui.adsabs.harvard.edu/abs/1970A&A.....5..184H},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{PhysRevD.98.123016,
  title = {Fast radio bursts from primordial black hole binaries coalescence},
  author = {Deng, Can-Min and Cai, Yifu and Wu, Xue-Feng and Liang, En-Wei},
  journal = {Phys. Rev. D},
  volume = {98},
  issue = {12},
  pages = {123016},
  numpages = {7},
  year = {2018},
  month = {Dec},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.98.123016},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.98.123016}
}

@article{PhysRevD.103.123030,
  title = {Earth-mass primordial black hole mergers as sources for nonrepeating fast radio bursts},
  author = {Deng, Can-Min},
  journal = {Phys. Rev. D},
  volume = {103},
  issue = {12},
  pages = {123030},
  numpages = {9},
  year = {2021},
  month = {Jun},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.103.123030},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.103.123030}
}