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REVIEW 4 major objections 5 minor 64 references

BBN-simple: How to Bake a Universe-Sized Cake

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A simple, from-scratch, twelve-reaction code reproduces the Big Bang's light-element abundances, with helium-4 good to about a percent and deuterium and helium-3 to a few percent.

desk verdict A genuinely useful pedagogical BBN code with an overstated accuracy claim and a typoed pressure integral; fix those and it's a solid teaching paper. read the letter →

arxiv 2412.07893 v2 pith:Q6VD2ZRB submitted 2024-12-10 astro-ph.CO

Aidan Meador-Woodruff , Dragan Huterer This is my paper · ORCID
classification astro-ph.CO
keywords BigBangnucleosynthesislightelementabundances12-reactionnetworkstiffODEintegrationneutrinodecouplinghelium-4massfractiondeuteriumabundancebaryon-to-photonratio
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to show that a deliberately simple, from-scratch numerical treatment of Big Bang nucleosynthesis can reproduce the observed light-element abundances well enough for practical cosmology. The setup uses standard early-universe thermodynamics, a twelve-reaction nuclear network, and a fixed effective number of relativistic species, and is pitched at an advanced undergraduate or beginning graduate level. The fiducial calculation puts helium-4 within about a percent of four established public codes, deuterium and helium-3 within a few percent, and tritium within about ten percent. The point of the exercise is pedagogical: a student who writes this code learns the physics by building it, rather than treating a professional package as a black box.

What carries the argument

The load-bearing object is the twelve-reaction network of Box 2: one weak-interaction block for the six neutron-proton reactions, plus eleven charged-particle and radiative-capture reactions linking deuterium, tritium, helium-3, helium-4, lithium-7, and beryllium-7, with the forward rates taken from a publicly compiled reaction-rate database and reverse rates reconstructed from detailed balance. The evolution equations are the coupled mass-fraction ODEs (Eq. (49)), which are stiff because reaction rates and temperatures span many orders of magnitude; the paper demonstrates that an implicit integration method is required, while common explicit methods fail even with very small steps. The weak rates use the integrals in Eqs. (28)-(29) evaluated by Gaussian quadrature with 64 points, giving a nearly constant 0.5% accuracy over the BBN temperature range. The temperature-time relation uses a fixed effective relativistic degree count $g_* \simeq 9.2$ throughout the BBN epoch, following earlier treatments.

What would settle it

Run the same code with a time-dependent $g_*(T)$ and the full modern reaction set, and compare the resulting helium-4, deuterium, and helium-3 abundances to the values in Table I; if any species moves by more than about a percent (helium-4) or a few percent (deuterium and helium-3), the claim of reasonably good agreement weakens. A minimal version of that test is to change only the fixed $g_* \simeq 9.2$ to the exact evolving effective degree count and see whether D/H moves from $2.152\times 10^{-5}$ toward the modern-code value near $2.46\times 10^{-5}$.

Watch

Extended reading notes

Core claim

The central discovery is that a full precision BBN network is not needed to get the main answers: twelve reactions, solved as a stiff system of mass-fraction equations, reproduce the principal light-element abundances in the standard cosmological model. Starting from nuclear statistical equilibrium at high temperature, the calculation tracks weak neutron-proton conversion through the integrals of Eqs. (28)-(29), then evolves the fusion chain from deuterium up to beryllium. With $\eta_b = 6.12\times 10^{-10}$, $N_{\rm eff} = 3.046$, and $\tau_n = 880.2$ s, the code returns a hydrogen mass fraction of 0.7565, helium-4 $Y_p = 0.2434$, $D/H = 2.152\times 10^{-5}$, $^3{\rm He}/H = 0.945\times 10^{-5}$, $T/H = 7.337\times 10^{-8}$, and $(^7{\rm Be} + {}^7{\rm Li})/H = 5.207\times 10^{-10}$. Against the four public codes, the helium-4 prediction agrees to about a percent, deuterium and helium-3 to a few percent, and tritium to within roughly ten percent. The authors additionally show that the weak-interaction rates can be evaluated by Gaussian quadrature with about 0.5% accuracy, and that the final abundances are not strongly sensitive to that choice.

Load-bearing premise

The load-bearing premise is that a twelve-reaction network combined with one fixed value of the effective number of relativistic species ($g_* \simeq 9.2$) captures the abundance evolution well enough, so that every reaction left out and every approximation in the expansion history shifts the final abundances by less than the quoted few-percent agreement.

Editorial extensions

If this is right

  • A student or beginning researcher can write a working BBN code from scratch, following the paper's steps, and obtain abundances that are quantitatively usable rather than merely schematic.
  • Because the abundances respond sharply to the baryon-to-photon ratio and to the expansion rate, the simple code can illustrate how measurements of deuterium and helium-4 constrain $\Omega_b h^2$ and $N_{\rm eff}$.
  • The weak-rate evaluation can be chosen freely between the polynomial fit and Gaussian quadrature without materially changing the final abundances, since the two differ by only about 0.5% in the final results.
  • Adopting modern experimentally measured reaction rates would bring the simple network even closer to the precision codes, since the paper identifies the rate inputs as the main place where accuracy is currently lost.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A reader wanting to test the paper's accuracy ceiling could rerun the fiducial calculation with a time-dependent $g_*(T)$ instead of the fixed value; the comparison table suggests this is the most likely source of the roughly 12% shortfall in deuterium and helium-3 relative to the modern codes.
  • The same twelve-reaction code could be used as a hands-on probe of new physics: raising or lowering $N_{\rm eff}$ shifts helium-4 and deuterium in opposite directions, giving students a direct feel for how BBN constrains extra relativistic species.
  • Since helium-4 already comes out at the percent level with so few reactions, the dominant physics of primordial helium is evidently set by the neutron-proton freeze-out ratio and the deuterium bottleneck; a simplified analytic model built on just those two ingredients might predict $Y_p$ without solving any network.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper presents BBN-simple, a from-scratch, pedagogical numerical Big Bang Nucleosynthesis code intended for advanced undergraduates or beginning graduate students. The authors derive the early-universe thermodynamics (time-temperature relation, neutrino decoupling), the weak proton-neutron rates, and a 12-reaction nuclear network using ReacLib rates, then integrate the stiff abundance equations. They compare their final abundances for H, 4He, D, 3He, T, and 7Li+7Be with Kawano, PRIMAT, AlterBBN, and PArthENoPE for a standard set of cosmological inputs. The central claim is that the simplified calculation achieves "reasonably good agreement" with the precision codes: about a percent for helium-4, a few percent for deuterium and helium-3, and within 10% for tritium.

Significance. If the presentation were fully corrected, this would be a genuinely useful educational contribution: it walks through a complete BBN calculation with explicit numerical methods, uses public reaction-rate databases, and makes the code available, without tuning any parameter to match the final abundances. The comparison table is a valuable benchmark for students. However, the quantitative accuracy claims are materially overstated by the paper's own table, and several equations in the derivation need correction. The paper is not a precision BBN code and should not be advertised as one; its value is pedagogical, and the accuracy discussion should be revised to match that framing.

major comments (4)
  1. [Section IV, Table I] The statement that deuterium and helium-3 are accurate to a few percent is not supported by Table I. Relative to PRIMAT, D/H is 12.5% low (2.152e-5 vs 2.459e-5) and 3He/H is 11.3% low (0.945e-5 vs 1.066e-5); deviations from the other codes are similar or larger (D/H 11-16% low, 3He/H 8-11% low). The 4He claim (about a percent) is acceptable, and T/H is within or close to 10% depending on the reference code, but the few-percent claim for D and 3He should be replaced by a quantitative statement of the actual spread. The same correction is needed in the concluding sentence that describes "percent-level" agreement for deuterium and helium-3.
  2. [Equation (20)] The electron/positron pressure integral is written with a y^2 factor in the integrand. Dimensional analysis, and the derivation from Eq. (16), give y^4 / sqrt(x^2 + y^2) in the integrand with the same prefactor. As printed, Eq. (20) would produce a pressure with the wrong scaling and would corrupt the T_gamma/T_nu relation in Eq. (9) and hence the expansion history. Please correct the equation and verify that the code evaluates the y^4 form.
  3. [Equations (43)-(48)] The conversion from number-density equations to mass-fraction equations omits the necessary mass-number factors. With X_i = A_i N_i / N_b (Eq. 24), applying Eq. (38) gives dX_i/dt = rho_b N_A [ X_i X_j / A_j <sigma v>_{ij,kl} - A_i X_k X_l / (A_k A_l) <sigma v>_{kl,ij} ] (up to identical-particle factors), not the A-free expression in Eq. (48). As written, the network equations do not conserve baryon mass; for example, the D-production term in p+n -> D+gamma is off by a factor A_D/(A_p A_n) = 2. Please either define the bracket rates to absorb these factors or amend the equations, and confirm which form the code actually implements.
  4. [Equation (51)] The worked proton equation for the reaction p+n <-> D+gamma appears to have the forward and reverse terms interchanged. With the notation [np]_{Dgamma} for the forward p+n -> D+gamma rate and [Dgamma]_{np} for the reverse, the proton equation should read -X_p X_n [np]_{Dgamma} + X_D [Dgamma]_{np}. The printed equation contains -X_D [np]_{Dgamma} + X_p X_n [Dgamma]_{np}, which describes the opposite effect: it destroys D and creates protons through the reverse reaction while destroying protons through the forward reaction. This typo/error should be corrected, and the same check applied to the corresponding terms in the code.
minor comments (5)
  1. [Equation (36)] The prefactor in the thermal averaging formula is printed with an exponent 2; the standard expression is (8/(pi mu))^{1/2}, not squared. Please check the typesetting of this equation.
  2. [Section II.B] There is a typo in the sentence "for a a simple accounting of the relativistic degrees of freedom," which should read "for a simple accounting."
  3. [Section IV summary bullet] The summary bullet says "Set up the weak rates between the photons and neutrons"; this should presumably read "between the protons and neutrons."
  4. [Section II.A] The fixed value g_* ~ 9.2 is adopted without an estimate of the systematic error it introduces in the time-temperature relation and hence in all abundances. Since the paper claims specific accuracy levels, a sentence quantifying this approximation would strengthen the accuracy discussion.
  5. [Table I and text] The code name PRIMAT is spelled inconsistently as "Primat" in Table I and "PRIMAT" elsewhere; please standardize the capitalization.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: BBN-simple is a forward simulation using external reaction rates and standard inputs; the overstated agreement in Sec. IV is an accuracy issue, not circular reasoning.

full rationale

The derivation chain is self-contained in the sense that no abundance result is fed back into the calculation as an input or fitted parameter. The weak-interaction normalization K is set to the inverse neutron lifetime ("K is the normalization constant set so that these integrals asymptote at late (post-BBN) times to the inverse of the neutron decay lifetime, 1/tau"), an external PDG input, not tuned to match the comparison codes. Nuclear rates come from ReacLib ("All the reactions between nuclei were taken from the ReacLib database"), and the baryon-to-photon ratio is adopted from Planck, not from a fit to the final abundances. The comparison to Kawano, PRIMAT, AlterBBN, and PArthENoPE is an independent benchmark. The only self-citation is the co-author's textbook [49], used for standard background material (natural units, neutrino decoupling, Saha/NSE expressions), which is not load-bearing and does not import an unverified premise. There is an internal accuracy inconsistency: the text claims deuterium and helium-3 agree to "a few percent," while Table I shows D/H and 3He/H about 11-12% below PRIMAT; this is a correctness/quantitative-claims problem, not circularity. Likewise, Eq. (20) appears to have a dimensional typo in the pressure integrand, but that would be a computational bug, not a circular step. Overall, the central claim is a forward prediction with external, independently sourced inputs, so the circularity burden is minimal.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The calculation rests on standard early-universe thermodynamics (Friedmann equations, radiation density), nuclear statistical equilibrium for initial conditions, the 12-reaction network, and external nuclear rates from ReacLib. No new physics is introduced. The main free parameter is the fixed g_* approximation.

free parameters (2)
  • Effective relativistic degrees of freedom g_* = 9.2 (approximation)
    Assumed constant during BBN following prior work [8,37]; used in the time-temperature relation Eq. (6)-(8). This approximation neglects the change in g_* during e± annihilation, which affects the expansion rate.
  • Weak-rate normalization constant K = Set so rates asymptote to 1/τ_n (τ_n=880.2 s)
    In Eq. (28), K is chosen to match the neutron decay lifetime, an external input. This is a calibration, not a fit to the final abundances.
assumptions (6)
  • domain assumption Friedmann equations with radiation-dominated expansion
    Used to derive dT/dt in Eq. (4) and the T-t relation Eq. (6).
  • domain assumption Nuclear statistical equilibrium (Saha) initial abundances
    Sets initial Xi at T >> 1 MeV via Eq. (23).
  • ad hoc to paper The 12-reaction network captures the principal BBN pathways
    Box 2 lists only 12 reactions; the paper argues these are sufficient for the tracked species. Missing reactions could affect abundances.
  • domain assumption Weak rates in Eq. (28)-(29) neglect nuclear recoil and QED corrections
    Footnote 5 notes this approximation can cause a 2% underestimate of 4He.
  • domain assumption Electron chemical potential xi_e = 0
    Stated in Sec. III.B after Eq. (28).
  • domain assumption ReacLib reaction rates are used without uncertainties
    Stated in Sec. III.D: 'ignore any uncertainties in them'.

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Cite this review

Pith. "Pith review of BBN-simple: How to Bake a Universe-Sized Cake." pith.science (2026). https://pith.science/paper/Q6VD2ZRB

@misc{pith2026241207893,
  author       = {Pith},
  title        = {Pith review of: BBN-simple: How to Bake a Universe-Sized Cake},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q6VD2ZRB}},
  note         = {Machine review of arXiv:2412.07893}
}
read the original abstract

Big Bang Nucleosynthesis (BBN), the process of creation of lightest elements in the early universe, is a highly robust, precise, and ultimately successful theory that forms one of the three pillars of the standard hot-Big-Bang cosmological model. Existing theoretical treatments of BBN and the associated computer codes are accurate and flexible, but are typically highly technical and opaque, and not suitable for pedagogical understanding of the BBN. Here we present BBN-simple -- a from-scratch numerical calculation of the lightest element abundances pitched at an advanced undergraduate or beginning graduate level. We review the physics of the early universe relevant for BBN, provide information about the reaction rates, and discuss computational-mathematics background that is essential in setting up a BBN calculation. We calculate the abundances of the principal nuclear species in a standard cosmological model, and find a reasonably good agreement with public precision-level BBN codes.

Figures

Figures reproduced from arXiv: 2412.07893 by the authors.

Figure 1
Figure 1. FIG. 1. Neutrino and photon temperatures as a function of [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Proton-neutron weak interactions and their effects. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Abundances of the elements created during BBN, produced using [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

64 extracted references · 39 canonical work pages

  1. [1]

    looking ahead

    Nuclear Cross-Sections The reaction rates governing the evolution of nuclear species are essential for calculating BBN abundances, yet they are not directly measurable (as that would require doing experiments in a gas with temperatureT∼ 109 K), nor can they be predicted from theory alone. Therefore, some combination of experimental and theoretical treat- ...

    work page

  2. [2]

    radiative capture

    Assembling the Network Consider the general two-body nuclear reaction; it in- volves four species, labeledi,j,k andl, wherei andj are the reactants andk andl are the products. This reaction can be organizationally expressed as i +j ⇋k +l. (37) The rate of change of the number density of one of these species, sayNi, can be expressed as dNi dt =NiNj⟨σv⟩ij,k...

    work page

  3. [3]

    R. A. Alpher and R. Herman, Evolution of the Universe, Nature 162, 774 (1948)

    work page 1948

  4. [4]

    R. A. Alpher, H. Bethe, and G. Gamow, The origin of chemical elements, Phys. Rev.73, 803 (1948)

    work page 1948

  5. [5]

    Gamow, The Evolution of the Universe, Nature162, 680 (1948)

    G. Gamow, The Evolution of the Universe, Nature162, 680 (1948)

    work page 1948

  6. [6]

    R. A. Alpher, J. W. Follin, and R. C. Herman, Physical Conditions in the Initial Stages of the Expanding Uni- verse, Phys. Rev.92, 1347 (1953)

    work page 1953

  7. [7]

    R. A. Alpher, A Neutron-Capture Theory of the Forma- tion and Relative Abundance of the Elements, Phys. Rev. 74, 1577 (1948)

    work page 1948

  8. [8]

    Hayashi, Proton-Neutron Concentration Ratio in the Expanding Universe at the Stages preceding the Forma- tion of the Elements, Prog

    C. Hayashi, Proton-Neutron Concentration Ratio in the Expanding Universe at the Stages preceding the Forma- tion of the Elements, Prog. Theor. Phys.5, 224 (1950)

    work page 1950

Show all 64 references
  1. [9]

    freeze-out

    Similarly, the photon pressure and energy density obey the familiar relationship Pγ = 1 3ργ. (12) For non-degenerate neutrino species, the expression for their energy density is similarly given by ρν = 7 8 π2 15NeffT 4 ν (13) where g = 7/8 is the effective number of relativist...

  2. [10]

    M. S. Turner, KICP/UChicago, and T. K. Foundation, Understanding BBN: the physics and its history, (2021), arXiv:2111.14254 [astro-ph.CO]

    2021 arXiv

  3. [11]

    R. V. Wagoner, W. A. Fowler, and F. Hoyle, On the Synthesis of Elements at Very High Temperatures, ApJ 148, 3 (1967)

    1967

  4. [12]

    P. J. E. Peebles, Primordial Helium Abundance and the Primordial Fireball. 2, Astrophys. J.146, 542 (1966)

    1966

  5. [13]

    W. A. Fowler, G. R. Caughlan, and B. A. Zimmerman, Thermonuclear Reaction Rates, Ann. Rev. Astron. As- troph. 5, 525 (1967)

    1967

  6. [14]

    W. A. Fowler, G. R. Caughlan, and B. A. Zimmerman, Thermonuclear Reaction Rates, II, Ann. Rev. Astron. Astroph. 13, 69 (1975)

    1975

  7. [15]

    M. J. Harris, W. A. Fowler, G. R. Caughlan, and B. A. Zimmerman, Thermonuclear reaction rates, III., Ann. Rev. Astron. Astroph.21, 165 (1983)

    1983

  8. [16]

    G. R. Caughlan, W. A. Fowler, M. J. Harris, and B. A. Zimmerman,TablesofThermonuclearReactionRatesfor Low-Mass Nuclei (1≤ Z≤ 14), Atomic Data and Nu- clear Data Tables32, 197 (1985)

    1985

  9. [17]

    G. R. Caughlan and W. A. Fowler, Thermonuclear Re- action Rates V, Atomic Data and Nuclear Data Tables 40, 283 (1988)

    1988

  10. [18]

    C. J. Copi, D. N. Schramm, and M. S. Turner, Big bang nucleosynthesis and the baryon density of the universe, Science 267, 192 (1995), arXiv:astro-ph/9407006

    1995 arXiv

  11. [19]

    K. A. Olive, G. Steigman, and T. P. Walker, Primordial nucleosynthesis: Theory and observations, Phys. Rept. 333, 389 (2000), arXiv:astro-ph/9905320

    2000 arXiv

  12. [20]

    T. P. Walker, G. Steigman, D. N. Schramm, K. A. Olive, and H.-S. Kang, Primordial nucleosynthesis redux, As- trophys. J. 376, 51 (1991)

    1991

  13. [21]

    R. H. Cyburt, B. D. Fields, K. A. Olive, and T.-H. Yeh, Big Bang Nucleosynthesis: 2015, Rev. Mod. Phys. 88, 015004 (2016), arXiv:1505.01076 [astro-ph.CO]

    2016 arXiv

  14. [22]

    E. W. Kolb and M. S. Turner, The Early Universe , Vol. 69 (1990)

    1990

  15. [23]

    R. E. Lopez and M. S. Turner, An Accurate Calcula- tion of the Big Bang Prediction for the Abundance of Primordial Helium, Phys. Rev. D 59, 103502 (1999), arXiv:astro-ph/9807279

    1999 arXiv

  16. [24]

    Burles, K

    S. Burles, K. M. Nollett, J. W. Truran, and M. S. Turner, Sharpening the predictions of big bang nucle- osynthesis, Phys. Rev. Lett.82, 4176 (1999), arXiv:astro- ph/9901157

    1999

  17. [25]

    Burles, K

    S. Burles, K. M. Nollett, and M. S. Turner, What is the BBN prediction for the baryon density and how reli- able is it?, Phys. Rev. D63, 063512 (2001), arXiv:astro- ph/0008495

    2001

  18. [26]

    Burles, K

    S. Burles, K. M. Nollett, and M. S. Turner, Big bang nu- cleosynthesis predictions for precision cosmology, Astro- phys. J. Lett.552, L1 (2001), arXiv:astro-ph/0010171

    2001 arXiv

  19. [27]

    E. G. Adelberger et al. , Solar fusion cross sections II: the pp chain and CNO cycles, Rev. Mod. Phys.83, 195 (2011), arXiv:1004.2318 [nucl-ex]

    2011 arXiv

  20. [28]

    Pettini and D

    M. Pettini and D. V. Bowen, A new measurement of the primordial abundance of deuterium: toward convergence with the baryon density from the cmb?, Astrophys. J. 560, 41 (2001), arXiv:astro-ph/0104474

    2001 arXiv

  21. [29]

    Fumagalli, J

    M. Fumagalli, J. M. O’Meara, and J. X. Prochaska, De- tection of Pristine Gas Two Billion Years after the Big Bang, Science 334, 1245 (2011), arXiv:1111.2334 [astro- ph.CO]

    2011 arXiv

  22. [30]

    Noterdaeme, S

    P. Noterdaeme, S. Lopez, V. Dumont, C. Ledoux, P. Mo- laro, and P. Petitjean, Deuterium at high-redshift: Pri- mordial abundance in the zabs = 2.621 damped Ly-alpha system towards CTQ247, Astron. Astrophys. 542, L33 (2012), arXiv:1205.3777 [astro-ph.CO]

    2012 arXiv

  23. [31]

    Y. I. Izotov, T. X. Thuan, and N. G. Guseva, A new de- termination of the primordial He abundance using the He iλ10830Åemissionline: cosmologicalimplications,Mon. Not. Roy. Astron. Soc.445, 778 (2014), arXiv:1408.6953 [astro-ph.CO]

    2014 arXiv

  24. [32]

    E. Aver, K. A. Olive, and E. D. Skillman, The effects of He Iλ10830 on helium abundance determinations, JCAP 07, 011, arXiv:1503.08146 [astro-ph.CO]

    arXiv

  25. [33]

    R. J. Cooke, M. Pettini, and C. C. Steidel, One Percent Determination of the Primordial Deuterium Abundance, Astrophys. J. 855, 102 (2018), arXiv:1710.11129 [astro- ph.CO]

    2018 arXiv

  26. [34]

    Mossaet al., The baryon density of the Universe from an improved rate of deuterium burning, Nature587, 210 (2020)

    V. Mossaet al., The baryon density of the Universe from an improved rate of deuterium burning, Nature587, 210 (2020)

    2020

  27. [35]

    K. M. Nollett and G. P. Holder, An analysis of con- straints on relativistic species from primordial nucleosyn- thesis and the cosmic microwave background, (2011), arXiv:1112.2683 [astro-ph.CO]

    2011 arXiv

  28. [36]

    Schöneberg, The 2024 BBN baryon abundance up- date, JCAP 06, 006, arXiv:2401.15054 [astro-ph.CO]

    N. Schöneberg, The 2024 BBN baryon abundance up- date, JCAP 06, 006, arXiv:2401.15054 [astro-ph.CO]

    2024

  29. [37]

    Iocco, G

    F. Iocco, G. Mangano, G. Miele, O. Pisanti, and P. D. Serpico, Primordial Nucleosynthesis: from precision cos- mology to fundamental physics, Phys. Rept. 472, 1 (2009), arXiv:0809.0631 [astro-ph]. 16

    2009 arXiv

  30. [38]

    Jedamzik and M

    K. Jedamzik and M. Pospelov, Big Bang Nucleosynthe- sis and Particle Dark Matter, New J. Phys.11, 105028 (2009), arXiv:0906.2087 [hep-ph]

    2009 arXiv

  31. [39]

    Pospelov and J

    M. Pospelov and J. Pradler, Big Bang Nucleosynthesis as a Probe of New Physics, Ann. Rev. Nucl. Part. Sci.60, 539 (2010), arXiv:1011.1054 [hep-ph]

    2010 arXiv

  32. [40]

    Kawano, Let’s go: Early universe

    L. Kawano, Let’s go: Early universe. 2. Primordial nu- cleosynthesis: The Computer way, (1992)

    1992

  33. [41]

    Arbey, AlterBBN: A program for calculating the BBN abundances of the elements in alternative cos- mologies, Comput

    A. Arbey, AlterBBN: A program for calculating the BBN abundances of the elements in alternative cos- mologies, Comput. Phys. Commun. 183, 1822 (2012), arXiv:1106.1363 [astro-ph.CO]

    2012 arXiv

  34. [42]

    Arbey, J

    A. Arbey, J. Auffinger, K. P. Hickerson, and E. S. Jenssen, AlterBBN v2: A public code for calculating Big-Bang nucleosynthesis constraints in alternative cos- mologies, Comput. Phys. Commun.248, 106982 (2020), arXiv:1806.11095 [astro-ph.CO]

    2020 arXiv

  35. [43]

    Pisanti, A

    O. Pisanti, A. Cirillo, S. Esposito, F. Iocco, G. Mangano, G. Miele, and P. D. Serpico, PArthENoPE: Public Al- gorithm Evaluating the Nucleosynthesis of Primordial Elements, Comput. Phys. Commun. 178, 956 (2008), arXiv:0705.0290 [astro-ph]

    2008 arXiv

  36. [44]

    Pitrou, A

    C. Pitrou, A. Coc, J.-P. Uzan, and E. Vangioni, Preci- sion big bang nucleosynthesis with improved Helium-4 predictions, Phys. Rept.754, 1 (2018), arXiv:1801.08023 [astro-ph.CO]

    2018 arXiv

  37. [45]

    T. M. C. Abbottet al. (DES), Dark Energy Survey Year 1 Results: A Precise H0 Estimate from DES Y1, BAO, and D/H Data, Mon. Not. Roy. Astron. Soc.480, 3879 (2018), arXiv:1711.00403 [astro-ph.CO]

    2018 arXiv

  38. [46]

    A. G. Adameet al. (DESI), DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations, (2024), arXiv:2404.03002 [astro-ph.CO]

    2024 arXiv

  39. [47]

    Di Valentino, O

    E. Di Valentino, O. Mena, S. Pan, L. Visinelli, W. Yang, A. Melchiorri, D. F. Mota, A. G. Riess, and J. Silk, In the realm of the Hubble tension—a review of solutions, Class. Quant. Grav.38, 153001 (2021), arXiv:2103.01183 [astro-ph.CO]

    2021 arXiv

  40. [48]

    Mukhanov,Physical Foundations of Cosmology (Cam- bridge University Press, Oxford, 2005)

    V. Mukhanov,Physical Foundations of Cosmology (Cam- bridge University Press, Oxford, 2005)

    2005

  41. [49]

    Esmailzadeh, G

    R. Esmailzadeh, G. D. Starkman, and S. Dimopoulos, Primordial nucleosynthesis without a computer, Astro- phys. J. 378, 504 (1991)

    1991

  42. [50]

    V. F. Mukhanov, Nucleosynthesis without a com- puter, Int. J. Theor. Phys.43, 669 (2004), arXiv:astro- ph/0303073

    2004

  43. [51]

    B. S. Ryden,Introduction to Cosmology (Cambridge Uni- versity Press, 2017)

    2017

  44. [52]

    Huterer,A Course in Cosmology (Cambridge Univer- sity Press, 2023)

    D. Huterer,A Course in Cosmology (Cambridge Univer- sity Press, 2023)

    2023

  45. [53]

    W. A. Fowler and F. Hoyle, Neutrino Processes and Pair Formation in Massive Stars and Supernovae., ApJS9, 201 (1964)

    1964

  46. [54]

    Chandrasekhar,Principles of stellar dynamics (1942)

    S. Chandrasekhar,Principles of stellar dynamics (1942)

    1942

  47. [55]

    Dodelson and F

    S. Dodelson and F. Schmidt,Modern Cosmology (2020)

    2020

  48. [56]

    P. A. Zylaet al. (Particle Data Group), Review of Par- ticle Physics, PTEP2020, 083C01 (2020)

    2020

  49. [57]

    R. H. Cyburt, A. M. Amthor, R. Ferguson, Z. Meisel, K. Smith, S. Warren, A. Heger, R. D. Hoffman, T. Rauscher, A. Sakharuk, H. Schatz, F. K. Thielemann, and M. Wiescher, The jina reaclib database: Its recent updates and impact on type-i x-ray bursts, The Astro- physical Journa...

    2010

  50. [58]

    M. S. Smith, L. H. Kawano, and R. A. Malaney, Exper- imental, Computational, and Observational Analysis of Primordial Nucleosynthesis, ApJS85, 219 (1993)

    1993

  51. [59]

    R. J. Scherrer, Primordial element production in uni- verses with large lepton-baryon ratio, MNRAS205, 683 (1983)

    1983

  52. [60]

    Arnett, Supernovae and Nucleosynthesis: An Investi- gation of the History of Matter, from the Big Bang to the Present (Princeton University Press, 1996)

    D. Arnett, Supernovae and Nucleosynthesis: An Investi- gation of the History of Matter, from the Big Bang to the Present (Princeton University Press, 1996)

    1996

  53. [61]

    Rolfs and W

    C. Rolfs and W. Rodney, Cauldrons in the Cosmos (1988)

    1988

  54. [62]

    L. M. Krauss and P. Romanelli, Big Bang Nucleosynthe- sis: Predictions And Uncertainties, Astrophys. J. 358, 47 (1990)

    1990

  55. [63]

    Angulo, M

    C. Angulo, M. Arnould, M. Rayet, P. Descouvemont, D. Baye, C. Leclercq-Willain, A. Coc, S. Barhoumi, P. Aguer, C. Rolfs, R. Kunz, J. Hammer, A. Mayer, T. Paradellis, S. Kossionides, C. Chronidou, K. Spyrou, S. Degl’Innocenti, G. Fiorentini, B. Ricci, S. Zavatarelli, C. Provide...

    1999

  56. [64]

    Aghanim et al

    N. Aghanim et al. (Planck), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

    2020 arXiv

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