Pith.

Astrophysics · arXiv:astro-ph/0408076 v3 · submitted 4 Aug 2004 · 194 references

Nuclear Reaction Network for Primordial Nucleosynthesis: a detailed analysis of rates, uncertainties and light nuclei yields

P.D. Serpico, S. Esposito, F. Iocco, G. Mangano, G. Miele, O. Pisanti

PDF · arXiv · The abstract, sentence by sentence · Cite

The paper says

“We analyze in details the standard Primordial Nucleosynthesis scenario. In particular we discuss the key theoretical issues which are involved in a detailed prediction of light nuclide abundances, as the weak reaction rates, neutrino decoupling and nuclear rate modeling.”

more of the abstract

We also perform a new analysis of available data on the main nuclear processes entering the nucleosynthesis reaction network, with particular stress on their uncertainties as well as on their role in determining the corresponding uncertainties on light nuclide theoretical estimates. The current status of theoretical versus experimental results for 2H, 3He, 4He and 7Li is then discussed using the determination of the baryon density as obtained from Cosmic Microwave Background anisotropies.

from the abstract

Pith says

Machine review · deepseek-v4.1-flash · 13 Nov 2026 · what was read was not recorded · not checked by a person

Reviewed in 2026 with later literature in view.

It can be wrong. Challenge this review or reply to it.

Holds up, with conditions. A genuinely useful BBN rate compilation, but its headline error-budget claims rest on an untested scale-error convention and a two-point linearization of a factor-10 rate. This line is wrong

3 major objections · 9 minor

How often objections from reviews like this one are right: not yet measured

Are you an author? What you can do.

Not checked: figures, code, what the 194 references say.

The paper says, at §3.3 (final paragraph), Tables 3 and 5–8

The review did not quote this passage.

Pith says: Objection 1 of 3 · major

The overall scale error for each reaction is set to 'the lowest experimentally determined ϵk for that reaction', and this single convention propagates into every entry of Appendix E and therefore into every number in Tables 3 and 5–8. The choice is defended on the grounds that combining several datasets should yield a better estimate with a smaller error, which is reasonable, but it is a convention and it is never varied.

more of objection 1

Because the headline comparison is precisely whether σii has fallen below σωb, the reader cannot tell how much of that conclusion is data and how much is the minimum-ϵk rule. A sensitivity scan is needed: repeat the propagation with the scale error set to the weighted mean and to the maximum of the quoted ϵk, and report how σii for 2H, 3He, 4He and 7Li shifts and whether the 'nuclear errors below ωb errors' statement survives. The paper already concedes in §4.2.3 that the reduction relative to [20] comes from dropping the 'large maximal error' used there, which is a change of convention rather than new data; quantifying the convention dependence would make that concession concrete.

The paper says, at §3.5.4, Eq. (E.37), Table 8, Eq. (4.10)

The review did not quote this passage.

Pith says: Objection 2 of 3 · major

The be7nα rate is adopted from Wagoner with a factor-10 uncertainty (Eq. E.37, δf ≈ 0.9f), and Table 8 assigns it 40.9% of the squared error on X7Li. That share is obtained with Eq. (4.10), which evaluates the yield only at Γ ± 1σ, i.e. a two-point central difference.

more of objection 2

Over a factor-10 range the response of X7Li to this rate is unlikely to be linear, and the paper's justification that the method is supported by the Central Limit Theorem does not obviously cover a single rate varied over an order of magnitude. The same concern applies, less severely, to αdγ, whose asymmetric temperature-dependent uncertainty (Eq. E.27) is entirely responsible for the 100% error quoted on 6Li. Please show the actual response curve X7Li(Γ_be7nα) over at least a factor of 3 in each direction, or replace the linearized estimate for these two rates with a direct scan or a small Monte Carlo, and report whether the 40.9% share and the quoted 8–10% total 7Li error are recovered.

The paper says, at §4.2.3 and §5 (7Li discussion)

The review did not quote this passage.

Pith says: Objection 3 of 3 · major

The paper states that the 7Li discrepancy is 'more severe than in our previous analysis in [20] because of the different treatment of nuclear rate errors', and elsewhere that X7Li is not used in the likelihood analysis. The 4σ statement is therefore a comparison whose severity is set by the same error convention flagged above, and it is presented in the Conclusions without that qualification attached.

more of objection 3

Either state explicitly, at the point where the 4σ is quoted, that the significance depends on the scale-error convention and give the value obtained under the alternative conventions of the first comment, or soften the claim to a range. This matters because the 7Li tension is the paper's most-quoted result and is routinely cited downstream as a fixed number of sigma.

9 minor objections

The paper says, at Appendix D(v) vs §3.4.5

Pith says: minor objection 1 of 9

The tdn fit in Eq. (D.5) uses a Lorentzian centred at 0.0479 MeV with width parameter 0.0392, whereas §3.4.5 quotes the 5He resonance at ER = 0.064 MeV with Γ = 0.076 ± 0.012 MeV. Please clarify whether the fit parameters are an effective shape or the physical resonance, and if the latter, reconcile the two sets of numbers.

The paper says, at §3.4.1 (pnγ)

Pith says: minor objection 2 of 9

The rate is taken from the Rupak calculation for T9 ≤ 1.5 and matched to the rate of [14] above T9 = 1.5, with the uncertainty jumping from 1.2% to about 8% at the matching point. Please state whether the matched rate is continuous at T9 = 1.5 and whether the error is interpolated across the join, since a discontinuous or discontinuous-derivative rate can produce a numerical artefact in the network integration.

show 7 more

The paper says, at Table 3

Pith says: minor objection 3 of 9

The X6Li entry is 1.1·10⁻¹⁴ with σii = ±1.7, i.e. a symmetric error larger than the central value. Since the underlying αdγ uncertainty is explicitly one-sided (Eq. E.27), the table should say that the 6Li error is effectively an upper bound rather than a Gaussian σ.

The paper says, at Table 3, column header

Pith says: minor objection 4 of 9

The column is labelled 'uncertainties due to nuclear rates errors', but for Yp Table 7 shows that 98.5% of the squared error comes from wnp, the weak n↔p rate, which is dominated by the neutron lifetime rather than by a nuclear cross-section measurement. Relabel the column or add a footnote distinguishing weak from nuclear contributions, so that the Yp entry is not read as a nuclear-data uncertainty.

The paper says, at §3.4.3, footnote

Pith says: minor objection 5 of 9

The exclusion of the [101] data as a preliminary report of [98], and the note about a misprint in [19], both affect which data enter the ddn fit and hence a rate that carries 37% of the 2H squared error. These belong in the main text rather than in a footnote.

The paper says, at §2.1, footnote on Yp

Pith says: minor objection 6 of 9

The footnote correctly warns that 4X4He differs from the true mass fraction by about 0.5%, which is not negligible at the quoted 0.1% theoretical precision. Please state explicitly which convention is used for the Yp values in Tables 3 and 4 and in Eq. (4.2)–(4.4) comparisons.

The paper says, at §4.2.2, Eq. (4.19)

Pith says: minor objection 7 of 9

The claim that the uncertainties on Yp, GN and Tγ0 propagate to only 0.1% in η is stated without the arithmetic. A short table or a line of numbers would let the reader verify that this is indeed sub-leading against the 4% ωb error.

The paper says, at Appendix F

Pith says: minor objection 8 of 9

The covariance fits (Eqs. F.2–F.7) are stated to be accurate to better than 10%, which is loose relative to the few-percent σii values they are meant to represent. Please quote the maximum fractional residual of each fit over the stated η and ΔN ranges, and state clearly that the fits are not to be used outside those ranges.

The paper says, at Fig. 23

Pith says: minor objection 9 of 9

The 4He likelihood curve is extremely broad and the quoted interval ωb = 0.016 (+0.026/−0.009) at 68% C.L. is asymmetric. State the prior range and the normalization used for the plotted curves so that the three likelihoods can be compared on the same footing.

What would settle it

Recompute Table 3 and Table 8 twice. (a) Replace the §3.3 scale error (minimum ϵk) with the weighted mean, then with the maximum ϵk, for each reaction, holding all else fixed; report σ_2H, σ_7Li and the resulting 2H and 7Li tensions. (b) For be7nα, evaluate X7Li at Γ × {0.1, 0.5, 1, 2, 10} and check whether the response is linear across the ±1σ points that Eq. (4.10) actually samples. If σ_2H rises above σ_ωb, or the 7Li tension falls below roughly 3σ, or the be7nα response is strongly nonlinear, the headline comparative claim needs restating with the convention dependence made explicit.

from the skeptic's reading

How the review went

4 readings by deepseek-v4.1-flash · 13 Nov 2026

  1. Reader holds up, with conditions confidence high
  2. Skeptic partly agrees 1 min 16 s · 55,394 tokens read, 4,177 written
  3. Editor wrote the verdict above 30 s · 56,392 tokens read, 1,624 written
  4. Referee major revision: 3 major objections, 9 minor 1 min 45 s · 55,704 tokens read, 5,694 written

Not run on this paper: the simulated authors' defence.

Pith did not check this review's objections against the paper.

The review in full

The review in brief, machine-written

This is the Serpico et al. BBN rate paper — the one people cite when they need a rate table with uncertainties attached. What's actually new: the regression protocol in §3.3 with per-dataset normalization parameters and a penalty term (Eqs. 3.49–3.51), which handles discrepant data sets more honestly than fixing normalizations to unity; new fits incorporating LUNA's d(p,γ)3He data; and the error decomposition in Tables 5–8, which tells you which reaction to measure next for each nuclide. The neutrino decoupling and weak-rate sections are review, tagged as such, and honestly so. The physics is standard and the appendices are unusually complete — the S-factor fits and the rate/uncertainty fits in Appendix E are why this gets cited at all. That is real, reusable work, and it is the reason to keep the paper on the shelf regardless of how the error budget shakes out. Where it's soft: the scale-error convention in §3.3 — set equal to the lowest experimentally determined εk — is a choice, and every number in Tables 3 and 5–8 scales with it. The paper itself notes the reduction relative to [20] comes from dropping the maximal-error treatment used there; that is a change of convention, not new data, and no sensitivity scan is shown. It cuts both ways: it produces both the 1σ deuterium agreement and the 'more severe than [20]' 4σ lithium tension. Worth flagging, but it is a defensible convention, not an error. The sharper problem is the one the stress-test names, and it lands: be7nα carries a factor-10 uncertainty (Eq. E.37) and contributes 40.9% of the 7Li squared error (Table 8), but Eq. 4.10 evaluates the yield only at Γ±1σ. Over a factor-10 range that response is unlikely to be linear, so the 40.9% share — and the quoted 8–10% total 7Li error — is not established by the method actually used. Same issue, milder, for the other hand-assigned uncertainties (tpγ, li7dnα, be7dpα, αdγ from NACRE). The missing data/code is a minor complaint for a paper of this vintage; the appendix fits are enough to reimplement. Who it's for: anyone doing BBN, anyone needing rate uncertainties, anyone arguing about the lithium problem. It deserves a serious referee — the be7nα linearization is exactly what a referee should push on.

The strongest objection

The paper's comparative claims rest on the error budget of Tables 3 and 5–8, and every entry there scales with two conventions fixed in §3.3 that are never varied. First, the overall scale error is set to 'the lowest experimentally determined ϵk for that reaction' (§3.3, final paragraph). Choosing the minimum rather than the weighted mean or the maximum of the quoted normalization errors systematically shrinks σii. Second, residual scatter is inflated by √χ²ν. The paper itself notes (§4.2.3) that the reduction relative to [20] comes from dropping the 'large maximal error' used there — a change of convention, not new data. The convention cuts both ways and only one side is reported: it makes σ_2H (1.6%) fall below σ_ωb (7.8%), supporting the 1σ deuterium agreement, and simultaneously makes the 7Li discrepancy 'more severe than in our previous analysis in [20] because of the different treatment of nuclear rate errors' — the 4σ lithium claim is produced by the same shrinkage. No sensitivity scan is presented anywhere in §4.2 or Appendix F. A sharper sub-case: be7nα carries a factor-10 uncertainty (§3.5.4; Eq. E.37, δf ≈ 0.9f) and contributes 40.9% of the 7Li squared error (Table 8). Eq. (4.10) evaluates the yield only at Γ±1σ, a two-point central difference. Over a factor-10 range the response of X7Li to that rate is unlikely to be linear, so the 40.9% share — and hence the quoted 8–10% total 7Li error and the 4σ tension — is not established by the method actually used.

The reader's weakest_assumption points at the right locus: the §3.3 scale-error convention. I agree that this is where the load sits, and I would sharpen it in two ways the reader does not state. First, the convention is not merely a one-directional shrinkage that flatters the paper; it is the same choice that produces the paper's most-quoted negative result, the 4σ lithium tension, which §4.2.3 explicitly attributes to 'the different treatment of nuclear rate errors' relative to [20]. A convention that simultaneously manufactures the good deuterium agreement and the bad lithium disagreement deserves a sensitivity scan, and none is given. Second, the be7nα case is a concrete technical failure mode rather than a matter of taste: a factor-10 uncertainty propagated through the two-point central difference of Eq. (4.10) is outside the regime where that estimator is meaningful, and it carries 40.9% of the 7Li squared error. That is a checkable defect, not a preference. Beyond this I find the paper in good order. The physics is standard and correctly assembled; the weak-rate treatment in §3.1 (radiative, finite-mass, thermal, and non-instantaneous-decoupling corrections) is carefully sourced; the neutrino-decoupling machinery of §2.2–2.3 is a re-presentation of cited work and is flagged as such. I verified that the percentage contributions in Tables 5, 6, 7 and 8 each sum to 100, so the error decomposition is arithmetically self-consistent. The Appendix E rate fits are unusually complete for a compilation of this era. One minor internal mismatch worth noting but not load-bearing: §4.2.3 states the 2H error reduction is 'mainly because of our analysis of the two leading reactions ddn and ddp', whereas Table 5 assigns dpγ the largest single share (49%) against ddn 37% and ddp 14%. The authors also acknowledge, in §3.5.2, that tpγ parameter correlations were never published and so their propagation method cannot be applied there — an acknowledged limitation, not a new finding. On the reader's stated reason for CONDITIONAL (withheld data and code, §3.3's invitation to email the authors), I have no quarrel; it is a real reuse barrier. My concern does not move the verdict, because the paper's claims are hedged and the qualitative picture — standard BBN consistent with WMAP ωb for deuterium, lithium discrepant — survives any plausible widening of the error bars. It does mean the specific numbers in the abstract-level comparison should be read as convention-dependent rather than as measured precision. CONDITIONAL remains the right verdict, for the reader's reason plus this one.

The referee's report

The paper's durable contributions are methodological and reproducible rather than rhetorical. The regression protocol of §3.3 is stated explicitly enough to be re-implemented, and the full set of S-factor fits (Appendix D) and rate-plus-uncertainty fits (Appendix E) is published, which is more than most compilations in this literature provide. The detailed-balance check of the weak rates against z̄⁻¹ (Fig. 9) is a genuine internal validation, and the reaction-by-reaction error decomposition in Tables 5–8 is a falsifiable deliverable that later work can check against. The neutrino-decoupling treatment with QED corrections is carried through consistently into the BBN equations rather than bolted on. If the error budget holds up under the sensitivity checks requested below, the claim that nuclear uncertainties no longer dominate over the baryon-density uncertainty for 2H and 4He would be a useful and citable result.

Pith's reading of the paper (a machine's summary, not the authors')

This paper asks what standard Big Bang nucleosynthesis predicts once the baryon density stops being a free parameter. Taking $ω_b = Ω_b h^2 = 0.023 ± 0.001$ from the WMAP-era combination of cosmic microwave background data, the authors work through every remaining input that could shift the light-element yields: the weak neutron–proton interconversion rates, the incomplete decoupling of neutrinos during electron–positron annihilation, and above all the nuclear reaction network. The bulk of the effort goes into that network, where they re-fit the astrophysical $S$-factors of the reactions that matter, letting each experiment carry its own normalization parameter rather than forcing every data set onto a common scale. They then propagate those rate uncertainties into the yields and decompose each nuclide's error bar reaction by reaction, which is the paper's most reusable product. The payoff is a scorecard: deuterium lands within one $\sigma$ of the quasar absorption measurements, helium-4 is theoretically very tight but sits above the most careful observational estimates, and lithium-7 comes out two to three times too high.

What carries the argument. The load-bearing device is the fitting protocol for each reaction. Rather than a single $χ^2$ against a common curve, the authors minimize $χ^2(a_l, ω_k) = χ^2_{stat} + χ^2_{norm}$ where $χ^2_{stat} = Σ_{ik} (S_{th}(E_{ik}, a_l) - S_{ik} ω_k)^2 / (ω_k^2 σ_{ik}^2)$ and $χ^2_{norm} = Σ_{ik} (ω_k - 1)^2 / ε_k^2$. Each data set $k$ gets a free multiplicative normalization $ω_k$, penalized by its own quoted normalization error $ε_k$; this keeps correlated scale uncertainties inside the fit instead of discarding discrepant experiments, and the authors argue it avoids the downward bias that a naive covariance-matrix treatment produces. The fitted $S(E)$ or $R(E)$ functions are then convolved numerically with the Gamow or Maxwell–Boltzmann kernel to give thermal rates, and the rate error $δf$ follows from full error propagation through the fitted-parameter covariance matrix. The second device is the yield-error decomposition: each rate is shifted by its own $±1σ$, the network is re-solved, and the resulting yield shifts are combined into a covariance matrix $σ^2_{ij} = Σ_k [(X_i(Γ_k^+) - X_i(Γ_k^-))(X_j(Γ_k^+) - X_j(Γ_k^-))]/4$, which allows asymmetric and temperature-dependent rate errors without a Monte Carlo. Tables 5 through 8 are where this machinery pays off, assigning, for example, 49 percent of the deuterium variance to $d(p,γ)^{3}$He, 81 percent of the helium-3 variance to $^{3}$He$(d,p)^{4}$He, and splitting the lithium-7 variance among $^{7}$Be$(n,α)$, $^{4}$He$(^{3}$He$,γ)^{7}$Be and $^{7}$Be$(d,pα)$.

Core claim. The central claim is that once the baryon density is supplied externally, the propagated nuclear-rate uncertainties on the light-nuclide yields have shrunk to the point where they are comparable to, or smaller than, the uncertainty coming from $ω_b$ itself, at least for deuterium and helium-4. For $ω_b = 0.023$ the authors report $X_{^2H}/X_p = 2.44^{+0.19}_{-0.16} × 10^{-5}$ with a nuclear-rate error of only 1.6 percent, $Y_p = 0.2481$ with a total theoretical error near 0.1 percent that is almost entirely the neutron-lifetime uncertainty, $X_{^3He}/X_p = 1.01 × 10^{-5}$, and $X_{^7Li}/X_p = 4.9 × 10^{-10}$ with roughly an 8 percent nuclear error. The comparison against observation is then a parameter-free consistency test of the simplest cosmology: deuterium agrees with the quasar value $(2.78^{+0.44}_{-0.38}) × 10^{-5}$ at about one $\sigma$, $Y_p$ agrees only if one adopts the most conservative observational error budget, and lithium-7 remains low by a factor of two to three, which the authors put at the four-$\sigma$ level and read as possible evidence for depletion in old halo stars rather than as a failure of the network. A secondary claim is that deuterium alone constrains the baryon density to $ω_b = 0.021 ± 0.002$, a precision competitive with the microwave background.

The premise it rests on. The load-bearing premise is the convention that each reaction's overall scale error can be set equal to the smallest normalization error quoted among its experiments, with any residual scatter absorbed by inflating the error by the square root of the reduced chi-squared; every rate uncertainty and therefore the claim that nuclear errors now sit below the baryon-density error depends on that choice.

If the paper is right (Pith's inferences, not the authors')

Deuterium becomes a genuine baryometer on its own: the paper derives $ω_b = 0.021 ± 0.002$ from the quasar deuterium value alone, close enough to the microwave-background number that the two are already a meaningful cross-check.

The helium-4 prediction carries only about 0.1 percent theoretical error, so any remaining disagreement with observation is chargeable to the observational systematic budget of extragalactic HII regions rather than to nuclear physics.

Lithium-7 stays discrepant at roughly four sigma after the error reduction, sharpening the case that the Spite plateau value has been depleted by processes inside the stars rather than produced differently in the early universe.

Helium-3 is predicted at $1.01 × 10^{-5}$, essentially saturating the tightest reported upper limit from the S209 HII region, which makes it a live if difficult discriminant.

The error budget names the reactions worth new measurements: $^{7}$Be$(n,α)^{4}$He, $^{4}$He$(^{3}$He$,γ)^{7}$Be, $^{7}$Be$(d,pα)$, $^{3}$He$(d,p)^{4}$He and the deuterium–deuterium channels, the last of which have no data at all between 0.2 and 1 MeV.

If the nuclear errors really are below the baryon-density error for deuterium, then a future discrepancy between a deuterium-derived baryon density and a Planck-quality microwave-background value would be a cleaner signal of new physics at the MeV scale than it is today, because the nuclear escape route would be narrow.

The lithium gap surviving at four sigma after error shrinkage points at a specific experimental target: a measurement of the low-energy $^{7}$Be$(d,pα)$ cross section, or of $^{7}$Be$(n,α)$, at the percent level would either close the gap or force the depletion explanation.

Because every quoted rate uncertainty scales with the convention that the overall scale error equals the smallest quoted normalization error, the field would benefit from a blind comparison of error budgets computed under the smallest, weighted-mean and largest conventions on the same data compilation; the comparative claim about nuclear errors versus $ω_b$ errors is exactly what such a comparison

The same machinery applies directly to non-standard scenarios: since the paper's error covariance is tabulated as a function of $η$ and the effective number of extra relativistic degrees of freedom, the marginalised sensitivity of each nuclide to extra relativistic energy can be read off without re-running the network.

Check this review

Pith stored no record of this review's passes and took no fingerprint of it. Reviews made by code from 13 Nov 2026 on carry both.

How often reviews like this one are right

Reviews like this one: written by deepseek-v4.1-flash, where what was read was not recorded.

How often objections from reviews like this one are right: not yet measured

Every value above, in the review's public record (JSON)

Reviews by people

This review was written by a machine. No person has reviewed this paper on Pith yet. A scientist listed on Pith can review it for a fee, and their review is published here whatever it concludes.

Request a human review

How Pith checks papers · The full audit of this paper

The paper

Abstract

We analyze in details the standard Primordial Nucleosynthesis scenario. In particular we discuss the key theoretical issues which are involved in a detailed prediction of light nuclide abundances, as the weak reaction rates, neutrino decoupling and nuclear rate modeling. We also perform a new analysis of available data on the main nuclear processes entering the nucleosynthesis reaction network, with particular stress on their uncertainties as well as on their role in determining the corresponding uncertainties on light nuclide theoretical estimates. The current status of theoretical versus experimental results for 2H, 3He, 4He and 7Li is then discussed using the determination of the baryon density as obtained from Cosmic Microwave Background anisotropies.

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. No sentence in this record was written by a model.

abstract compiled · 2026-09-23

The authors' main claim, as the classifier picked it out 0.79

“The current status of theoretical versus experimental results for 2H, 3He, 4He and 7Li is then discussed using the determination of the baryon density as obtained from Cosmic Microwave Background anisotropies.”

How the main claim is stated: asserted 0.72

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.10 · human participants 0.02 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.73 · mentions code or data availability 0.03

The abstract, sentence by sentence

This table labels the abstract only (arXiv listing abstract v3). The number is the probability the classifier gave the label.

SentenceRoleThe authors' own workStates the main conclusionStrength
We analyze in details the standard Primordial Nucleosynthesis scenario. contribution 0.87 0.89 0.04 asserted 0.91
In particular we discuss the key theoretical issues which are involved in a detailed prediction of light nuclide abundances, as the weak reaction rates, neutrino decoupling and nuclear rate modeling. contribution 0.74 0.52 0.04 asserted 0.86
We also perform a new analysis of available data on the main nuclear processes entering the nucleosynthesis reaction network, with particular stress on their uncertainties as well as on their role in determining the corresponding uncertainties on light nuclide theoretical estimates. contribution 0.87 0.93 0.09 asserted 0.99
The current status of theoretical versus experimental results for 2H, 3He, 4He and 7Li is then discussed using the determination of the baryon density as obtained from Cosmic Microwave Background anisotropies. contribution 0.53 0.39 0.15 asserted 0.72

What kind of paper the classifier reports this is: review 0.54 · evidence from analysis of existing data 0.98

What was examined, and what was not

Sources read

  • arXiv listing abstract v3

Not examined

  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers

Levels run

  • P abstract

Not run

  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

How the labels were made

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,702 input tokens.

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON

Figures (23)
Figure 1 of the paper
Figure 1. The evolution of ¯z = T /Tν versus z = me/T. The asymptotic value at small temperatures is ¯z=1.3984 Since at high temperature, T ∼ 10 MeV, the neutrinos are in thermal equilibrium with the electromagnetic plasma, the initial condition for the coefficients is a α i = 0 and we can always choose the initial value for the scale factor such that we have, at 10 MeV, z¯ = 1. From Equation (2.25), neglecting the terms proportional to the derivative of neutrino distributions, as well as QED corrections, one gets the asymptotic value z¯ D eq = (11/4)1/3 = 1.4010 which represents the ratio…
Figure 2 of the paper
Figure 2. The evolution of the electron neutrino distortion coefficients c e 0 (solid), c e 1 (dashed), c e 2 (dotted) and c e 3 (dot-dashed) versus z = me/T
Figure 3 of the paper
Figure 3. The evolution of the µ, τ neutrino distortion coefficients c x 0 (solid), c x 1 (dashed), c x 2 (dotted) and c x 3 (dot-dashed) versus z = me/T
Figure 4 of the paper
Figure 4. Nuclear abundances depart from their equilibrium values, undergo an out￾of-equilibrium phase, and eventually reach their final values 3. The Nuclear rates 3.1. Weak Reactions ∗ The weak reactions transforming n ↔ p, namely (a) νe + n → e − + p , (d) νe + p → e + + n , (b) e − + p → νe + n , (e) n → e − + νe + p , (c) e + + n → νe + p , (f) e − + νe + p → n . (3.1) are the leading processes in fixing the neutron abundance at the onset of BBN and thus a key quantity in determining the 4He mass fraction. In view of this, much effort has been devoted to refining the theoretical acc
Figure 5 of the paper
Figure 5. The total Born rates, ωB, for n → p (solid line) and p → n transitions (dashed line). results to be, at best, of the order of 7%. This can be estimated by comparing the prediction of Equation (3.2) for the neutron lifetime at very low temperatures, with the experimental value τ ex n = (885.7±0.8) s [3]. A sensible improvement is obtained by considering four classes of effects 1) electromagnetic radiative corrections, which largely contribute to the rates of the fundamental processes; 2) finite nucleon mass corrections, which are of the order of T/MN or me/MN , MN being the nucleon
Figure 6 of the paper
Figure 6. The tree level Born (a), the one-loop (b),(c), and the photon emission/absorption diagrams (d) for n → p processes. All field propagators get additional on shell contributions proportional to the number density of that particular specie in the surrounding medium. For γ and e ±, neglecting in this case the small electron chemical potential, we have i∆ µν γ (k) = −  i k 2 + 2π δ(k 2 ) fγ(k0)  g µν , (3.8) i Se(p 0 ) = i /p 0 − me − 2π δ(p 02 − m2 e ) fe(p 0 0 ) (/p 0 + me) , (3.9) with fγ the photon distribution function. The entire set of thermal/radiative c
Figure 7 of the paper
Figure 7. The relative correction to the n → p (solid line) and p → n (dashed line) total rates due to the γ + p → e + + νe + n and inverse processes. effects of the QED interaction in the plasma also show up in modifying the equation of state of electron/positron and photons, as well as they induce thermal contribution to their mass. These effects, first considered in [4], have been already described in Section 2.2. In particular the thermal averaged weak rates get an order α corrections when the electron thermal mass is introduced in the corresponding distribution function. 3.1.4. Non…
Figure 8 of the paper
Figure 8. The relative correction to the n → p (solid line) and p → n (dashed line) total rates, due to the neutrino distortion. δω is the difference of the n ↔ p rates calculated by numerically solving the neutrino decoupling and the ones for an instantaneous neutrino decoupling at TD = 2.3 MeV. For p → n the effect is shown down to T ∼ 0.3 MeV, since for lower temperatures the total rate becomes negligibly small. obtained, satisfy the detailed balance condition, namely ρ(T) = ω(n → p)nn ω(p → n)np = 1 , (3.13) where nn(p) are the neutron (proton) number density. In
Figure 9 of the paper
Figure 9. The detailed balance ratio ρ(T) (solid line) versus temperature in unit of me. The dashed line is the neutrino to photon temperature ratio ¯z −1 . Dotted line corresponds to ρ(T) for the case Tν = T. temperature region is however irrelevant for neutron to proton ratio which has been already frozen out well before the e ± annihilation phase. 3.2. Nuclear reaction rates: analytical calculations. In the primordial plasma during BBN the energy of colliding nuclei is always much lower than their masses, and their density is very far from values needed to produce relevant quantum effects
Figure 10 of the paper
Figure 10. The low energy data and the fit of the auxiliary function R(E) for the p + n ↔ γ + 2H reaction. The solid line is the overall best fit, the dashed curve is based only on experimental data. The theoretical points taken from [80] have a negligible error bar on this scale. The error bars for the experimental points also include the propagated uncertainty on the energies. sections [66]. The uncertainty grows to ∼ 8% for T9 > 1.5, being based on the error budget of [14] and the matching and normalization errors. For comparison, the analysis performed in [83] gives a sample variance…
Figure 11 of the paper
Figure 11. The data and fit for the astrophysical factor of 2H + p → γ + 3He. The fit of S(E) is with a cubic polynomial. older analysis performed in [83], not including them and with a less accurate treatment of the other experiments systematics gave a sample variance error of 13.2%, while our present study suggests an overall uncertainty for the rate less than 3%. In the recent compilation [19] the estimated error is close to 7%, but this number is dominated by the normalization error and so it is likely to be overestimated (see our discussion in Section 3.3). We get a data normalization…
Figure 12 of the paper
Figure 12. The data and fit for the S factor of the 2H + 2H ↔ n + 3He reaction. be excluded††. The data of [95] quite accurately fix the high energy behavior of this astrophysical factor, and the data in [98] allow to quote a normalization of the S factor (and then of the rate) of 1.3%. As many data are available, and they are generally affected by a small normalization or overall uncertainties (at the level of few percent), even relatively low discrepancies on the scale and/or the behavior of the S(E) will show up in the value of the reduced χ 2 , which is of the order of 10 or greater at…
Figure 13 of the paper
Figure 13. The data and fit for the S factor of the 2H + 2H ↔ p + 3H reaction. experimental campaign to determine accurately (say at the 1% level) both the magnitude and shape of the S(E) in the wide range useful for BBN studies (E≤ 2.5 MeV), and in particular for 0.2 ≤ E ≤ 1 MeV, where actually no data presently exist. 3.4.4. Reaction ddp: 2H + 2H ↔ p + 3H . This process is the leading source of direct tritium synthesis (see Figure B2). The discussion of its experimental situation closely follows our analysis of the previous reaction ddn, apart from the fact that very low energy data are…
Figure 14 of the paper
Figure 14. The S(E) data and fit for the 3H + 2H ↔ n + 4He channel to use a Breit-Wigner shape to extrapolate with some accuracy the S factor also to energies below the range covered by the data. The data sets we used are [104]-[111], with the Conner data [105] excluded at energies greater than 240 keV, where the isotropy assumption for σ(E) fails. The rate and error estimate were both calculated numerically. Our error estimate is ' 0.6%, and ε ∼ 0.02 (for a χ 2 ν ' 1.4), while for comparison the analysis performed in [83] gives a sample variance error of ∼ 4%, while the discrepancy error…
Figure 15 of the paper
Figure 15. The S(E) data and fit for the 3He + 2H ↔ p + 4He reaction 3.4.7. Reaction he3np: 3He + n ↔ p + 3H . This process keeps 3He and 3H in equilibrium at (relatively) high temperatures. During BBN it plays an important role in determining the final abundances of 3He and 7Li. In our regression we used the data reported in [126]-[130], by limiting the analysis to E ≤ 1MeV as in [19]: this allows to cover the most interesting range for the BBN by significantly reducing the numbers of parameters needed to have a good fit. Thanks to the new measurements of the reverse reaction cross section…
Figure 16 of the paper
Figure 16. The S factor data and fit of the 3He + n ↔ p + 3H. than the non-resonant he3np reaction, whose rate was obtained analytically, this process has a resonance at E ' 0.32 MeV that suggests to use a fully numerical approach, both for the rate and the uncertainties. Note that despite of the few data set available, the Koeler data [131] fix the overall scale error to the ' 2.1% level, thus making this process quite accurately known for the purpose of BBN studies. The statistical error is of the order of 0.7%. 3.4.9. Reaction αhe3γ: 4He + 3He ↔ γ + 7Be . It is the dominant channel for…
Figure 17 of the paper
Figure 17. The S factor data and fit of the 7Be + n ↔ p + 7Li reaction
Figure 18 of the paper
Figure 18. The S factor fit and data for the 4He + 3He ↔ γ + 7Be reaction
Figure 19 of the paper
Figure 19. The data and fit for the S factor of the 7Li + p ↔ 4He + 4He reaction. This is the main process destroying 7Li during the BBN. The data used in our analysis are the ones quoted in [142]-[146]. A self-consistent correction for the screening potential was also performed, whose effect is particularly significant for the low-energy data of Engstler et al [145, 146]. Our estimate for the overall error is of the order of 2% in the relevant temperature range, while ε ∼ 0.01. 3.4.11. Reaction αdγ: 4He + 2H ↔ γ + 6Li . Even if it is a weak electric quadrupole transition, this reaction is…
Figure 20 of the paper
Figure 20. The data and fit for the S factor of the 6Li + p ↔ 3He + 4He reaction. abundant and accurate We used the data [148]-[153] as well as those in References [143, 145], already cited for the li7pα process, with the last one self-consistently corrected for the screening effect. The estimated error is lower than 2% and, quite negligibly contributing to the eventual accuracy of 6Li estimate, with respect to the one coming from the αdγ reaction. We estimate ε ∼ 0.09. 3.5. Main sub-leading processes 3.5.1. Reaction αtγ: 4He + 3H ↔ γ + 7Li . This is the main channel for the direct synthesis o
Figure 21 of the paper
Figure 21. The data and fit for the S factor of the 4He + 3H ↔ γ + 7Li reaction. 4He synthesis, but its influence on the final error budget of all nuclides is marginal. The old rate for this reaction is that published in the compilation [12]. Meanwhile, new data were taken [158, 159], and a new fitting of the astrophysical S factor is now available [159] S(E) = S0 + S1E + S2E 2 , (3.55) S0 = 2.0±0.2 keV mb , (3.56) S1 = (1.6±0.4)×10−2 mb , (3.57) S2 = (1.1±0.3)×10−4 mb/keV . (3.58) We used these parameters to estimate the best rate, while its uncertainty is assumed to be ∆S(0)/S(0) ' 10%. No
Figure 22 of the paper
Figure 22. The data and fit for the S factor for the 7Li + p ↔ γ + 8Be reaction. non-resonant contribution by more than a factor 10, thus further increasing its role. Tough sub-leading, it is worthwhile to note that within the actual uncertainties and assuming the WMAP range for ωb, this process acquires a role comparable to that of 7Li +p → 4He + 4He and 4He+3H→ γ+7Li reactions in determining the final prediction of 7Li. The data sets used in our analysis are [160]-[162]. We estimate an overall error of 3% and a large value of the normalization spread parameter, ε ∼ 0.14. 3.5.4. Reaction…
Figure 23 of the paper
Figure 23. The ωb determination using different cosmological observables. We report the likelihood function for WMAP result on CMB anisotropies (full line), 2H measurement (dashed line) and 4He analysis (dotted line). A similar analysis can be performed using 4He. In this case we get ωb = 0.016+0.026 −0.009, at 68 % C.L., which is not very constraining in view of the generous uncertainty we have adopted for the experimental error on Yp. A comparison of all results is shown in Figure (23), where we report the likelihood profiles for the two determination of ωb from 2H and 4He, as well as the…

Figures are the authors', reproduced from the paper.

References (194)
  1. [20] Cuoco et al 2004 Int. J. Mod. Phys. A vol. 19, no. 26, 4431 on Pith
  2. [1] Spergel D N et al 2003 Astrophys. J. Suppl. 148 175 on Pith
  3. [2] SDSS Collaboration website http://www.sdss.org/ on Pith
  4. [3] Eidelman S et al (Particle Data Group) 2004 Phys. Lett. B592 1 on Pith
  5. [4] Lopez R E and Turner M S 1999 Phys. Rev. D59 103502 on Pith
  6. [5] Esposito S et al 1999 Nucl. Phys. B540 3 on Pith
  7. [6] Dolgov A D 2002 Phys. Rept. 370 333 on Pith
  8. [7] Mangano G et al 2002 Phys. Lett. B534 8 on Pith
  9. [8] Fowler W A, Hoyle F 1964 Astrophys. J. Suppl. 9 210 on Pith
  10. [9] Wagoner R V 1969 Astrophys. J. 18, 247 on Pith
  11. [10] Fowler W A et al 1967 Annu. Rev. Astron. Astrophys. 5 525 on Pith
  12. [11] Fowler W A et al 1975 Annu. Rev. Astron. Astrophys. 13 69 on Pith
  13. [12] Caughlan G R and Fowler W A 1988 At. Data Nucl. Data Tables 40 283 on Pith
  14. [13] Krauss L M and Romanelli P 1990 Astrophys. J. 358 47 on Pith
  15. [14] Smith M S et al 1993 Astrophys. J. Suppl. 85 219 on Pith
  16. [15] Angulo C et al 1999 Nucl. Phys. A656 3. Website pntpm.ulb.ac.be/nacre.htm on Pith
  17. [16] EXFOR-CSISRS database. Website http://www-nds.iaea.or.at/exfor/ on Pith
  18. [17] Table of Isotopes 8th edition. CD-ROM Edition available on line at the website http://www.tunl.duke.edu/nucldata/ on Pith
  19. [18] Casella C et al 2002 Nucl. Phys. A706 203 on Pith
  20. [19] Cyburt R H 2004 Phys. Rev. D70 023505 on Pith
show 80 more
  1. [21] Descouvemont P et al , Compilation and R-matrix analysis of Big Bang nuclear reaction rates Preprint astro-ph/0407101 on PithPith's reviewarXiv
  2. [22] Kawano L, Let’s go Early Universe Preprint Fermilab-Pub-92/04-A on Pith
  3. [23] Wagoner R V et al 1967 Astrophys. J. 148 3; Wagoner R V 1969 Astrophys. J. Suppl. 18 247; Wagoner R V 1973 Astrophys. J. 179 343 on Pith
  4. [24] Esposito S et al 2000 Nucl. Phys. B568 421 on Pith
  5. [25] Esposito S et al 2000 JHEP 0009 038 on Pith
  6. [26] Hannestad S 2002 Phys. Rev. D92 083006 on Pith
  7. [27] Dolgov A D et al 2002 Nucl. Phys. B632 363 on Pith
  8. [28] Esposito S et al 2001 Phys. Rev. D63 043004 on Pith
  9. [29] Hansen S H et al 2002 Phys. Rev. D65 023511 on Pith
  10. [30] Abazajian K N, Beacom J F and Bell N F, 2002 Phys. Rev. D 66 013008 on Pith
  11. [31] Le Bellac M 1996 Finite temperature field theory (Cambridge University Press) on Pith
  12. [32] Heckler A F 1994 Phys. Rev. D49 611 on Pith
  13. [33] Fornengo N et al 1997 Phys. Rev. D56 5123. Nuclear Reaction Network for Primordial Nucleosynthesis 80 on Pith
  14. [34] Esposito S et al 2000 Nucl. Phys. B590 539 on Pith
  15. [35] Dolgov A D et al 1997 Nucl. Phys. B503 426 on Pith
  16. [36] Dolgov A D et al 1999 Nucl. Phys. B543 269 on Pith
  17. [37] Wilkinson D M 1982 Nucl. Phys. A377 474 on Pith
  18. [38] Sirlin A 1967 Phys. Rev. 164 1767 on Pith
  19. [39] Marciano W J and Sirlin A 1986 Phys. Rev. Lett. 56 22 on Pith
  20. [40] Marciano W J and Sirlin A 1981 Phys. Rev. Lett. 46 163 on Pith
  21. [41] Seckel D 1993 Nuclear mass corrections to the p-n rates during Big Bang NucleosynthesisPreprint hep-ph/9305311; Lopez R E et al 1997 Phys. Rev. D56 3191 on PithPith's reviewarXiv
  22. [42] Dicus D A et al 1982 Phys. Rev. D26 2694 on Pith
  23. [43] Cambier J L et al 1982 Nucl. Phys. B209 372 on Pith
  24. [44] Donoghue J F et al 1985 Ann. Phys. (N.Y.) 164 23; Donoghue J F and Holstein B R 1983 Phys. Rev. D28 340; Donoghue J F and Holstein B R 1984 Phys. Rev. D29 3004 on Pith
  25. [45] Johansson A E et al 1986 Nucl. Phys. B278324 on Pith
  26. [46] Keil W 1989 Phys. Rev. D40 1176 on Pith
  27. [47] Baier R et al 1990 Nucl. Phys. B336 157 on Pith
  28. [48] Keil W and Kobes R L 1989 Physica A158 47 on Pith
  29. [49] LeBellac M and Poizat D 1990 Z. Phys. C47 125 on Pith
  30. [50] Altherr T and Aurenche P 1989 Phys. Rev. D40 4171 on Pith
  31. [51] Kobes R L and Semeneff G W 1985 Nucl. Phys. B260 714; Kobes R L and Semeneff G W 1986 Nucl. Phys. B272 329 on Pith
  32. [52] Sawyer R F 1996 Phys. Rev. D53 4232 on Pith
  33. [53] Chapman I A 1997 Phys. Rev. D55 6287 on Pith
  34. [54] Esposito S et al 1998 Phys. Rev. D58 105023 on Pith
  35. [55] Brown L S and Sawyer R F 2001 Phys. Rev. D63 083503 on Pith
  36. [56] Fields B D et al 1993 Phys. Rev. D47 4309 on Pith
  37. [57] Blatt D W E and Weisskopf V 1952 Theoretical Nuclear Physics (John Wiley & Sons) on Pith
  38. [58] Clayton D D 1983 Principles of Stellar Evolution and Nucleosynthesis 2nd edition (The University of Chicago Press) on Pith
  39. [59] Rolfs C E and Rodney W S 1988 Cauldrons in the Cosmos (The University of Chicago Press) on Pith
  40. [60] Anderson W J et al 1994 Astrophysics and Space Science 214 49 on Pith
  41. [61] Raiola F et al 2002 Phys. Lett. B547 193 on Pith
  42. [62] Itoh N et al 1995 Astrophys. J. 488 507 on Pith
  43. [63] Bishop M C 1995 Neural Networks for Pattern Recognition (Oxford Clarendon Press) on Pith
  44. [64] Nollett M and Burles S 2000 Phys. Rev. D61 123505 on Pith
  45. [65] D’Agostini G 1994 Nucl. Instrum. Meth. A346 306 on Pith
  46. [66] Cokinos D and Melkonian E 1977 Phys. Rev. C15 1636 on Pith
  47. [67] Suzuki T S et al 1995 Astrophys. J. 439 59 on Pith
  48. [68] Nagai Y et al 1997 Phys. Rev. C56 3173 on Pith
  49. [69] Bishop G R et al 1950 Phys. Rev. 80 211. Erratum 1951 Phys. Rev. 81 644 on Pith
  50. [70] Snell A H et al 1950 Phys. Rev. 80 637 on Pith
  51. [71] Arenhovel H and Sanzone M 1991 Photodisintegration of the Deuteron: a Review of Theory and Experiment (Springer Verlag Berlin) on Pith
  52. [72] Hara K Y et al 2003 Phys. Rev. D68 072001 on Pith
  53. [73] Tornow W et al 2003 Phys.Lett. B574 8 on Pith
  54. [74] Bethe H A and Morrison P 1956 Elementary Nuclear Theory 2nd edition (John Wiley & Sons) on Pith
  55. [75] Evans R D 1955 The Atomic Nucleus (McGraw-Hill) on Pith
  56. [76] Hughes D J and Schwartz R B 1958 Brookhaven Natl. Lab. Rep. BNL 325 2nd ed on Pith
  57. [77] Hale G M et al 1991 ENDF/B-VI Evaluation Material 125 Revision 1 on Pith
  58. [78] Mughabghab S F et al 1981 Neutron Cross sections Vol.1 Neutron Resonance Parameters and Nuclear Reaction Network for Primordial Nucleosynthesis 81 Thermal cross Sections Part A Z=1-60 (NY) Academic Press on Pith
  59. [79] Bosman M et al 1979 Phys. Lett. B82 212 on Pith
  60. [80] Rupak G 2000 Nucl. Phys. A678 409 on Pith
  61. [81] Chen J W and Savage M J 1999 Phys. Rev. C60 60205 on Pith
  62. [82] Cox A E et al 1965 Nucl. Phys. 74 497 on Pith
  63. [83] Cyburt R H et al 2001 New Astron. 6 215 on Pith
  64. [84] Schiavilla R et al 1996 Phys. Rev. C54 553 on Pith
  65. [85] Griffiths G M et al 1962 Can. J. Phys. 40 402 on Pith
  66. [87] Warren J B et al 1963 Phys. Rev. 132 1691 on Pith
  67. [88] Geller K N et al 1967 Nucl. Phys. A96 397 on Pith
  68. [89] Schmid G J et al 1995 Phys. Rev. C52 R1732 on Pith
  69. [90] Schmid G J et al 1996 Phys. Rev. Lett. 76 3088 on Pith
  70. [91] Schmid G J et al 1997 Phys. Rev. C56 32565 on Pith
  71. [92] Griffiths G M et al 1963 Can. J. Phys. 41 724 on Pith
  72. [93] Ma L et al 1997 Phys. Rev. C55 588 on Pith
  73. [94] McNeill K G and Keyser G M 1951 Phys. Rev. 81 602 on Pith
  74. [95] Schulte R L et al 1972 Nucl. Phys. A192 609 on Pith
  75. [96] First Research Group 1985 Chin. J. Nucl. High En. Phys. 9 723 on Pith
  76. [97] Krauss A et al 1987 Nucl. Phys. A465 150 on Pith
  77. [98] Brown R E and Jarmie N 1990 Phys. Rev. C41 1391 on Pith
  78. [99] Bosch H S and Hale G M 1992 Nucl. Fusion 32 611 on Pith
  79. [100] Greife U et al 1995 Z. Phys. A351 107 on Pith
  80. [101] Jarmie N and Brown R E 1985 Nucl. Inst. and Methods B10/11 405 on Pith

The first 100 of 194 references are listed here. All of them are in this paper's citation record.

Cited by 30 Pith papers

Reviewed papers on Pith that cite this one. The full citation record

  1. Consistent $N_{\rm eff}$ fitting in big bang nucleosynthesis analysis hep-ph · Jul 2025
  2. Ponderomotive Effects of Ultralight Dark Matter hep-ph · Feb 2025
  3. Cosmological and astrophysical probes of dark baryons hep-ph · Dec 2020
  4. Planck 2013 results. XVI. Cosmological parameters astro-ph.CO · Mar 2013
  5. Constraining the cosmic radiation density due to lepton number with Big Bang Nucleosynthesis astro-ph.CO · Nov 2010
  6. Relic neutrino decoupling including flavour oscillations hep-ph · Jun 2005
  7. Boltzmann or Bogoliubov? Approaches Compared in Gravitational Particle Production astro-ph.CO · Jun 2022
  8. Cosmological Bound on the QCD Axion Mass, Redux astro-ph.CO · May 2022
  9. Improving Helium Abundance Determinations with Leo P as a Case Study astro-ph.CO · Oct 2020
  10. Precision Early Universe Thermodynamics made simple: $N_{\rm eff}$ and Neutrino Decoupling in the Standard Model and beyond hep-ph · Jan 2020
  11. Observational Constraints on Secret Neutrino Interactions from Big Bang Nucleosynthesis hep-ph · Dec 2017
  12. Revisiting Big-Bang Nucleosynthesis Constraints on Dark-Matter Annihilation hep-ph · Sep 2015
  13. The effects of He I 10830 on helium abundance determinations astro-ph.CO · Mar 2015
  14. Unveiling secret interactions among sterile neutrinos with big-bang nucleosynthesis astro-ph.CO · Sep 2014
  15. Multi-momentum and multi-flavour active-sterile neutrino oscillations in the early universe: role of neutrino asymmetries and effects on nucleosynthesis astro-ph.CO · Feb 2013
  16. An analysis of constraints on relativistic species from primordial nucleosynthesis and the cosmic microwave background astro-ph.CO · Dec 2011
  17. A robust upper limit on N_eff from BBN, circa 2011 astro-ph.CO · Mar 2011
  18. Cosmological bounds on dark matter-neutrino interactions astro-ph · Jun 2006
  19. PRyMordial: The First Three Minutes, Within and Beyond the Standard Model hep-ph · Jul 2023
  20. Indications for a Nonzero Lepton Asymmetry from Extremely Metal-Poor Galaxies hep-ph · Jun 2022
  21. PArthENoPE Revolutions astro-ph.IM · Mar 2021
  22. The primordial helium abundance from updated emissivities astro-ph.CO · Aug 2013
  23. Sterile neutrinos with eV masses in cosmology -- how disfavoured exactly? astro-ph.CO · Aug 2011
  24. Using BBN in cosmological parameter extraction from CMB: a forecast for Planck astro-ph · Dec 2007
  25. PArthENoPE: Public Algorithm Evaluating the Nucleosynthesis of Primordial Elements astro-ph · May 2007
  26. Lepton asymmetry and primordial nucleosynthesis in the era of precision cosmology astro-ph · Jun 2005
  27. A White Paper on keV Sterile Neutrino Dark Matter hep-ph · Feb 2016
  28. Dark Matter Candidates - Axions, Neutralinos, Gravitinos, and Axinos hep-ph · Nov 2008
  29. Non Thermal Features in the Cosmic Neutrino Background astro-ph · Mar 2006
  30. Massive neutrinos and cosmology astro-ph · Mar 2006
How later papers used it

49 later papers cite it

Evidence: substantial. 42 of the citing papers share no author with it, and 12 of those carry a confident label from Pith's citation classifier.

Pith read 17 of the 72 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its method or tool 1 of 7 papers with this label · 1 by the same authors

By the same authors

How the literature uses it

42 arXiv papers cite this in 61 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 33 sentences without a confident label

Uses its method or tool 6 papers
Uses its data or values 5 papers
  • Here we consider constraints from D [ref] and $^4$He [ref] abundances as averaged by the PDG [ref] : [equation] in addition to constraints from $N_eff$ as measured by Planck [ref] : [equation] We establish exclusion regions that result in abundances and $N_eff$ within 1$σ$ from the observed values, taking into account theoretical uncertainties on the abundance coming from uncertainties on the input parameters $η_b$ and $τ_n$ as well as the nuclear uncertainties as parameterized in [ref] .

    Early Dark Energy During Big Bang Nucleosynthesis · Transition into SM photons · 0.97

  • In WMAP5++ we then included the galaxy power spectrum from the 2dF survey [ref] , SNIa data from the SNLS survey [ref] , and added gaussian priors on the Hubble parameter of $h=0.72 ±0.08$ from the HST key project [ref] , the physical baryon density, $ω_b = 0.022 ±0.002$ [ref] inferred from the $^4$He abundance after Big Bang nucleosynthesis, and BAO data from [ref] .

    Coupling between cold dark matter and dark energy from neutrino mass experiments · Cosmological data · 1.00

  • For completeness, we list here the thermal averaged nuclear cross sections from [ref] and express them in terms of the temperature ratio $T_9≡T'/(10^9 K)=T'/(86 )$:

    Fireball anti-nucleosynthesis · Nuclear cross sections · 0.98

Compares with it 2 papers
Cites it as support 1 paper
  • Considering exclusively the variations for the reactions including only $d$, $^3H$, $^3He$ and $^4He$ is justified as these are the reactions most relevant for the abundances of these light nuclei, as was shown, e.g., in [ref] .

    Bounds on variations of the strange quark mass from Big Bang nucleosynthesis · Modeling the nucleon mass dependence of nuclear reaction rates · 1.00

Cites it as background 9 papers

Challenges and discussion

Disagree with the review, or know something it missed? Leave a comment, or challenge this review formally: a challenge becomes a permanent entry in this paper's record, and its decision is published here.

No comments yet.

Sign in to comment