Standard Big-Bang Nucleosynthesis after Planck

This is a short update letter and it does what an update letter should: re-run the standard network at the Planck baryon density, swap in the 2012 neutron lifetime, and tabulate the four light-element yields with Monte Carlo error bars. The useful part is Table 1, which decomposes the change input by input — you can read off that the neutron lifetime revision lowers Y_p by 0.44% and 7Li/H by 0.39%, and that the Planck Ω_b moves 7Li/H by about 4% and D/H by about 2.7%. That bookkeeping is worth having in one place. The D/H error bar narrowing to ±0.09 is a real consequence of Planck and is the number most people will actually cite. The 7Li value, (4.89 +0.41/−0.39)e−10, is not in the Planck paper, so this is where you go for it. The lithium discrepancy survives at factor three, and the paper says so without spin. The Neff = 3 choice is flagged with a correction path via the Mangano et al. tables, which is the right way to handle it, and the rejection of the Pettini & Cooke deuterium point is argued rather than silent. Both are good practice in a letter this short. Two things to note. First, §3 reports Planck's own Y_p = 0.24725 ± 0.00032 at essentially the same Ω_b and calls it 'similar' to their 0.2463 ± 0.0003. That is a 0.00095 difference against a combined 0.00044 — about 2σ — and it goes unremarked. The likely explanation is that Ade et al. used the older τ_n = 885.7 s, which Table 1 itself shows raises Y_p by roughly 0.0011; if so the comparison is not like-for-like and one sentence would settle it. As written, the ±0.0003 reads as a theory error when it is a within-code rate-sampling width. Minor, but Y_p is one of the four headline numbers. Second, the 7Li error bar inherits its calibration from the same group's earlier rate evaluation with no correlation treatment. Fair criticism, but not load-bearing — the factor-3 gap is far bigger than 8%. I would push back on the reader's deduction for missing code: the rates are all from published compilations and the network is described in Coc et al. (2012). Not shipping code in a letter is normal. Who it is for: anyone who needs Planck-era primordial abundances, especially 7Li, and people working on the lithium problem or new-physics constraints. Worth a referee.

The paper's headline precision claim for helium is Y_p = 0.2463 ± 0.0003 (Table 1, col. 7; abstract:s5). In §3 the authors themselves report the Planck BBN evaluation of Ade et al. (2013): Y_p = 0.24725 ± 0.00032 at Ω_b h² = 0.02207 ± 0.00027. The difference is 0.00095 against a combined error of 0.00044, i.e. ~2.2σ, yet the text calls the two 'similar' and does not reconcile them. The ±0.0003 is the Monte Carlo width of one rate set (Descouvemont et al. 2004, plus Ando et al. 2006 and Cyburt & Davids 2008) at fixed τ_n = 880.1 s and N_eff = 3; it is not a theory systematic. If Ade et al. used the same τ_n and N_eff, the 0.001 offset is a code/rate-compilation systematic that the quoted error omits, and the 'reference primordial abundance' framing is ambiguous at that level. If they used a different τ_n (e.g. 885.7 s, which Table 1 shows raises Y_p by ~0.0011) or N_eff = 3.046, the comparison is not like-for-like and the paper should say so. Either way the reconciliation is missing, and it matters because Y_p is one of the four numbers the letter is cited for. Note this does not threaten the comparison with observation (0.2534 ± 0.0083), which is consistent under either reading; the concern is confined to the precision claim. The reader's concern about correlated rates and the 7Li error bar is real but not load-bearing: the factor-3 lithium discrepancy is far larger than the ~8% error bar, so miscalibration there cannot change the qualitative conclusion.

This is a short, competent update letter and the core physics is standard. Table 1 is the strongest element: it isolates each input substitution (WMAP→Planck Ω_b, τ_n 885.7→880.1, 15→424 rates) so a reader can see the size of each effect, and the paper is honest that the lithium problem survives and that the Pettini & Cooke (2012) deuterium point is excluded for stated reasons. The qualitative conclusions — D/H narrowed to (2.67 ± 0.09)e-5, 7Li/H lowered to (4.89 +0.41/-0.39)e-10, lithium still ~3× the Spite-plateau value — are supported by the calculation as presented. The reader's weakest_assumption (independent lognormal rates, no correlations, 7Li error dominated by 3He(α,γ)7Be) identifies a genuine methodological soft spot, but it is not the load-bearing one: the factor-3 lithium discrepancy is an order of magnitude larger than the ~8% error bar, so even a factor-2 miscalibration of that bar leaves the conclusion intact. I therefore agree only partially. The sharper concern is the Y_p precision claim. The paper's own §3 quotes Planck's 0.24725 ± 0.00032 alongside its 0.2463 ± 0.0003 and calls them 'similar', but the offset is ~2.2σ and is not reconciled. Because the letter is offered as the source of 'reference primordial abundances', the ±0.0003 needs to be understood either as a within-code Monte Carlo width (in which case a systematic term is missing) or as a like-for-like comparison (in which case the input assumptions must match). The paper does not say which. This is a precision/transparency issue, not a correctness failure: the comparison with the observed Y_p = 0.2534 ± 0.0083 is unaffected, and the qualitative claims stand. I would keep ACCEPT, with a request that the Y_p error bar be labelled as a within-model Monte Carlo width and the Planck comparison reconciled.

If the numbers hold, these become the standard reference primordial abundances for the Planck cosmology, and the persistence of the factor-of-three lithium discrepancy at the new baryon density is a useful, falsifiable statement: it closes off the possibility that the lithium problem was an artifact of the WMAP baryon density. The calculation is a genuine forward nuclear-network evaluation from an independently measured Omega_b, with no fitting to the abundances being predicted, so Table 2 is a consistency test rather than a calibration. The step-by-step bookkeeping in Table 1 is a real strength and is what makes the letter citable as a reference update rather than a bare re-run. The authors are also candid that the extended network does not resolve lithium, which is the honest framing.

This paper asks a narrow but consequential question: if you take the baryon density that the Planck satellite measured from the cosmic microwave background, add the current neutron lifetime, and run the nuclear reaction network of Big-Bang nucleosynthesis with present-day rates, what primordial abundances of the light elements come out, and how precisely are they now pinned down? The authors' answer is that nothing dramatic has changed — the standard picture survives the switch from the older WMAP baryon density to the Planck one — but the error bars have moved, most visibly for deuterium, whose predicted abundance is now quoted at about three percent precision. The exercise matters because these predicted numbers are the yardstick against which every claim about primordial gas, stellar processing, and the chemical history of the universe is measured. The one place the yardstick still does not fit is lithium: the calculation lands roughly a factor of three above the abundance seen in the oldest halo stars, and the authors show that shifting the cosmological parameters within their allowed range does not close that gap.

What carries the argument. The machinery is a Monte-Carlo nucleosynthesis calculation: a nuclear reaction network evolved through the first twenty minutes, with each rate drawn from a lognormal distribution, $x = exp(μ + pσ) ≡ x_{med}(f.u.)^p$, where the median rate and factor uncertainty are tabulated as functions of temperature from a prior evaluation, and $p$ is sampled normally. The baryon-to-photon ratio $η$ is sampled normally instead. Running many draws and taking the 0.16, 0.5 and 0.84 quantiles of the resulting distributions produces the quoted central values and asymmetric error bars. The network is extended from the 15 rates that control the light elements to 424 rates reaching up to the CNO cycle, which is what makes the small shift in the late neutron abundance — and hence in ⁷Li — visible. The load-bearing element of the error budget is the $^3$He($α$,$γ$)$^7$Be rate, which the authors state still dominates the ⁷Li uncertainty.

Core claim. The central claim is an updated set of standard-BBN predictions, and the headline result is that the update is a refinement rather than a revision. Adopting $Ω_b h^2 = 0.02207 ± 0.00033$ from Planck instead of the earlier WMAP value lowers the predicted abundances slightly and, crucially, shrinks the uncertainty: D/H becomes $(2.67 ± 0.09)×10^{-5}$, a noticeably tighter error bar than the previous $(2.68 ± 0.15)×10^{-5}$, because deuterium yields track the baryon density almost one-for-one and the baryon density is now better known. Helium is quoted at $Y_p = 0.2463 ± 0.0003$, ³He/H at $(1.05 ± 0.03)×10^{-5}$, and ⁷Li/H at $(4.89^{+0.41}_{-0.39})×10^{-10}$. The authors also quantify each step: the neutron lifetime revision from $885.7$ s to $880.1$ s lowers $Y_p$ by 0.44 percent and ⁷Li/H by 0.39 percent, the Planck baryon density moves ⁷Li/H by about 4 percent and D/H by about 2.7 percent, and extending the network from 15 to 424 rates raises the ⁷Li yield modestly through a roughly 4 percent change in the late neutron abundance. Against the adopted spectroscopic values — $Y_p = 0.2534 ± 0.0083$, D/H $= (3.02 ± 0.23)×10^{-5}$, ³He/H $= (1.1 ± 0.2)×10^{-5}$ and ⁷Li/H $= (1.58 ± 0.31)×10^{-10}$ — three of the four agree within errors, and lithium does not, by a factor of about three.

The premise it rests on. The quoted error bars assume that the 424 nuclear reaction rates are independent lognormal deviates with the widths taken from a prior evaluation, even though the lithium uncertainty is stated to be dominated by one rate whose true uncertainty and correlations with the others are not independently verified here.

The deuterium prediction becomes a sharper baryometer: at $(2.67 ± 0.09)×10^{-5}$ it can discriminate between competing high-redshift D/H measurements at a level the previous error bar could not.

The predicted $Y_p = 0.2463 ± 0.0003$ sets a benchmark against which extrapolations of helium abundance to zero metallicity in dwarf galaxies can be tested for systematic error.

Because the ⁷Li/H error bar is dominated by a single reaction rate, a better measurement of $^3$He($α$,$γ$)$^7$Be would directly sharpen or soften the lithium discrepancy.

Varying the effective number of neutrino species within the CMB-allowed range does not remove the lithium mismatch, so non-standard neutrino physics at the allowed level is not a candidate solution.

The authors recommend applying the small non-instantaneous-neutrino-decoupling corrections as additive shifts to the $N_{eff}=3$ tables rather than rerunning with $N_{eff}=3.046$, since for nuclides other than helium the approximation moves results the wrong way.

The persistence of the lithium gap across a baryon-density shift that moved ⁷Li/H by 4 percent is a useful quantitative statement: any proposed solution must be larger than a few percent in its effect on ⁷Be or ⁷Li destruction, which rules out a broad class of small corrections.

If the true uncertainties on the 424 rates are correlated rather than independent, the quoted ⁷Li error bar is likely optimistic, and the discrepancy significance should be recomputed with a correlated covariance before being treated as a fixed number.

The same machinery could be rerun with a time-varying or spatially varying electron-to-photon ratio; the authors' tables give the sensitivity slopes needed to translate such a variation into an observable shift in D/H and ⁷Li/H.

The tension between the predicted $Y_p$ and the extrapolated spectroscopic value is smaller than the spectroscopic error bar, so improved helium systematics — plasma temperature, stellar absorption — would be the cheapest way to test whether that channel hides a second discrepancy.

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