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Big Bang nucleosynthesis and physics beyond the Standard Model

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Subir Sarkar (Oxford)

High Energy Physics - Phenomenology · Submitted 8 Feb 1996 · 19 references

Pith's verdict: A solid, honest review whose real value is the running commentary on how the N_nu and eta numbers moved, not any single quoted figure.

T0 · AI review

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arXiv IDhep-ph/9602260 (version 2)
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CitationSubir Sarkar (Oxford). "Big Bang nucleosynthesis and physics beyond the Standard Model." arXiv:hep-ph/9602260 (1996). https://pith.science/paper/JDDM5X3L
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The paper

The paper claims

The paper argues that the observed light-element abundances, read through standard Big Bang nucleosynthesis, constrain any new particle physics that changes the expansion rate or injects energy around the first second.

The reading

This review asks how much new particle physics the early universe will tolerate. It reconstructs the thermal history back through the nucleosynthesis era, when the temperature was about $1$ MeV and the age about one second, and then compares calculated yields of deuterium, helium-3, helium-4 and lithium-7 with abundances inferred from stars, interstellar gas and high-redshift clouds. The central claim is that these comparisons bound the energy density in any extra relativistic species, conventionally counted as extra neutrino flavours, and also bound massive relics that decay after nucleosynthesis, either by speeding the expansion or by injecting photons and hadrons that reprocess the light elements. The payoff is a cosmological constraint that often reaches particle candidates beyond the reach of accelerators, provided the primordial abundances and the nucleon-to-photon ratio can be pinned down.

What carries the argument

The argument turns on neutron-to-proton freeze-out and the deuterium bottleneck. Weak interactions keep neutrons and protons in equilibrium until the expansion rate overtakes the weak rate at $T sim 1$ MeV; the surviving neutron fraction then sets the helium yield, so anything that changes the expansion rate at that time changes $Y_p$. Extra relativistic species enter through $g_rho$, usually parametrized as $Delta N_ u$; a massive relic enters through $rho_x propto T^3$, which can come to dominate the expansion before it decays. The second half of the machinery is the nuclear reaction network and, for decaying relics, the electromagnetic cascade: high-energy decay products pair-produce and inverse-Compton scatter on the background until they populate a spectrum below $E_{max} sim m_e^2/22T$, and photons above the deuterium or helium thresholds then alter the abundances.

Extended reading notes

Core claim

The paper's central claim is that Big Bang nucleosynthesis is a quantitative constraint on physics beyond the Standard Model, not merely a consistency check of the hot Big Bang. In the conservative reading the author advocates, the helium-4 mass fraction below $0.25$ and the deuterium and lithium bounds allow up to $N_ u le 4.53$ equivalent light neutrino species, while a tighter but less robust set of abundance assumptions gives $N_ u le 3.75$ or below. For massive relics, the paper derives upper limits on $m_x n_x/n_gamma$ as a function of lifetime: entropy-producing radiative decays are restricted by the shift in $eta$, invisible decays by the increased expansion rate, and late decays by electromagnetic or hadronic cascades that photodissociate deuterium and helium and overproduce lithium. The review's contribution is to assemble the chain from thermodynamics to nuclear network to observed abundance, and to show where each link is uncertain.

Load-bearing premise

The bound on extra light species depends on a lower limit to the nucleon-to-photon ratio, and that lower limit is inferred from the same light-element abundances that the bound is meant to constrain.

Editorial extensions

If this is right

  • If the conservative bound holds, any extension predicting even one extra light species that decouples above the electroweak scale is under pressure, because such a species contributes a calculable fraction of a neutrino flavour.
  • A stable or long-lived massive relic with $m_x n_x/n_gamma$ above roughly $10^{-4}$ and a lifetime after about one second is excluded unless its decay products are sufficiently invisible and its energy density is diluted.
  • Late radiative decays with lifetimes above about $10^4$ s are constrained by photodissociation of deuterium and helium, and hadronic decays by overproduction of lithium and rare isotopes.
  • The same logic makes Big Bang nucleosynthesis a probe of neutrino degeneracy, additional Goldstone bosons, and supersymmetric or technicolour relics that would otherwise escape laboratory searches.

Reading between the lines

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

  • The review's conservative $N_ u le 4.53$ is only as good as the lower bound on $eta$; if future deuterium measurements settle near the low value $D/H sim 2.4 imes 10^{-5}$, the bound tightens toward $N_ u lesssim 3$, turning Big Bang nucleosynthesis into a sharper discriminator of new light species.
  • The same framework suggests a clean test for any model that predicts a light scalar or sterile neutrino: compute its decoupling temperature, dilute by the entropy release, and compare the resulting $Delta N_ u$ with the nucleosynthesis bound rather than with the $Z$ invisible width.
  • For decaying relics, the most discriminating future handle is a joint fit of D, $^3$He, $^7$Li and $^6$Li, because the cascade constraints depend on which element is being destroyed or created at a given lifetime.
  • The paper's distinction between entropy-producing and invisible decays implies that a particle with mixed decay modes cannot be constrained by either limit alone; the branching ratios must be weighted, which is a calculational gap the review leaves to model builders.
Original abstract

The Hubble expansion of galaxies, the $2.73\dK$ blackbody radiation background and the cosmic abundances of the light elements argue for a hot, dense origin of the universe --- the standard Big Bang cosmology --- and enable its evolution to be traced back fairly reliably to the nucleosynthesis era when the temperature was of $\Or(1)$ MeV corresponding to an expansion age of $\Or(1)$ sec. All particles, known and hypothetical, would have been created at higher temperatures in the early universe and analyses of their possible effects on the abundances of the synthesized elements enable many interesting constraints to be obtained on particle properties. These arguments have usefully complemented laboratory experiments in guiding attempts to extend physics beyond the Standard $SU(3)_{\c}{\otimes}SU(2)_{\L}{\otimes}U(1)_{Y}$ Model, incorporating ideas such as supersymmetry, compositeness and unification. We first present a pedagogical account of relativistic cosmology and primordial nucleosynthesis, discussing both theoretical and observational aspects, and then proceed to examine such constraints in detail, in particular those pertaining to new massless particles and massive unstable particles. Finally, in a section aimed at particle physicists, we illustrate applications of such constraints to models of new physics.

The compiled record

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. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,603 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.17 · compares with prior results 0.12 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

The Hubble expansion of galaxies, the $2.73\dK$ blackbody radiation background and the cosmic abundances of the light elements argue for a hot, dense origin of the universe --- the standard Big Bang cosmology --- and enable its evolution to be traced back fairly reliably to the nucleosynthesis era when the temperature was of $\Or(1)$ MeV corresponding to an expansion age of $\Or(1)$ sec. All particles, known and hypothetical, would have been created at higher temperatures in the early universe and analyses of their possible effects on the abundances of the synthesized elements enable many interesting constraints to be obtained on particle properties. These arguments have usefully complemented laboratory experiments in guiding attempts to extend physics beyond the Standard $SU(3)_{\c}{\otimes}SU(2)_{\L}{\otimes}U(1)_{Y}$ Model, incorporating ideas such as supersymmetry, compositeness and unification. We first present a pedagogical account of relativistic cosmology and primordial nucleosynthesis, discussing both theoretical and observational aspects, and then proceed to examine such constraints in detail, in particular those pertaining to new massless particles and massive unstable particles. Finally, in a section aimed at particle physicists, we illustrate applications of such constraints to models of new physics.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The Hubble expansion of galaxies, the $2.73\dK$ blackbody radiation background and the cosmic abundances of the light elements argue for a hot, dense origin of the universe --- the standard Big Bang cosmology --- and enable its evolution to be traced back fairly reliably to the nucleosynthesis era when the temperature was of $\Or(1)$ MeV corresponding to an expansion age of $\Or(1)$ sec. background 1.00 0.05 0.13 asserted 0.92
s1 All particles, known and hypothetical, would have been created at higher temperatures in the early universe and analyses of their possible effects on the abundances of the synthesized elements enable many interesting constraints to be obtained on particle properties. background 0.83 0.06 0.14 hedged possibility 0.61
s2 These arguments have usefully complemented laboratory experiments in guiding attempts to extend physics beyond the Standard $SU(3)_{\c}{\otimes}SU(2)_{\L}{\otimes}U(1)_{Y}$ Model, incorporating ideas such as supersymmetry, compositeness and unification. background 0.81 0.08 0.13 asserted 0.93
s3 We first present a pedagogical account of relativistic cosmology and primordial nucleosynthesis, discussing both theoretical and observational aspects, and then proceed to examine such constraints in detail, in particular those pertaining to new massless particles and massive unstable particles. contribution 0.92 0.67 0.06 asserted 0.89
s4 Finally, in a section aimed at particle physicists, we illustrate applications of such constraints to models of new physics. contribution 0.92 0.69 0.05 asserted 0.96

What kind of paper the classifier reports this is: review 1.00 · evidence from argument 0.65.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
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

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. The cosmological history of the universe
Figure 2. The number of relativistic degrees of freedom characterizing the entropy density gs (dashed line) and the energy density gρ (solid line), as a function of temperature in the Standard SU(3)c⊗SU(2)L⊗U(1)Y Model
Figure 3. Evolution of the abundances of primordially synthesized light elements with temperature according to the Wagoner (1973) numerical code as upgraded by Kawano (1992). The dashed lines show the values in nuclear statistical equilibrium while the dotted lines are the ‘freeze-out’ values as calculated analytically by Esmailzadeh et al (1991)
Figure 4. Dependence of primordially synthesized light element abundances on the nucleon-to-photon ratio η, calculated using the upgraded Wagoner code
Figure 5. Monte Carlo results (Krauss and Kernan 1995) for the 95% c.l. limits (dashed lines) on primordially synthesized elemental abundances, along with their central values (full lines). Note that the 4He mass fraction Yp is shown on a linear scale
Figure 6. Regressions of the helium mass fraction against the oxygen and nitrogen abundances in extragalactic low-metallicity HII regions, with (filled circles) and without (open circles) broad Wolf-Rayet features. Panel (a) shows abundances for 33 objects obtained using the Brocklehurst (1972) emissivities by Pagel et al (1992), with the maximum-likelihood linear fits (with ±1σ limits) for the latter category. Panel (b) shows abundances for 27 objects obtained using the Smits (1996) emissivities by Izotov et al (1996) along with the maximum-likelihood linear fits (with ±1σ limits)
Figure 7. The interstellar deuterium abundance as observed by Copernicus and IUE towards distant hot stars. The band shows the value measured towards the nearby star Capella (at 12.5 kpc) by the Hubble Space Telescope (Linsky et al 1995)
Figure 8. The Lithium abundance in 90 halo dwarf and main-sequence turnoff stars versus their effective surface temperature. Error bars indicate the 1σ interval for detections while triangles denote 3σ upper limits for non-detections; the dotted line is a fit which minimizes the absolute deviation of the detections (from Thorburn 1994)
Figure 9. Concordance of the predicted abundances with present observational bounds (from Kernan and Sarkar 1996). Note that only the 4He abundance inferred from BCG is established to be primordial. The two conflicting measurements of the D abundance in QAS are shown along with its ISM value, and both the Pop I and Pop II 7Li abundances are shown
Figure 10. Monte Carlo predictions for the 4He versus the D+3He abundances (taking Nν = 3 and τn = 889±2.1 sec) for (a) η = 2.71×10−10 and (b) η = 3.08×10−10. The dashed lines indicate the adopted “reasonable” observational upper bounds. In panel (a), a gaussian contour with ±2σ limits (dotted lines) on each variable is also shown (from Kernan and Krauss 1994)
Figure 11. The upper limit to the nucleon-to-photon ratio (in units of 10 −10) implied by the ISM bound D/H > 1.1 × 10−5 combined with (a) the Pop II bound 7Li/H < 2.6 × 10−10, and (b) the Pop I bound 7Li/H < 1.5 × 10−9 , as a function of the maximum 4He mass fraction
Figure 12. Number of Monte Carlo runs (out of 1000) which simultaneously satisfy the assumed abundance bounds, as a function of η (in units of 10−10), for various values of Nν. Panel (a) is obtained adopting Yp( 4He) ≤ 0.24 and [(D + 3He)/H]p ≤ 10−4 (from Kernan and Krauss 1994) while panel (b) is obtained taking Yp( 4He) ≤ 0.25, [D/H]p ≤ 2.5 × 10−4 and [7Li/H]p ≤ 2.6 × 10−10 (from Kernan and Sarkar 1996)
Figure 13. Upper bounds on the decaying-particle abundance as a function of its lifetime obtained from considerations of (a) entropy generation and increase in the expansion rate and (b) increase in the expansion rate alone (for ‘invisible’ decays). Above the full lines 4He is overproduced whereas above the dashed lines D + 3He is overproduced; the dot-dashed lines in panel (a) assume in addition that the initial nucleon-to-photon ratio is less than 10−4 (Scherrer and Turner 1988a,b). The dotted lines indicate the approximate bounds given by Ellis et al (1985b)
Figure 14. Normalized rates for photodissociation of light elements (as labelled) by electromagnetic cascades generated by massive unstable particles, as a function of the particle lifetime (Ellis et al 1992)
Figure 15. Upper bounds on the abundance of an unstable particle as a function of its lifetime from the effects of electromagnetic (Ellis et al 1992) and hadronic cascades (Reno and Seckel 1988) on the primordially synthesized abundances. Other results shown are from Dimopoulos et al (1989) (dot-dashed line), Ellis et al (1985b) (dashed line) and Protheroe et al (1995) (dotted line)
Figure 16. Upper bounds (dot-dashed curves) on the lifetime for ντ → e −e +νe (or ντ → νe,µγ) from nucleosynthesis compared with lower bounds (full lines) from laboratory experiments (updated from Sarkar and Cooper 1984). Curves (a) and (b) are calculated from limits on the mixing angle |Ue3| 2 obtained from, respectively, searches for additional peaks in π → eν decay (Britton et al 1992, De Leener-Rosier 1991) and measurement of the branching ratio π → eν/π → µν (Britton et al 1994). Curve (d) is the bound from entropy production and speed-up of the expansion rate, while curve (e) is obtained
Figure 17. Nucleosynthesis bounds on the reheating temperature after inflation, from consideration of the generation of massive unstable gravitinos (Ellis et al 1984b) and the effects of their hadronic (Reno and Seckel 1988) and radiative (Ellis et al 1992) decays on elemental abundances
Figure 18. The contribution of nucleons to the cosmological density parameter as a function of the assumed Hubble parameter (after Hogan 1994). The full lines (with dotted ‘2σ’ error bands) show the standard BBN values according as whether the primordial D abundance is taken to be the high value (Songaila et al 1994, Rugers and Hogan 1996a,b) or the low value (Tytler et al 1996, Burles and Tytler 1996) measured in QAS. The dashed line is the lower limit from an audit of luminous matter in the universe (Persic and Salucci 1992). The dot-dashed line indicates the value deduced from the observed…

Figures reproduced from arXiv:hep-ph/9602260 by the authors.

References
How later papers used it

119 later papers cite it

Evidence: some. 117 of the citing papers share no author with it, and 14 of those carry a confident label from Pith's citation classifier.

Pith read 9 of the 146 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 data or values 2 of 9 papers with this label
How the literature uses it

117 arXiv papers cite this in 143 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 · 96 sentences without a confident label

Uses its method or tool 5 papers
  • Following Ref. [ref] (see Appendix A.4), the Helium abundance $Y_p$ was estimated as $Y_p ≃2 X_n|_T_D$ with $T_D = 0.07$ MeV and we picked some representative benchmark points within the currently unconstrained parameter space. $T_D$ is the temperature at which Deuterium is no longer dissociated by photons [ref] and thus all neutrons at that time are expected to form Helium.

    A Cosmic Window on the Dark Axion Portal · Cosmological constraint from BBN · 0.90

  • Using the cascade spectrum and shower analysis of Refs. [ref] , we obtain the green (D) and magenta ($^4$He) bounds in Fig. [ref], labeled as D and $^4$He photofissions, respectively (SM [ref]).

    Gravitational waves decay in vacuum · Introduction · 0.96

  • When $N_ν$ varies due to the extra radiation contribution, one can use the BBN code to obtain a semi-analytic formula of $Y_p(N_ν)$ by fixing the two free parameters $η_b$ and $τ_n$ to their experimental measurements [ref] .

    Simple estimate of BBN sensitivity to light freeze-in dark matter · Effective neutrino number shift from extra radiation · 0.85

Uses its data or values 9 papers
Compares with it 1 paper
  • The differential equation for the neutron fraction $X_n≡n_n/(n_n+n_p)$ is [equation] Solving this differential equation numerically, we find that $X_n$ reaches the freeze-out value [equation] around $T = T_n^FO ≈0.2$, in agreement with [ref] .

    Cosmological Signatures of a Mirror Twin Higgs · BBN in the SM · 0.92

Cites it as background 29 papers
  • Equipped with the CMB inference of the small cosmological baryonic abundance, $Ω_B ∼4%$, the theory of Big Bang Nucleosynthesis (BBN) within the Standard Model (SM) of Particle Physics is highly predictive, and confronted with accurate measurements of primeval elements such as the mass density fraction of helium-4, $Y_P$, and the relative abundance of deuterium, $D/H$, offers important constraints on New Physics (NP) [ref] active during the first few minutes of the lifetime of the Universe [ref] .

    Indications for a Nonzero Lepton Asymmetry from Extremely Metal-Poor Galaxies · Introduction · 0.94

  • BBN has been studied extensively as a probe of new physics scenarios with late decays of long-lived particles [ref] , while its utility as a probe of annihilation has received less attention as it is generally less sensitive than other observables, particularly for higher-mass DM candidates [ref] .

    BBN Constraints on the Hadronic Annihilation of sub-GeV Dark Matter · Introduction · 0.97

  • The time-dependent quantity being the neutron abundance at $t τ_n$, which regulates the primordial fraction of baryonic mass in $^4$He, [equation] where $δN_ν^eff = N_ν^eff -3$ is the effective number of extra (non-SM) light neutrino species, $τ_n$ is the neutron half life, and $η$ is the ratio of the baryon number density to the photon number density [ref] .

    Neutrino Cosmology after WMAP and LHC7 · Introduction · 0.88

Discussion

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