Pith. Sign in

REVIEW

Neutrinos in cosmology

PaperPDF from arXiv

data files

ReviewThe objections and verdict, as JSON Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
A.D. Dolgov

High Energy Physics - Phenomenology · Submitted 13 Feb 2002 · 300 references

Pith's verdict: A genuinely useful review with the assumptions spelled out, but where numerical groups disagree it settles the argument in favor of its own calculations, and the quoted m_ντ < 1 MeV inherits that.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

  1. T0 AI review An AI read the paper and answered a fixed list of questions.
  2. T1 Audit Automatic checks that the references and files the paper relies on exist and match.
  3. T2 Compute The paper's code or calculations re-run with the same results.
  4. T3 Formal statement The claims written out in a formal math language a computer can read.
  5. T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 2 major objections · 8 minor · Ask about this paper · The compiled record · Read the full review →
Challenge this review Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDhep-ph/0202122 (version 2)
Pith IDFQVWUO75, Pith's permanent record of this paper and its review
CitationA.D. Dolgov. "Neutrinos in cosmology." arXiv:hep-ph/0202122 (2002). https://pith.science/paper/FQVWUO75
Cite this reviewBibTeX for Pith's review of this paper
Claim paper

Why Pith says this

Highlight any text to comment on it.

Referee report

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

A review arguing that cosmology is a neutrino laboratory: the relic neutrino sea, primordial helium and deuterium, and the microwave background together convert neutrino mass, lifetime, and flavor count into measured numbers.

The reading

This is a review with a thesis: the early universe is not merely a place where neutrinos happen to be, but a precision instrument for measuring their properties, often more sharply than terrestrial experiments. The argument runs through a chain of standard cosmological machinery. Neutrinos decouple at 2–3 MeV, their number is frozen at $n_ν/n_γ = 3/11$ after electron-positron annihilation, and their present-day density is therefore known, so a non-zero mass translates directly into a contribution to the cosmic energy budget. That gives the Gerstein–Zeldovich bound $Σ m_{ν j} < 94$ eV $Ω h^2$, the paper's anchor result. The same logic, run through big bang nucleosynthesis, bounds the number of light species, the mass of a tau neutrino that survives past nucleosynthesis, the mass of a stable fourth-generation neutrino from annihilation freeze-out, and the magnetic moment, lifetime, and mixing of sterile states. A sympathetic reader should care because the review's claim is that a tabletop-scale particle property can be read off the sky at a precision laboratory searches cannot match.

What carries the argument

Two pieces of machinery carry the argument. The first is the freeze-out equation for a relic species, $dn_h/dt + 3Hn_h = ⟨σ_{ann}v⟩[(n_h^{eq})^2 - n_h^2]$ (eq. 80), which says that a particle annihilates until its rate falls below the expansion rate, after which its number in a comoving volume is frozen and its present density follows from the cross-section and mass. This single equation yields both the Gerstein–Zeldovich bound for light neutrinos (where the number is not Boltzmann-suppressed) and the few-GeV lower mass bound for a heavy stable neutrino (where it is). The second is the neutron-to-proton freezing calculation, in which the weak rates $n + ν_e ↔ p + e^-$ and $n + e^+ ↔ p + anti-ν_e$ compete against the Hubble rate; the freezing temperature scales as $g_*^{1/6}$, so any additional relativistic species or any distortion of the $ν_e$ spectrum shifts the frozen ratio and hence the helium mass fraction. The review packages the outcome of both as an effective number of neutrino species, $N_{eff}$, which lets very different physics — a heavy tau neutrino, a sterile state, a distorted spectrum, a non-zero chemical potential — be compared on one axis.

Extended reading notes

Core claim

The review's central claim is that a small set of cosmological observables — the relic neutrino density, the primordial abundances of $^{2}$H, $^{3}$He, $^{4}$He and $^{7}$Li, and the angular spectrum of the microwave background — collectively impose quantitative, sometimes leading, constraints on neutrino properties. The cleanest instance is the mass bound: because neutrinos decouple while relativistic and are not reheated by $e^+e^-$ annihilation, their number density today is fixed at $3/11$ of the photon density, so demanding that their energy density not exceed the critical density gives $Σ m_{ν j} < 94$ eV $Ω h^2$ (eq. 66), roughly 10–14 eV for plausible cosmological parameters. The second instance is nucleosynthesis: extra relativistic species raise the expansion rate, shift the neutron-proton freezing temperature, and raise the helium mass fraction, so the observed helium and deuterium bound the effective number of neutrino species. The review reports that the modern consensus is close to three, with an allowed excess somewhere between 0.2 and 1 extra species depending on which deuterium measurements are trusted. The third instance is the tau neutrino: if it is stable on nucleosynthesis timescales, a mass in the 1–22 MeV range would produce too much helium, so the mass is pushed below about 1 MeV. The review also argues in the opposite direction for heavy neutrinos: annihilation freeze-out means a stable fourth-generation neutrino lighter than a few GeV would overclose the universe, so such a particle must be heavier than roughly 2–2.5 GeV, with an upper bound near a few TeV from unitarity once the annihilation cross-section into $W^+W^-$ grows with mass.

Load-bearing premise

The bounds assume that neutrinos carry no significant lepton asymmetry, that is, that their chemical potentials are essentially zero; the review states this as an explicit assumption and admits it has never been checked observationally, resting only on the analogy with the small baryon asymmetry.

Editorial extensions

If this is right

  • A laboratory measurement of the neutrino mass sum above roughly 94 eV times $Ω h^2$ would contradict the standard relic-density argument, and a sum well below it would confirm that neutrinos are a subdominant component of cosmic energy density.
  • A confirmed primordial helium abundance appreciably above the standard prediction would point to extra relativistic degrees of freedom at nucleosynthesis, whether a fourth light neutrino, a sterile state, or a light scalar.
  • If the tau neutrino were found with a mass in the MeV range and a lifetime longer than a few hundred seconds, the review's nucleosynthesis calculation would be falsified or would require a compensating distortion of the electron-neutrino spectrum.
  • Precision measurements of the microwave background damping tail could detect the roughly 0.03 extra effective neutrino species produced by residual neutrino heating and finite-temperature electromagnetic corrections, turning a per-cent-level calculational detail into an observable.

Reading between the lines

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

  • The review's two directions of constraint — an upper bound on light neutrino mass and a lower bound on heavy stable neutrino mass — leave an intermediate window that cosmology forbids but colliders also forbid for the three known flavors; the window is only open to a fourth-generation neutral lepton, which makes the bound a statement about unknown physics rather than about known particles.
  • Because the helium bound depends on the expansion rate, any new light particle that was ever in thermal equilibrium behaves like a fractional neutrino; the review's effective-species bookkeeping therefore functions as a general audit of the cosmic relativistic inventory, not just of neutrinos.
  • The paper concedes that lepton asymmetry is unmeasured, and its own later sections show that a non-zero neutrino chemical potential shifts both the mass bound and the freezing temperature. A modest degeneracy in the muon or tau sector would relax the species-count limit while leaving helium nearly unchanged, which suggests the nucleosynthesis bound on $N_ν$ and the bound on lepton asymmetry should
  • The review documents disagreement among numerical groups computing the same distortion and the same heavy-neutrino abundance, with differences traced to integration grids and matrix-element symmetrization factors. That suggests the quoted per-cent-level bounds are limited by calculational bookkeeping as much as by data, and would tighten if the kinetic-equation treatments were reconciled.
Original abstract

Cosmological implications of neutrinos are reviewed. The following subjects are discussed at a different level of scrutiny: cosmological limits on neutrino mass, neutrinos and primordial nucleosynthesis, cosmological constraints on unstable neutrinos, lepton asymmetry of the universe, impact of neutrinos on cosmic microwave radiation, neutrinos and the large scale structure of the universe, neutrino oscillations in the early universe, baryo/lepto-genesis and neutrinos, neutrinos and high energy cosmic rays, and briefly some more exotic subjects: neutrino balls, mirror neutrinos, and neutrinos from large extra dimensions.

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, 2,381 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.13 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Cosmological implications of neutrinos are reviewed. The following subjects are discussed at a different level of scrutiny: cosmological limits on neutrino mass, neutrinos and primordial nucleosynthesis, cosmological constraints on unstable neutrinos, lepton asymmetry of the universe, impact of neutrinos on cosmic microwave radiation, neutrinos and the large scale structure of the universe, neutrino oscillations in the early universe, baryo/lepto-genesis and neutrinos, neutrinos and high energy cosmic rays, and briefly some more exotic subjects: neutrino balls, mirror neutrinos, and neutrinos from large extra dimensions.

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 Cosmological implications of neutrinos are reviewed. contribution 0.85 0.35 0.10 asserted 0.55
s1 The following subjects are discussed at a different level of scrutiny: cosmological limits on neutrino mass, neutrinos and primordial nucleosynthesis, cosmological constraints on unstable neutrinos, lepton asymmetry of the universe, impact of neutrinos on cosmic microwave radiation, neutrinos and the large scale structure of the universe, neutrino oscillations in the early universe, baryo/lepto-genesis and neutrinos, neutrinos and high energy cosmic rays, and briefly some more exotic subjects: neutrino balls, mirror neutrinos, and neutrinos from large extra dimensions. contribution 0.96 0.25 0.06 asserted 0.78

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

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. Abundances of light elements 2H (by number) 4He (by mass), and 7Li (by number) as functions of baryon-to-photon ratio η10 ≡ 1010nB/nγ. results of these measurements are grouped around two very different values, normal deuterium, (D/H)p ≈ 3·10−5 [98]-[100], which is reasonably close to what is observed in the Galaxy, and high deuterium, (D/H)p ≈ (1−2)· 10−4 [101]-[105]. The observed variation may not be real; for example, uncertainties in the velocity field allow the D/H ratio in the system at z = 0.7 [105] to be as low as in the two high-z systems [106]- [108]. An interpretation of t
Figure 2. Evolution of non-equilibrium corrections to the d
Figure 3. The distortion of the neutrino spectra δj = (fνj − f eq ν )/f eq ν as functions of the dimensionless momentum y at the final ”time” x = 60. The dashed lines a and c correspond to Maxwell-Boltzmann statistics, while the solid lines b and d correspond to Fermi-Dirac statistics. The upper curves a and b are for electronic neutrinos, while the lower curves c and d are for muonic (tau) neutrinos. All the curves can be well approximated by a second order polynomial in y, δ = Ay(y − B). universe was recently proposed in ref. [142]. Though significantly less accurate, it gives a simple in
Figure 4. Cosmological energy density of massive neutrinos
Figure 5. Mass fraction of 4He as a function of the number of massless neutrino species. Different curves correspond to different values of the baryon-to-photon ratio η10 ≡ 1010nB/nγ = 2, 3, 4, 5, 6 in order of increasing helium abundance. bounds on the allowed value of Nν . The most restrictive limit is advocated in refs. [180, 112], ∆Nν < 0.20 (at 95% C.L.). To obtain such a restrictive result the authors used the measurements of deuterium in high z-clouds [99, 100] which give (D/H)p = (3.4 ± 0.25) · 10−5 . However, uncertain velocity corrections and the possibility of a two-component system
Figure 6. Deuterium-to-hydrogen by number as a function of t
Figure 7. Distortion of spectral distribution of electroni
Figure 8. Relative energy density of massive tau-neutrinos
Figure 9. The effective number of equivalent massless neutri
Figure 10. The effective number of equivalent massless neutr
Figure 11. The number of equivalent massless neutrino speci
Figure 12. Primordial deuterium (by number) for different
Figure 13. Primordial helium-4 (by mass) for different
Figure 14. Summary of the exclusion regions in the (sin
Figure 15. (a) An example of an angular spectrum of CMB anisot
Figure 16. Angular power spectrum of CMB anisotropy in the de
Figure 17. The evolution of the absolute value of the effectiv
Figure 18. LSS and CMB constraints in (ξ, n) space for ΩΛ = 0 (left) and ΩΛ = 0.6 (right). The underlying cosmological model is flat, with h = 0.65, Ωb = 0.05, Qrms−ps = 18 µK, no reionization, no tensor contribution. The allowed regions are those where the labels are. For LSS constraints, we can distinguish between degen￾erate neutrinos with mν = 0 (solid lines) and mν = 0.07 eV (dotted lines). effect of neutrino degeneracy is a larger free streaming mentioned above. It leads to a further suppression of small scale matter fluctuations. In figure 18 taken from ref. [449] the region in the…
Figure 19. Spectrum of angular fluctuations of CMB for differe
Figure 20. Growth rate of the CDM density field, f ≡ d log δ/d log a, in four flat C+HDM models at cosmological scale factor a = 1 (solid) and 0.1 (dashed). The four models assume different neutrino masses: mν = 1.2, 2.3, 4.6, and 6.9 eV (from top down), corresponding to Ων = 0.05, 0.1, 0.2, and 0.3. 184
Figure 21. Effect of a 1 eV neutrino on the bright red galaxy (BR
Figure 22. Bounds for (να − νs)-mixing. The middle full line describes the mass￾mixing relationship if sterile neutrinos are the dark matter for (ντ − νs)-mixing. The two other full lines allow a factor 2 uncertainty in the amount of dark matter, ΩDM = 0.15−0.6. The dashed line is for (νe −νs)-mixing. The hatched region for big masses is excluded by the Diffuse Gamma Background. The region above the dotted line is excluded by the duration of SN 1987A for (ντ − νs)-mixing. (for discussion and references see the paper [537]) for νs mass density and the existing data on the X-ray background.…
Figure 23. Evolution of L (e) = 2Lνe + η for νe → νs oscillations with sin2 2θ0 = 10−8 and, from left to right, δm2/eV 2 = −0.25, −0.5, −1.0, −2.0, −4.0 obtained from numerical solution of the kinetic equations. The initial Lνe = 0 is taken and η = 5 × 10−10 is assumed. The low temperature evolution is weakly dependent on these values. a certain moment q the resonance condition is fulfilled for neutrinos (antineutrinos) with momentum: y (or ¯y) = q 2 y ! ± d q2/3  N − N¯ + ηo  , (384) where d = 1.65 · 10−3 (cos 2θ δm2 ) −1/3 , ηo is the charge asymmetry of other particles, exc
Figure 24. Region of parameter space where the final sign does
Figure 25. The distribution of the final sign of neutrino asym
Figure 26. Evolution of neutrino chemical potentials for LM
Figure 27. Evolution of the neutrino degeneracy parameters
Figure 28. Change in the effective number of neutrino species
Figure 29. Fluxes of neutrinos, γ−rays, and nucleons predicted by the Z-burst mech￾anism for mν = 0.5 eV, assuming sources exclusively emitting neutrinos with fluxes equal for all flavors [835]. Three cases of the source evolution parameter, m = −3, 0, 3 are shown by solid, dashed, and dotted lines, respectively. Values assumed for the other parameters are: extragalactic magnetic field strength B = 10−9 G, minimal ra￾dio background strength, zmin = 0, zmax = 3, Eν max = 2×1022 eV, qν = 1. For each case the neutrino flux amplitude f is obtained from minimizing χ 2 for Emin = 2.5×1019 eV. Also…

Figures reproduced from arXiv:hep-ph/0202122 by the authors.

References
How later papers used it

143 later papers cite it

Evidence: substantial. 141 of the citing papers share no author with it, and 14 of those carry a confident label from Pith's citation classifier.

Pith read 20 of the 216 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 7 papers with this label
Compares with it 2 papers
How the literature uses it

131 arXiv papers cite this in 199 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 · 107 sentences without a confident label

Uses its method or tool 5 papers
  • We neglect the influence of chemical potential and write down the temperature evolution equations from Eq.([ref]) and Eq.([ref]) by assuming that the temperature of three generation active neutrinos are the same, [equation] where $δρ_ν_e/δt$ and $δρ_ν_μ/δt$ are collision terms induced by neutrino interactions calculated in the Refs. [ref] .

    $\mathbf{{N}_{eff}}$ from Excited DM state · The effective number of neutrinos · 0.91

  • Here we use the matrix elements outlined in Table 2 of [ref] and follow the integration method developed in [ref] to obtain the relevant rates[The reader is referred to the appendices of [ref] and [ref] which very recently appeared in the literature and which explain in more detail and with explicit formulae how to perform the different integration steps.].

    Neutrino decoupling beyond the Standard Model: CMB constraints on the Dark Matter mass with a fast and precise $N_{\rm eff}$ evaluation · Derivation of the temperature evolution equations · 0.96

  • Following [ref] , we have computed the collision terms for SM $ν$ decoupling, considering Fermi-Dirac (FD) distribution function for all the SM fermions and appropriate Pauli blocking factors.

    Imprints of MeV Scale Hidden Dark Sector at Planck Data · Boltzmann equations and Numerical analysis · 1.00

Uses its data or values 5 papers
  • Following Ref. [ref] , we apply a 95% upper limit $N_eff<0.17$ [ref] as a half Gaussian likelihood.

    Light Thermal Dark Matter Beyond $p$-Wave Annihilation in Minimal Higgs Portal Model · Cosmological and astrophysical constraints · 0.94

  • [ref] over $∫^̣3 p E g_ϕ/(2π)^3$.[However, we find that for numerical calculations it is best to determine $q̇_ϕ(t)$ directly from its definition $q̇_ϕ(t) = ρ̇_ϕ(t) + 3H(t)[ ρ_ϕ(t) + _ϕ(t)]$, since the numerical evaluation of $f_ϕ(t, p) - f̅_ϕ(t, p)$ can easily lead to cancellation of significant digits.] Given that the reaction rate which keeps the neutrinos in thermal equilibrium scales as $T^5$, it is a good approximation to assume that neutrino decoupling happens instantaneously when $T^5 / H$ reaches the value it has at neutrino decoupling only considering the SM degrees of freedom, i.e. $T_ν^5 / H (T_ν) ≃1.62 ×10^-10 GeV^4$ taking $T_ν^≃1.4 MeV$ [ref] .

    Updated BBN constraints on electromagnetic decays of MeV-scale particles · Evolution of the decaying particle $ϕ$ · 0.81

  • By assuming Maxwell-Boltzmann statistics for all the particles involved in the process, neglecting the electron mass, neglecting statistical factors, and by considering the matrix elements reported in Table 2 of [ref] we arrive to the following annihilation collision term: [equation] where $G_F$ is the Fermi constant, $g_L^ν_e = 1/2 + s_W^2$, $g_R^ν_e = s_W^2$, $g_L^ν_μ, τ = -1/2 + s_W^2$, $g_L^ν_μ, τ = s_W^2$, and $s_W$ is the sinus of the Weinberg angle.

    Neutrino decoupling beyond the Standard Model: CMB constraints on the Dark Matter mass with a fast and precise $N_{\rm eff}$ evaluation · Neutrino collision terms in the SM in the Maxwell-Boltzmann approximation · 0.88

Compares with it 2 papers
Cites it as support 2 papers
  • Firstly, neutrinos were tightly coupled to the thermal plasma for temperatures $T≳2 MeV$ [ref] , and secondly, the successful prediction of the light element abundances require neutrinos to have a Fermi-Dirac-like distribution at the time at which the proton-to-neutron interactions freeze-out $T∼0.7 MeV$, see [ref] .

    What can CMB observations tell us about the neutrino distribution function? · BBN and model building · 0.96

  • The sterile fields were decoupled from thermal bath at a sufficient early universe, and the chirality-flip production from the active $SU(2)_L$ doublets, $(ν_i,e_i)^(0)_L$, through the tiny Dirac mass terms are negligible as shown in Ref. [ref] .

    Active Dirac Neutrinos via $SU(2)_L$ Doublets in 5d · Summary and Discussion · 0.99

Cites it as background 67 papers
  • A precision calculation of $N_eff^SM$ requires one to solve the process of neutrino decoupling in the early Universe and this has been a subject of intense study for more than 40 years now, see [ref] for references devoted to this problem, see [ref] for reviews and [ref] for a book.

    Neff in the Standard Model at NLO is 3.043 · Introduction · 1.00

  • The prospect that precision cosmological measurements could reveal the effects of non-zero neutrino masses has drawn broad attention from both the cosmology and high energy physics communities [ref] .

    Cosmological Implications of a Neutrino Mass Detection · Introduction · 0.94

  • This is called the Dodelson-Widrow mechanism (DW) [ref] because they derived the analytic solution for the relic number density of sterile neutrinos produced in this manner[The original Dodelson-Widrow results were subsequently corrected by a factor of 2 [ref] .] (see also earlier work [ref] ).

    Cosmological Dependence of Non-resonantly Produced Sterile Neutrinos · Non-resonant sterile neutrino production · 0.91

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.