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Astrophysics · arXiv:astro-ph/0406095 v2 · submitted 3 Jun 2004 · 222 references

The Cosmic Energy Inventory

Masataka Fukugita, P. J. E. Peebles

The paper says

“We present an inventory of the cosmic mean densities of energy associated with all the known states of matter and radiation at the present epoch.”

more of the abstract

The observational and theoretical bases for the inventory have become rich enough to allow estimates with observational support for the densities of energy in some 40 forms. The result is a global portrait of the effects of the physical processes of cosmic evolution.

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. A genuinely useful reference table with honest bookkeeping, but the error bar on the largest baryonic entry does not cover the paper's own competing baryon determination. This line is wrong

2 major objections · 7 minor

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The paper says, at §2.3.7 and Table 1, entry 3.1

The review did not quote this passage.

Pith says: Objection 1 of 2 · major

Entry 3.1 (warm intergalactic plasma, 0.040) is the single largest baryonic entry and is defined as Ω_b minus the sum of every other baryonic entry, so it scales one-for-one with the adopted Ω_b h² = 0.0225 ± 0.0015 (eq. 17).

more of objection 1

The authors acknowledge this in §2.3.7, so the budget-driven nature is not hidden. What is not carried through is the paper's own competing determination of the same quantity: §2.2.2 quotes the Izotov & Thuan helium abundance as Ω_b h² = 0.013 (+0.002/−0.001), set aside as likely systematic in footnote 9. That is a 42% spread in the quantity that fixes entry 3.1. Propagating it with all other entries held fixed, entry 3.1 falls from 0.040 to roughly 0.022, and the derived headline fractions shift: '6.0 ± 1.3% of the total baryons' in stars (§2.3.1, from eqs. 17 and 27) becomes about 10%, and '90% of the baryons are in this intergalactic plasma' (§2.3.7) becomes about 80%. The quoted ±0.003 on entry 3.1 (±7%) is far narrower than this spread. Concrete test: recompute Table 1 with Ω_b h² = 0.013 and report the resulting range for entries 3.1 and 3.1a/b and for the two headline fractions, or state explicitly that the ±0.003 is conditional on eq. 17 and does not include the helium-based alternative. This is a correctness-risk concern about error propagation, not a claim that the inventory fails to close.

The paper says, at §3, 'closure of our inventory' sentence; abstract

The review did not quote this passage.

Pith says: Objection 2 of 2 · major

The statement in §3 that 'the closure of our inventory suggests that missing or unknown components cannot be energetically very significant' is partly true by construction. Entries 1.1 and 1.2 are fixed by the flat ΛCDM fit under the assumption that the density parameters sum to unity (§2.1: 'The other entries in the first category in Table 1 are computed …

more of objection 2

… from equation (8) and our estimates of the other significant contributions to the total mass density, under the assumption that the density parameters sum to unity'), and entry 3.1 is a residual (§2.3.7). The three largest entries in Table 1 are therefore not independent measurements, and the closure of the table is not by itself a check on them. The authors acknowledge each piece separately, so the issue is one of emphasis in the abstract's 'observational support for the densities of energy in some 40 forms' and in the §3 closure sentence, not of hidden reasoning. Concrete suggestion: add a column or a short table note distinguishing entries that are independent measurements from those fixed by the closure condition, and qualify the §3 sentence to say that closure constrains the sum of the non-dark, non-residual entries rather than the whole inventory.

7 minor objections

The paper says, at Table 1, error column

Pith says: minor objection 1 of 7

The error convention stated in §2 is informal and non-uniform: 'where no digit is presented after the decimal point we hope our estimate might within a factor of ten of the real value.' Entries such as 3.11 (10^−6), 8 (10^−5.5), 9 (10^−8.3), and 10 (10^−8.0) therefore carry factor-of-ten uncertainties, yet the category totals are quoted to two significant figures.

more of objection 1

A per-entry flag or a note in the Table 1 caption stating which entries are order-of-magnitude would let a reader use the table without repeatedly consulting §2.

The paper says, at Table 1, category 2 total

Pith says: minor objection 2 of 7

The category 2 total is given as 0.0010 ± 0.0005, but the sum of entries 2.1 (10^−4.3 ≈ 5 × 10^−5), 2.2 (10^−2.9 ≈ 1.3 × 10^−3), and 2.3 (−10^−4.1 ≈ −8 × 10^−5) is about 1.2 × 10^−3. Please check whether the total is a rounding of 10^−3.0 or whether one of the entries has been revised.

show 5 more

The paper says, at §2.1, eq. (14)

Pith says: minor objection 3 of 7

The r-band luminosity density is written as L_r = (2.3 ± 0.2) × 10^8 h L⊙ Mpc^3; the units should be Mpc^−3, as they are for L_B and L_z on the same lines.

The paper says, at §2.1, paragraph after eq. (63)

Pith says: minor objection 4 of 7

The text states that the integral of the Tegmark et al. (2004b) power spectrum over all wavenumbers is '2700 h^−2 Mpc'; since ∫P(k)dk has units of Mpc^2, this should read h^−2 Mpc^2.

The paper says, at §3, paragraph on the stellar mass density

Pith says: minor objection 5 of 7

The sentence 'The estimate in §2.7.1 of the mass density in stars uses the optical luminosity density and the stellar-mass-to-light ratio' points to the radiation-background subsection; the stellar mass estimate is in §2.3.1.

The paper says, at Table 4, footnote c

Pith says: minor objection 6 of 7

The citation reads 'Matilla (1990)' but the reference list gives 'Mattila, K. 1990'; please make the spelling consistent. The 0.10 µ entry from Henry (1999) is far below the others and appears to be a lower limit or a different band; a note in the caption would help.

The paper says, at Throughout, production artifacts

Pith says: minor objection 7 of 7

Several encoding artifacts will need fixing in proofs: 'So/suppress ltan' for Soltan (1982) in §1 and §2.5.4 and in the reference list; 'greaterorsimilar' and '/greaterorsimilar' for ≳ in §2.3.7, §2.3.8, and §2.5.2; 'W e' for 'We' throughout; 'higly' for 'highly' in §2.7.6; the mismatched bracket in 'eq. [(53]' in §2.1; and the spacing in '10 −5.4(1 + ǫn)' in Table 1. Footnote 3 cites 'Bennett 2003a' where 'Bennett et al. 2003a' is meant.

What would settle it

Recompute entry 3.1 and the fractions derived from it using Ω_b h² = 0.013 (the Izotov & Thuan helium value quoted in §2.2.2) instead of the adopted 0.0225, holding entries 3.2 through 3.13 fixed. Report the resulting shift in entry 3.1, in the stellar-to-total-baryon fraction (eqs. 17 and 27), and in the plasma fraction of §2.3.7. If any of these shifts exceeds the quoted errors (±0.003 on 3.1; ±1.3% on the stellar fraction), the error bar on 3.1 is understated and Table 1 should carry the helium systematic explicitly. Equivalently, check whether ±0.003 is consistent with propagating the full spread of the three Ω_b determinations quoted in §2.2.2.

from the skeptic's reading

How the review went

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

  1. Reader holds up confidence high
  2. Skeptic partly agrees 1 min 52 s · 48,963 tokens read, 5,926 written
  3. Editor wrote the verdict above 28 s · 50,046 tokens read, 1,506 written
  4. Referee minor revision: 2 major objections, 7 minor 2 min 24 s · 49,325 tokens read, 7,860 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

Bottom line: this is the table you will end up citing whenever you need an order-of-magnitude for some cosmic energy density, and it is unusually honest about which rows are measurements and which are bookkeeping. The one number to handle with care is entry 3.1, the warm intergalactic plasma at 0.040. It is defined as Omega_b minus everything else in category 3, so it inherits the full uncertainty in the adopted Omega_b h2 = 0.0225 (eq. 17) and none of the entries it absorbs can correct it. The authors say this outright in section 2.3.7, so it is not a hidden flaw. What the table does not display is that the paper itself quotes a competing determination: the Izotov & Thuan helium abundance gives Omega_b h2 = 0.013 in section 2.2.2, 42% below the adopted value. Footnote 9 argues the helium lines are technically difficult, which is fair, but the quoted +/-0.003 on entry 3.1 is far narrower than that spread. Propagate it and 3.1 drops to roughly 0.022, the '6% of baryons in stars' becomes about 10%, and '90% in intergalactic plasma' becomes about 80%. The qualitative conclusion survives; the specific numbers and their stated errors are softer than Table 1 implies. That is the main thing I would want a referee to press on. A second, smaller point: the consistency checks in sections 2.7.3 and 2.8.1 are presented as a network, but the stellar mass, the heavy element yield, the optical/FIR background and the stellar energy production all draw on the same IMF and the same star formation history. Their agreement is partly inherited rather than independent. The authors half-acknowledge this; I would state it more plainly. Minor: the error convention ('where no digit is presented after the decimal point we hope our estimate might within a factor of ten') is charming but makes the table hard to use quantitatively, and h is fixed at 0.7 with no scaling recipe. What is genuinely new and good: the broadening from the FHP baryon budget to a full inventory, the quasar mass conversion efficiency epsilon_n = 0.02 (eq. 86), the gravitational wave entries in 2.7.6, the cosmic ray density, and the neutrino budget. Those are estimates that did not exist in one place before. Who should read it: anyone who needs a defensible number for a subdominant component, and anyone writing about the baryon budget or the dark sector target. It deserves a serious referee, mainly to force the Omega_b spread into the table.

The strongest objection

The largest baryonic entry, 3.1 (warm intergalactic plasma, 0.040), is defined in §2.3.7 as Ω_b minus the sum of every other baryonic entry, so it scales one-for-one with the adopted Ω_b h² = 0.0225 ± 0.0015 (eq. 17). The authors are candid that this entry is budget-driven, and the reader correctly identifies that. What the reader does not flag is that the paper itself quotes a competing determination of the same quantity: the Izotov & Thuan helium abundance gives Ω_b h² = 0.013 (+0.002/−0.001) in §2.2.2, which the authors set aside as likely systematic (footnote 9 lists the λ4471 vs λ5876/λ6678 discrepancy). That is a 42% spread in the very quantity that sets entry 3.1. Propagating it with all other entries held fixed, entry 3.1 falls from 0.040 to roughly 0.022, and the derived headline fractions shift accordingly: '6.0 ± 1.3% of the total baryons' in stars (§2.3.1, from eqs. 17 and 27) becomes about 10%, and '90% of the baryons are in this intergalactic plasma' (§2.3.7) becomes about 80%. The quoted ±0.003 on entry 3.1 (±7%) is far narrower than this spread. So the error bar on the single largest baryonic entry is understated relative to the paper's own quoted alternatives, and the headline fractions inherit a systematic that Table 1 does not display. This is not a refutation: the inventory still closes because 3.1 is residual by construction, and the qualitative conclusion (most baryons are in diffuse plasma, and missing components are not energetically dominant) survives. The concern is that the specific numbers and their stated uncertainties are less secure than the table implies.

The reader's weakest_assumption points at the right entry: 3.1 is a residual, and the authors say so in §2.3.7. I agree with that identification and with the ACCEPT verdict, but I sharpen the concern in a way the reader did not. The residual's magnitude is not free-floating; it is pinned to Ω_b, and the paper's own §2.2.2 quotes a helium-based Ω_b h² = 0.013 that is 42% below the adopted 0.0225. The ±0.003 error on entry 3.1 does not reflect that spread, so the table's precision on its largest baryonic row is overstated even though the row's construction is acknowledged. This is a bookkeeping and error-propagation issue, not a soundness failure. The central claim — that an inventory of roughly 40 forms can be assembled with observational support and closes — survives, because closure is guaranteed by the residual construction and because the qualitative conclusion (most baryons in diffuse plasma; no energetically dominant missing component) is robust to the Ω_b shift. The paper also flags the dark sector as physically hypothetical and the helium measurement as technically difficult, so it does not overclaim. On the correlated-checks point the reader raises in the rationale, I agree: the agreement among eqs. (99), (108), (109) and (119) is partly inherited from a shared IMF and star-formation history, which is a reason to discount those checks rather than to reject the inventory. Independent support: the adopted numbers have aged well against later CMB results (Ω_b h² ≈ 0.0224, Ω_m ≈ 0.31), which is real external corroboration of the compilation's central parameters. For these reasons I would not move the verdict; the appropriate response is to widen the error bar on entry 3.1 and to state the helium systematic alongside the headline fractions, not to reject the paper.

The referee's report

As a reference compilation this is genuinely useful, and the cross-check network is the paper's real contribution rather than any single number. The agreement between the nuclear binding energy released in making the heavy elements and the present optical plus far-infrared radiation background (eqs. 108–109), and the consistency of the integrated star formation with the stellar mass and with the supernova rate, are non-trivial and are the kind of redundant test that lends credence to an inventory of this sort. The authors are also candid about which entries are measured and which are not: §1 states that the physical natures of the dark-sector entries 'remain quite hypothetical,' and §2.3.7 states plainly that the largest baryonic entry 'still is driven by the need to balance the budget rather than more directly by the observations.' That candor is a strength and should be preserved in any revision. The paper ships no code or machine-checked derivation, but it does make a falsifiable global prediction (the entries sum to unity and the radiation budget matches the nuclear budget), and it is honest about the precision of each entry.

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

This is an accounting exercise on the largest possible ledger. The authors ask a simple question: at the present epoch, how much energy sits in each known form, and can the numbers be made to add up? They answer with a single table of about 40 entries, each expressed as a fraction of the critical density, so that a neutrino background, the starlight in the night sky, the iron locked in white dwarfs, and the dark energy can all be compared directly. The dominant entries are dark energy (about 0.72) and dark matter (about 0.23). Ordinary baryonic matter is about 0.045, and of that only a small fraction has condensed into stars, galaxies, and plasma in clusters. Most of the baryons, roughly 90 percent, are assigned to a warm intergalactic plasma that has not been directly detected in bulk. The paper is explicit that this largest baryonic entry is set by subtracting all the other known baryonic components from the total baryon density inferred from the microwave background and primordial nucleosynthesis, rather than by direct observation. The rest of the paper is a long series of consistency checks: the nuclear binding energy stored in heavy elements is compared against the integrated optical and infrared background, the supernova rate implied by the assumed stellar initial mass function is compared against observed rates, and the mass in quasar remnants is compared against the integrated quasar light to infer a mass-to-radiation conversion efficiency of about 2 percent. None of these checks is decisive on its own, but together they form a network that the authors argue makes much of the inventory believable.

Core claim. The paper claims that a consistent inventory of the cosmic mean energy density in roughly 40 forms can now be assembled with observational support, and that the entries close and cross-check well enough to be believable. The load-bearing version is in Table 1 and in the discussion: the entries sum to unity, the dominant dark sector entries are fixed by the flat LCDM fit, and the baryonic entries are constrained well enough that, in the authors' words, 'missing or unknown components cannot be energetically very significant.' If correct, this is a validated global accounting of where cosmic energy resides at the present epoch.

The premise it rests on. Entry 3.1, the warm intergalactic plasma at 0.040, which is the single largest baryonic entry, is not measured. It is defined as the residual: the adopted total baryon density (eq. 17, Omega_b h^2 = 0.0225) minus the sum of every other baryonic entry (section 2.3.7). The authors state this plainly: the entry 'still is driven by the need to balance the budget rather than more directly by the observations.' Its quoted error is therefore inherited from Omega_b and from the sum of the other entries, not from any detection of the plasma itself. If the true baryon density is lower, or if any other entry is underestimated, this entry absorbs the discrepancy silently.

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The paper

Abstract

We present an inventory of the cosmic mean densities of energy associated with all the known states of matter and radiation at the present epoch. The observational and theoretical bases for the inventory have become rich enough to allow estimates with observational support for the densities of energy in some 40 forms. The result is a global portrait of the effects of the physical processes of cosmic evolution.

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 result is a global portrait of the effects of the physical processes of cosmic evolution.”

How the main claim is stated: asserted 0.99

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.18 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.34 · compares with prior results 0.07 · mentions code or data availability 0.03

The abstract, sentence by sentence

This table labels the abstract only (arXiv listing abstract v2). The number is the probability the classifier gave the label.

SentenceRoleThe authors' own workStates the main conclusionStrength
We present an inventory of the cosmic mean densities of energy associated with all the known states of matter and radiation at the present epoch. contribution 1.00 0.92 0.17 asserted 0.98
The observational and theoretical bases for the inventory have become rich enough to allow estimates with observational support for the densities of energy in some 40 forms. background 0.39 0.15 0.09 asserted 0.80
The result is a global portrait of the effects of the physical processes of cosmic evolution. interpretation 0.98 0.50 0.30 asserted 0.99

What kind of paper the classifier reports this is: dataset or benchmark 0.78 · evidence from analysis of existing data 0.56

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How the labels were made

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,866 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

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Cited by 17 Pith papers

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

  1. Shear-kSZ: A New Estimator for the Matter-Electron Power Spectrum from kSZ Tomography and Weak Lensing astro-ph.CO · Jul 2026
  2. Search for a Dispersion Measure Excess Toward Nearby Galaxy Halos Using Fast Radio Bursts from the Second CHIME/FRB Baseband Catalog astro-ph.GA · Nov 2026
  3. Too many quiescent late-type galaxies or a matter of misclassification? astro-ph.GA · Jul 2026
  4. Fuelling the central region of galaxies with misaligned gas accretion astro-ph.GA · Jul 2026
  5. FLAMINGO: The thermal history of the Universe from tSZ effect cross-correlations and its dependencies on cosmology and baryon physics astro-ph.CO · May 2026
  6. Missing baryons recovered: a measurement of the gas fraction in galaxies and groups with the kinematic Sunyaev-Zel'dovich effect and CMB lensing astro-ph.CO · Jul 2025
  7. Detecting patchy reionization in the CMB astro-ph.CO · Jul 2016
  8. On the later evolution of observationally selected protocluster candidates at $z\,{\gtrsim}\,5$ astro-ph.GA · Jun 2026
  9. Exploring neutrino loss with diffuse astrophysical neutrino fluxes hep-ph · May 2026
  10. Constraining the Baryon Fraction in Extragalactic Diffuse Ionized Gas with 124 Localized Fast Radio Bursts astro-ph.CO · Jun 2025
  11. Evidence for large baryonic feedback at low and intermediate redshifts from kinematic Sunyaev-Zel'dovich observations with ACT and DESI photometric galaxies astro-ph.CO · Jul 2024
  12. Observability of Dark Matter Substructure with Pulsar Timing Correlations astro-ph.CO · May 2020
  13. The Simons Observatory: Science goals and forecasts astro-ph.CO · Aug 2018
  14. Science Impacts of the SPHEREx All-Sky Optical to Near-Infrared Spectral Survey: Report of a Community Workshop Examining Extragalactic, Galactic, Stellar and Planetary Science astro-ph.CO · Jun 2016
  15. The Evolution of Compact Binary Star Systems astro-ph.HE · Mar 2014
  16. Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions astro-ph.CO · Dec 2011
  17. The Large-Scale Structure of the Universe through the SKA lenses astro-ph.CO · Jun 2026
How later papers used it

91 later papers cite it

Evidence: substantial. 90 of the citing papers share no author with it, and 22 of those carry a confident label from Pith's citation classifier.

Pith read 18 of the 119 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 6 of 16 papers with this label
Compares with it 1 of 6 papers with this label
How the literature uses it

35 arXiv papers cite this in 41 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 · 21 sentences without a confident label

Uses its data or values 9 papers
Compares with it 1 paper
  • This is somewhat smaller than the value of $5.4×10^5M_⊙$Mpc$^-3$ determined from the correlation between black hole mass and bulge luminosity [ref] , as computed by [ref] .

    Stellar Black Holes and the Origin of Cosmic Acceleration · Cosmic History of Black Holes and Cosmic Acceleration · 0.99

Cites it as background 9 papers

Challenges and discussion

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