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The Impact of Early Massive Galaxy Formation on the Cosmic Microwave Background

T0 review · 5 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The formation of massive early-type galaxies at $z\approx15$--$20$, with a top-heavy stellar IMF and dust thermalization, produces a present-day photon energy density between 1.4% and 100% of the observed CMB, implying the CMB may not be…

desk verdict A transparent order-of-magnitude estimate with a genuine 1.4% lower bound, but the upper 100% claim collapses under a circular dust-thermalization check and a non-global separation. read the letter →

arxiv 2505.04687 v1 pith:7ZHZFQT6 submitted 2025-05-07 astro-ph.GA

Eda Gjergo , Pavel Kroupa This is my paper · ORCID
classification astro-ph.GA
keywords cosmicmicrowavebackgroundCMBforegroundsearly-typegalaxiesdustthermalizationgalaxy-wideinitialmassfunctionhigh-redshiftgalaxyformation21-cmanomalymonolithiccollapse
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that the formation of massive early-type galaxies, giant ellipticals with present-day stellar masses above $10^{11.5}\,M_\odot$, at redshifts $15

What carries the argument

The argument rides on two linked identities. The expansion relation $1+\langle z_f\rangle=\langle d_0\rangle/\langle d_f\rangle$ turns a $\sim400$ kpc progenitor cloud radius and a $\sim15$ Mpc present-day mean ETG separation into $\langle z_f\rangle\approx16.5$. The Stefan-Boltzmann thermalization relation $L_{\mathrm{dust,ETG,em}}=4\pi R_{\mathrm{eff}}^2\sigma T_{\mathrm{dust,ETG,em}}^4$ turns the peak galaxy luminosity of about $10^{15}\,L_\odot$ radiated from $R_{\mathrm{eff}}\approx10\,\mathrm{kpc}$ into a dust temperature of about 50 K, close to the CMB temperature at $z\approx17$. The luminosity input is built on the integrated galaxy-wide initial mass function (IGIMF), a galaxy-wide IMF that becomes top-heavy at high star-formation rates; its luminosity evolution for a star-forming unit, convolved with a Gaussian cosmic birth function $B_{\mathrm{ETG}}(t_{\mathrm{cosmo}})$ anchored to $15<z<20$, produces the total ETG luminosity and hence the photon energy density.

What would settle it

Look for the thermal dust component directly at the formation epoch: if millimetre-wavelength observations of $z\approx15$--$20$ massive galaxy progenitors show dust covering fractions far below unity, or dust temperatures and infrared luminosities well below the $4\pi R_{\mathrm{eff}}^2\sigma T^4$ value required by their bolometric output, then the full thermalization assumption fails and the contribution cannot approach the CMB. A complementary check is to search CMB maps for the clustered shot-noise signal expected from roughly six forming ETGs per Planck beam at $z\approx17$.

Watch

Extended reading notes

Core claim

The central claim, stated on the paper's own terms, is that the same rapid, intense formation required to explain massive ellipticals also produces, without any CMB prior, a dust-thermalized photon field whose present-day energy density approaches the observed CMB value. Convolving the luminosity evolution of a single ETG, peaking near $10^{15}\,L_\odot$, with a Gaussian cosmic birth function of all ETGs in a flat-$\Lambda$CDM volume yields $U_{\mathrm{ETG}}(z=0)$ values from $5.9\times10^{-16}\,\mathrm{J\,m^{-3}}$, about 1.4% of the observed CMB energy density, up to values of the same order as the observed $4.17\times10^{-14}\,\mathrm{J\,m^{-3}}$. The formation redshift is fixed by equating the average present-day separation of massive ETGs, $\langle d_0\rangle\approx15\,\mathrm{Mpc}$, to their separation at formation derived from a $\sim400\,\mathrm{kpc}$ progenitor cloud radius, giving $\langle z_f\rangle\approx16.5$. Dust thermalization of the peak luminosity from an effective radius of about 10 kpc gives a dust temperature near 50 K, matching the CMB temperature at $z\approx17$, so the reprocessed light is naturally a microwave background. The paper concludes that today these galaxies would produce a photon field approaching the observed CMB photon energy density.

Load-bearing premise

The result collapses if dust did not absorb essentially all of the bolometric luminosity of each forming giant elliptical and re-radiate it thermally around 50 K with negligible energy loss, because that thermalization step is what converts the starburst light into a CMB-like photon field.

Editorial extensions

If this is right

  • CMB parameter estimation would need to be redone with this foreground included: at Planck resolution the birth function places roughly six forming ETGs in each pixel, so the contamination is not smooth.
  • The 21-cm absorption trough near $z\approx17.5$ would be accounted for by the same formation epoch, with intense star formation and a top-heavy galaxy-wide IMF providing the required cool gas or enhanced contrast, rather than requiring exotic physics.
  • The observed hemispheric CMB power asymmetry would find a natural connection to the anisotropic sky distribution of massive ETGs, which is denser in the southern hemisphere.
  • Even a few percent leakage of the peak ETG luminosity to the observer would bias CMB power-spectrum analyses, so foreground-subtraction schemes that omit massive-ETG formation would be systematically off.
  • At the upper end of the range, the microwave background would be at least partly reprocessed starlight rather than purely primordial radiation from recombination.

Reading between the lines

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

  • Beyond the paper: a $\sim50$ K dust component at $z\approx17$ redshifts to $\sim2.7$ K, so the reprocessed light is almost spectrally degenerate with the CMB; distinguishing the two would require angular clustering, polarization, or spectral-distortion statistics rather than the mean blackbody curve.
  • Beyond the paper: the same emission should appear as a high-redshift contribution to the cosmic infrared background at submillimetre wavelengths, so deep millimetre counts of $z>10$ dusty galaxies can test the upper end of the claimed range.
  • Beyond the paper: the calculation can be inverted, using CMB foreground residuals as a constraint on the formation epoch, star-formation efficiency, and dust properties of the first massive galaxies.
  • Beyond the paper: because the number density argument scales as $(1+z)^3$, the result is sensitive to the assumption that the local 15 Mpc ETG spacing applies throughout the universe; modestly smaller high-redshift separations would push the contribution up by a large factor.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper argues that the formation of massive early-type galaxies (ETGs) at redshifts 15–20, with a top-heavy galaxy-wide IMF and full thermalization of their bolometric luminosity by dust, produces a present-day photon energy density of 1.4% (for the local mean separation d0≈15 Mpc) up to approximately 100% (for d0≈9 Mpc) of the observed CMB energy density. The authors construct an analytic model for the luminosity evolution of a single ETG from IGIMF-based star-forming units, convolve it with a Gaussian cosmic birth function anchored to the 21-cm anomaly, and derive energy densities under 'naive' and 'convolved' formation scenarios. They interpret the result as evidence that the CMB may contain a significant contribution from reprocessed starlight in the first massive galaxies.

Significance. If the claim held, it would challenge the standard interpretation of the CMB as the pure recombination relic and would have far-reaching implications for foreground subtraction in cosmology. The calculation is transparent and largely built from independent inputs (IGIMF theory, downsizing timescales, stellar population models), and the lower bound (1.4%) is a well-defined quantitative prediction. The strongest part is the identification of a mechanism that could generate a 2.7 K blackbody-like background without any CMB fitting. However, the upper end of the claimed range depends on several unverified assumptions that are not adequately stress-tested in the paper.

major comments (5)
  1. [Section 3.2.2] The consistency check that 'U_ETG,0 ≈ U_CMB,0' is circular. The authors set T_dust,ETG,em ≈ 50 K at z=17 and then compute T_dust,obs = T_dust,em/(1+z) ≈ 2.7 K, concluding that the dust-thermalized photon field matches the CMB. But T_dust,em ≈ 50 K was adopted precisely because the CMB temperature at z=17 is 2.7255×(1+17) ≈ 48.9 K (Eq. 23). The check therefore does not independently verify the population-based energy density in Eqs. (25)–(26); it merely restates the temperature assumption. This section should be removed or replaced with a genuinely independent test, such as a comparison with COBE/FIRAS spectral distortion limits.
  2. [Section 2.3.3 and Section 3.2.2] The full-dust-thermalization assumption (L_bol ≈ L_dust, Eq. 27) is internally inconsistent with the paper's own statement that 'dust destruction timescales are extremely short, and comparable to the lifetime of a few 10^7 yr' while the peak-luminosity epoch in Eq. (24) lasts Δt ≈ 660 Myr. If dust is destroyed on a timescale 10–100 times shorter than the starburst, the efficiency of thermalization must be much less than unity over most of the burst. The numbers in Fig. 5 are therefore upper limits, not 'conservative estimates'. The authors should introduce a dust-covering fraction or a time-dependent dust survival factor and show the resulting attenuation of the quoted energy densities.
  3. [Section 2.2.2, Table 1, Figure 5] The 'up to the full CMB energy density' result is obtained only for d0=9 Mpc, which the paper itself describes as the separation 'in such regions' of overdensity at z≈2, not as a cosmic average. Using this value as a global input overstates the all-sky contribution. The most conservative global case is d0=15 Mpc, giving 1.4% of the CMB energy density; the d0=9 Mpc case should be presented as a local-overdensity limiting case, and the abstract and conclusions should not present it as the central scenario without explicit qualification of its restricted applicability.
  4. [Section 5 and Abstract] The claim that the calculation is 'derived entirely without priors or constraints from the CMB' is overstated. The formation epoch is set by the ansatz that the 21-cm anomaly marks the peak of massive ETG formation (Sections 2.1.4 and 2.2.1), and the 'consistency check' in Section 3.2.2 uses the observed CMB temperature as a target. While the luminosity and IMF inputs are indeed independent, the choice of z≈15–20 is partly motivated by a cosmological signal (the EDGES 21-cm anomaly), not purely by galaxy evolution. The CMB-independence claim should be reworded.
  5. [Section 5 (implied falsifiability)] The paper does not compare its predicted contribution to the COBE/FIRAS limits on CMB spectral distortions. If the ETG radiation is not perfectly thermalized (which the paper acknowledges as a possibility when it says 'even if the absorption coefficients and dust emissivity were not highly efficient'), a percent-level contribution would produce y- or μ-type distortions that FIRAS constrains to levels of order 10^-5. A concrete quantitative comparison with FIRAS would provide a falsifiable test of the upper range and is essential to supporting the claim that the ETG radiation could rival the CMB.
minor comments (5)
  1. [Eq. (5)] The arithmetic in Eq. (5) appears incorrect: 15 Mpc / 800 kpc = 18.75, so 1+z ≈ 18.75 and z ≈ 17.75, not 16.5. This affects the quoted ⟨z_f⟩ ≈ 16.5 and should be corrected or clarified.
  2. [Section 2.1.5] The Gaussian stellar birth function with μ_SFU = 2τ_down and FWHM = τ_down is an arbitrary choice; the paper acknowledges this but should list it explicitly in the assumptions or in a table of free parameters so the reader can track which results depend on it.
  3. [Figure 5 caption] The caption says 'The gray shaded region spans the full range of ⟨d0⟩ in the naive approach,' but the markers only show d0=10 and 15 Mpc. Clarify what the gray region represents and how it relates to the d0=9 Mpc value mentioned in the text.
  4. [Section 3.2.2] The sentence 'In each co-moving Gpc^3 volume there are N0 = n0 × 1 Gpc^3 ≈ 3.3×10^5 ETGs' uses n0 for d0=15 Mpc, but the surrounding paragraph discusses dust temperatures without stating which d0 is being used. Specify the assumed separation or state that N0 scales as d0^{-3}.
  5. [General] There are several typographical and naming inconsistencies (e.g., 'Jerabkova' vs. 'Jeřábková' in the Fig. 1 caption, 'e fficiently' in Section 4). A careful proofread is needed.

Circularity Check

2 steps flagged · score 6.0 of 10

The §3.2.2 'consistency check' is self-definitional (U_ETG,0 = U_CMB,0 by Stefan-Boltzmann identity), and the 'full CMB' upper bound leans on a same-group ⟨d0⟩ = 9 Mpc estimate; the 1.4% population calculation is otherwise independent.

  1. self definitional [Section 3.2.2, Eq. (30) and following paragraph]
    "Therefore, ETGs contribute an energy density of dust-thermalized photons at emission near z = 17 of: UETG, em = 4σ/c T^4_dust, ETG, em, (30) where T_dust, ETG, em(z) = (1 + z) T_dust, ETG, obs with z = 17. For average ETG peak luminosities of ≈ 10^15 L⊙, T_dust, ETG, obs ≈ 2.7 K. It follows that UETG,0≈ UCMB,0 verifying the more accurate calculation shown in Fig. 5."

    Eq. (30) is the same Stefan-Boltzmann energy-density formula used to define UCMB,0 in Eq. (22). With T_dust,em ≈ 50 K and z = 17 already fixed by the model, T_dust,obs = 50/18 K ≈ 2.7 K, so UETG,0 ≈ (4σ/c)(2.7 K)^4 ≈ UCMB,0 automatically. The equality is therefore an identity of blackbody temperature, not an independent check of the source population: it omits the number density n0 and sky-covering factor that enter the actual integrals in Eqs. (25)-(26) and Table 1. No matter how sparse the ETGs are, any blackbody seen at 2.7 K has the CMB energy density, so this 'verification' cannot validate the 1.4%-100% result.

  2. self citation load bearing [Table 1 caption; Sec. 2.2.2; Conclusions]
    "Haslbauer et al. (2023) found large inhomogeneities at scales of a few Gpc, where the present-day average separation of massive ETGs could be as small as 9 Mpc. These estimates are to be compared to the present-day energy density of the CMB: UCMB(z = 0) = 418 × 10−16 J m−3."

    The abstract's upper bound ('up to the full present-day CMB energy density') is obtained only for ⟨d0⟩ = 9 Mpc in Table 1. This value is imported from Haslbauer, Kroupa & Jerabkova (2023), whose author list overlaps with the present paper (P. Kroupa). While it is an external observational estimate rather than a fit to the CMB, it is load-bearing for the headline range: removing it leaves only the 1.4%-to-55% results from ⟨d0⟩ = 15 and 10 Mpc. The same group's Eappen et al. (2022) simulation is also the source of the 400 kpc cloud radius used to set z_f ≈ 16.5 (Eq. 5), so the formation epoch is largely inherited from prior work by the authors.

full rationale

The population-luminosity part of the calculation (SFU luminosity from Jerabkova et al. 2017, IGIMF birth function, convolution in Eq. 8, cosmological integration in Eq. 21) is self-contained and not fitted to the CMB; the 1.4% lower bound is a genuine model output. The circularity is localized. In Sec. 3.2.2 the paper presents as a 'consistency check' the fact that T_dust,em/(1+z) ≈ 2.7 K, which guarantees U_ETG,0 ≈ U_CMB,0 by the same blackbody formula; this is a definitional identity, not a check. The 'up to the full CMB' end of the range relies on ⟨d0⟩ = 9 Mpc from a same-group paper, a load-bearing self-citation. Additional internal tensions (dust destruction timescales ~10^7 yr vs the 660 Myr integration window; the 'continuum' assumption) weaken the upper bound but are correctness issues rather than circularity per se.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim rests on several literature-derived inputs (tau_down, d0, rf, SFU luminosity, IGIMF) plus two ad hoc modeling choices: the 21-cm-anomaly ansatz for the formation epoch and full dust thermalization. No new particles, forces, or dimensions are introduced. The absence of a radiative-transfer treatment means the energy-density ratio is an upper-end estimate, not a measured prediction.

free parameters (5)
  • downsizing formation timescale tau_down = 440 Myr (Mtot=1e11.5 Msun), 340 Myr (1e12 Msun)
    Adopted from Kroupa et al. (2020) Eq. 2, fitted to chemical evolution and downsizing data; sets the width and center of the SFU birth Gaussian (Eqs. 6-7).
  • average present-day ETG separation d0 = 9, 10, 15 Mpc
    Local value 15 Mpc from Davies et al. 1993; 9 Mpc from Haslbauer et al. 2023 is used for the upper CMB estimate. Directly sets n0 and the ETG number density (Eq. 14).
  • progenitor cloud radius rf = approximately 400 kpc
    From Eappen et al. (2022) Fig. 4, based on Milgromian collapse simulations; used in Eq. 5 to derive zf about 16.5.
  • dust effective radius Reff = approximately 10 kpc
    Chosen as fiducial in Section 2.3.3 and Eq. 27; sets Tdust about 50 K, which makes the observed dust temperature near 2.7 K in Section 3.2.2.
  • SFU peak luminosity / LSFU(t) = peak about 9.2e12 Lsun for a 1e7 Msun SFU
    Taken from Jerabkova et al. (2017) Fig. 7; normalized to SFU mass and used in the convolution Eq. 8.
assumptions (6)
  • domain assumption Flat Lambda-CDM geometry and Planck 2018 cosmological parameters (H0=67.66, Omega_m, Omega_Lambda).
    Used for all redshift-time conversions and volume elements (Section 2.2.1, Eq. 9); the paper later suggests Lambda-CDM may be invalid, which is tension within the same calculation.
  • domain assumption IGIMF theory with SFR- and metallicity-dependent galaxy-wide IMF.
    Foundation for SFU luminosity and top-heavy IMF (Section 1 and Section 2.1.1).
  • domain assumption Massive ETGs formed monolithically at high redshift with SFR near 1e3 Msun/yr.
    Inherited from Eappen et al. 2022, Thomas et al. 2005, and Yan et al. 2021; needed for the birth function and luminosity.
  • ad hoc to paper Dust forms quickly and thermalizes the full ETG luminosity without energy loss.
    Assumed in Section 2.3.3; no radiative transfer or dust optical depth calculation is provided, yet this assumption sets the conversion from L to UETG.
  • ad hoc to paper The 21-cm anomaly marks the peak of massive ETG formation at 15<z<20.
    Explicit ansatz in Section 2.2.1; sets the z range for the ETG birth function.
  • ad hoc to paper Stellar birth function and ETG birth function are Gaussians with mu=2*tau_down and FWHM=tau_down.
    Chosen in Section 2.1.5 and Eq. 7; the paper defers more realistic models to future photGalIMF work.

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Pith. "Pith review of The Impact of Early Massive Galaxy Formation on the Cosmic Microwave Background." pith.science (2026). https://pith.science/paper/7ZHZFQT6

@misc{pith2026250504687,
  author       = {Pith},
  title        = {Pith review of: The Impact of Early Massive Galaxy Formation on the Cosmic Microwave Background},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7ZHZFQT6}},
  note         = {Machine review of arXiv:2505.04687}
}
read the original abstract

The Cosmic Microwave Background (CMB) anisotropies, corrected for foreground effects, form the foundation of cosmology and support the Big Bang model. A previously overlooked foreground component is the formation of massive early-type galaxies (ETGs), which can no longer be ignored, particularly in light of JWST's detection of massive, evolved systems at extreme redshifts (z > 13). The rapid formation of massive ETGs has been advocated in galaxy evolution studies for decades, and recent evidence has compelled even proponents of hierarchical mass assembly to acknowledge the fact that massive ETGs evolve quickly. Constraints from chemical evolution are particularly stringent. Without both intense star formation and a top-heavy galaxy-wide initial mass function of stars (IMF), it is difficult to reconcile stellar population synthesis models with the high metallicity and abundance patterns of alpha elements. We infer from previous studies that the progenitor cloud of each massive ETG must have had a radius of approximately 400 kpc. Comparing this value to the average present-day separation of massive ETGs, their formation may have occurred around 15 < z < 20. We consider this epoch of formation in a flat-LCDM cosmological context, incorporating the known and necessary properties of massive ETGs. Such properties are encapsulated independently by the integrated galaxy-wide IMF (IGIMF) theory. The massive ETG evolution presented in this work is consistent with recent advancements in stellar and galaxy evolution, and is derived entirely without priors or constraints from the CMB. Yet, it emerges as a non-negligible source of CMB foreground contamination. Even in our most conservative estimates, massive ETGs account for 1.4% up to the full present-day CMB energy density.

Figures

Figures reproduced from arXiv: 2505.04687 by the authors.

Figure 1
Figure 1. In reality, the stellar birth distribution is unlikely to be [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Comparison of the bolometric luminosity evolution of massive ETGs [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 1
Figure 1. Evolution of a 1012 M⊙ massive early-type galaxy (ETG), as de￾scribed in Sec. 2.1. The top panel shows the bolometric luminosity evolution of a star-forming unit (SFU), the middle panel shows the stellar birth function, where the stellar mass is expressed in units of SFU. The bolometric luminosity of the whole ETG is shown on the bottom panel. 10 0 10 1 10 2 10 3 10 4 Galaxy Age [Myr] 10 11 10 12 10 13 10 14 10 15 1… view at source ↗
Figures from the paper (3 more)
Figure 3
Figure 3. Figure 3: Evolution of the stellar mass of individual ETGs in this work ( [PITH_FULL_IMAGE:figures/full_fig_p009_3.png]
Figure 4
Figure 4. Figure 4: Evolution of all massive ETGs, as described in Sec. 2.2. The [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: This figure represents the evolution (curves), as a function of redshift of the energy densities (Ui,em) at emission (markers) of multiple sources i, namely primordial plasma, massive ETGs born simultaneously, and cumulative massive ETGs. The red bold cross represents …

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.