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REVIEW 2 major objections 5 minor 88 references

Quasar X-ray and UV flux, baryon acoustic oscillation, and Hubble parameter measurement constraints on cosmological model parameters

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Pith's one-line read A joint analysis of quasar X-ray/UV fluxes, Hubble-parameter measurements, and baryon acoustic oscillations is consistent with flat $\Lambda$CDM but mildly favors a closed universe with dynamical dark energy.

desk verdict A careful and honest constraints paper extending the 2015 quasar sample to six cosmological models; the cosmological preferences are weak and the QSO relation's universality is the main caveat, but the analysis is sound and worth citing as a data-validation step. read the letter →

arxiv 1909.01400 v3 pith:T77ZSD56 submitted 2019-09-03 astro-ph.CO gr-qchep-exhep-ph

classification astro-ph.COgr-qchep-exhep-ph
keywords quasarcosmologyX-rayandUVluminosityrelationdarkenergyspatialcurvaturebaryonacousticoscillationsHubbleparameterLambdaCDMMarkovchainMonteCarlo
topics Dark Energy
open problems Dark Energy
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

This paper asks whether quasar X-ray and ultraviolet flux measurements can serve as a cosmological distance probe, and what they say about the composition and geometry of the universe when combined with more standard data. Using 808 quasars spanning redshifts $0.061$ to $6.28$ together with 31 Hubble-parameter measurements and 11 baryon acoustic oscillation measurements, the authors constrain six cosmological models: flat and curved versions of $\Lambda$CDM, the XCDM dark-energy parametrization, and the $\phi$CDM scalar-field model. The quasar data alone give much weaker constraints than the $H(z)$+BAO data, but they agree with them. In the joint analysis the data remain consistent with the standard flat $\Lambda$CDM model, while mildly favoring closed spatial hypersurfaces and dark energy whose density changes with time. If right, this establishes quasars as a high-redshift distance probe and gives a concrete target for future cosmological observations.

What carries the argument

The load-bearing object is the X-ray-to-UV luminosity relation of quasars, $\log(L_X)=\beta+\gamma\log(L_{UV})$, rewritten in terms of fluxes as $\log(F_X)=\beta+(\gamma-1)\log(4\pi)+\gamma\log(F_{UV})+2(\gamma-1)\log(D_L)$. This turns each quasar's measured UV and X-ray fluxes into a distance indicator through the luminosity distance $D_L(z,p)$, with $\beta$, $\gamma$, and a global intrinsic dispersion $\delta$ fitted together with the cosmological parameters. The likelihoods for the 31 $H(z)$ and 11 BAO measurements, including the correlated BAO points via the covariance matrix, are combined with the quasar likelihood, and the parameter space is explored with a Markov chain Monte Carlo, with model comparison via AIC and BIC. The $L_X$--$L_{UV}$ relation is what lets the quasar sample, reaching $z\simeq6.28$, act as a cosmological probe.

What would settle it

Fitting the $L_X$--$L_{UV}$ relation separately in narrow redshift bins and finding that $\beta$ or $\gamma$ drifts by more than the quoted uncertainties would falsify the universal-relation assumption; alternatively, re-running the joint analysis with the newer 1598-quasar compilation and finding that $\Omega_{k0}$ and $\omega_X$ move back to $0$ and $-1$ respectively would show that the mild preference was a statistical fluctuation.

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Extended reading notes

Core claim

The paper's central claim is that the combined QSO + $H(z)$ + BAO data are consistent with the currently standard spatially-flat $\Lambda$CDM model, but mildly favor a closed universe and dynamical dark energy. On its own, the quasar sample, calibrated through the assumed relation $\log(L_X)=\beta+\gamma\log(L_{UV})$, constrains cosmological parameters only loosely: in the non-flat $\Lambda$CDM model it yields $\Omega_{m0}=0.24^{+0.16}_{-0.10}$ and $\Omega_\Lambda=0.93^{+0.18}_{-0.39}$. Adding the quasars to the $H(z)$+BAO data tightens the constraints and, in several models, pushes the best fit away from the flat-$\Lambda$ baseline: the curvature parameter is negative (closed) in most cases, reaching $\Omega_{k0}=-0.22^{+0.09}_{-0.13}$ in the non-flat $\phi$CDM model with the high local Hubble-constant prior, and six of the eight dynamical-dark-energy cases prefer evolving dark energy over a cosmological constant at 1.3 to 2.6 $\sigma$. The strength of these preferences depends on the assumed prior on $H_0$.

Load-bearing premise

The argument rests on the assumption that the $L_X$--$L_{UV}$ relation has the same slope and intercept at every redshift from 0.061 to 6.28, with all remaining scatter captured by one constant dispersion; if the relation evolves with redshift or the sample is biased by how quasars are selected in X-ray and UV flux, the quasar distances and the joint cosmological constraints would be biased.

Editorial extensions

If this is right

  • If the joint preference is real, the quasar X-ray/UV method is a working distance probe that extends cosmological constraints to redshifts far beyond those reached by supernovae.
  • The mild preference for closed spatial hypersurfaces, if confirmed by future data, would mean the simplest flat $\Lambda$CDM geometry is incomplete.
  • Adding quasar data to $H(z)$+BAO noticeably tightens constraints in models with more free parameters, so larger quasar compilations should sharpen cosmological parameter estimates.
  • The fitted slope $\gamma\simeq0.6$ and dispersion $\delta\simeq0.32$ are stable across all six models, indicating that the quasar calibration is not strongly model-dependent.
  • The results depend on the Hubble-constant prior: the higher local $H_0$ prior strengthens the preference for closed geometry and dynamical dark energy, linking the finding to the broader $H_0$ tension.

Reading between the lines

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

  • If the same $L_X$--$L_{UV}$ relation is allowed to evolve with redshift, the mild curvature and dynamical-dark-energy signal could weaken or vanish; fitting $\beta$ and $\gamma$ in redshift bins with the current 808-quasar sample would be a direct test.
  • The newer 1598-quasar compilation mentioned in the paper should settle whether the preference for closed geometry persists or was a statistical fluctuation.
  • The correlation between the $H_0$ prior and the strength of the non-flat or dynamical preference suggests that part of the signal may be a projection of the Hubble tension rather than independent evidence for new physics.
  • The consistency between QSO-only and $H(z)$+BAO contours across all six models is itself informative: it means any unmodeled systematics in the quasar relation are not dominating the joint result, though it does not rule them out.
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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

2 major / 5 minor

Summary. The paper uses the 808-point Risaliti & Lusso (2015) compilation of quasar X-ray and UV flux measurements, alone and combined with 11 BAO and 31 H(z) measurements, to constrain cosmological parameters in six models: spatially flat and non-flat versions of ΛCDM, the XCDM parametrization, and the φCDM scalar-field model. The analysis simultaneously fits the LX-LUV intercept β, slope γ, and intrinsic dispersion δ, uses MCMC with two Gaussian H0 priors, and reports best-fit parameters, marginalized constraints, contour plots, and AIC/BIC values. The paper finds that the QSO data alone give weak but mostly consistent constraints compared with H(z)+BAO, and that the joint data are consistent with flat ΛCDM while mildly favoring closed spatial hypersurfaces and dynamical dark energy.

Significance. If the QSO distance estimate is valid, the paper provides a useful demonstration that X-ray/UV quasar fluxes can act as a high-redshift supplement to BAO and H(z) data, extending earlier work by Risaliti & Lusso (2015) to six cosmological models. The paper is methodologically careful in several respects: it uses the covariance matrix for the correlated BAO points, it reports AIC and BIC, it checks two H0 priors, and it explicitly fits the QSO nuisance parameters rather than presenting them as fixed predictions. The main limitation is that the central probe is calibrated through an assumed universal LX-LUV relation whose redshift independence and selection properties are not tested; this leaves the headline joint constraints vulnerable to systematic bias. The cosmological conclusions are not decisive, as the paper acknowledges, but the consistency check is a legitimate and useful step.

major comments (2)
  1. [Secs. 3, 4, and 5.2, Eq. (12)] The analysis assumes that the LX-LUV relation in Eq. (12) has constant β and γ over the full range 0.061 ≤ z ≤ 6.28, with all remaining scatter captured by the single fitted dispersion δ, and Sec. 5.2 states that the QSO analysis is 'based on the assumed validity' of this relation. Because Eq. (13) converts the flux-flux relation into distance information that enters the joint likelihood, any redshift evolution of γ or β, or any flux-limit selection effect that correlates FX and FUV at fixed DL, would bias the QSO-only and QSO+H(z)+BAO posteriors reported in Tables 4-5 and Figs. 1-12. Please add quantitative tests, for example splitting the sample into redshift bins, fitting a redshift-dependent slope γ(z) = γ0 + γ1 log(1+z), or comparing high- and low-redshift marginalised constraints, and discuss the selection-function literature for this sample. Without such tests, the claim that the QSO data are a valid supplementary cosmological probe is not fully established.
  2. [Sec. 5.3, Tables 1-2] The abstract's statement that the joint data 'mildly favor' closed spatial hypersurfaces and dynamical dark energy should be reconciled with the information criteria reported in Tables 1-2. For the H0 = 68 prior, flat ΛCDM has the lowest AIC among all joint fits (507.01 in Table 1, versus 508.65-508.73 for the other models), while for the H0 = 73.24 prior, non-flat ΛCDM has the lowest AIC (509.85) but several models are within ΔAIC ≲ 3.5 of it. Since differences of only a few units in AIC/BIC are not significant, the 'favors' language is somewhat stronger than the model-selection evidence; I recommend either removing the claim or restating it as parameter-interval shifts within 1σ-2.6σ for individual models, with an explicit look-elsewhere caveat for the 12 model/prior combinations.
minor comments (5)
  1. [Sec. 3] The text 'For a newer compilation of QSO data see ?' contains a missing citation; the reference clearly should be Risaliti & Lusso (2019), which is listed in the bibliography, and this should be completed.
  2. [Secs. 1, 5.2, and figure captions] There are several typographical errors: 'Plank Collaboration' should be 'Planck Collaboration'; Fig. 8 caption has 'Left pnnel'; Fig. 12 caption has 'These plots are the for H0'; and the surname 'López-Corredoira' is missing an 'o' in Sec. 3. These should be corrected.
  3. [Sec. 4] The prior range for α is stated as 0 ≤ α ≤ 3, with '(0 ≤ α ≤ 1.2 for QSO only)'. This prior inconsistency affects the QSO-only φCDM constraints in Table 4 and makes comparisons with the joint fits less direct; it should be justified or removed.
  4. [Secs. 5.1-5.3, Eq. (16)] Because the QSO likelihood in Eq. (16) includes the ln(2πs_i^2) term, the quantity called χ²_min = -2 ln(LFmax) in Tables 1-2 is a deviance rather than a standard chi-square statistic. The reported 'reduced χ²' values of 0.6-0.7 are therefore not directly comparable to ordinary reduced chi-squares, and this should be stated explicitly to avoid misleading readers.
  5. [Table 4] The QSO-only H0 posteriors are essentially identical to the priors (68 ± 2.8 and 73.24 ± 1.73 km s^-1 Mpc^-1), so the text in Sec. 5.2 that QSO constraints are insensitive to the H0 prior should be phrased as 'the QSO data do not constrain H0.'

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: cosmological parameters are fitted to external QSO, H(z), and BAO data, and the QSO nuisance parameters (β, γ, δ) are explicitly fitted, not presented as predictions.

full rationale

The paper's derivation chain does not reduce any claimed result to its inputs by construction. The central claim—that joint QSO+H(z)+BAO constraints are consistent with flat ΛCDM while mildly favoring closed spatial hypersurfaces and dynamical dark energy—is obtained by maximizing likelihood functions (eqs. 16–18) in which the cosmological parameters (Ωm0, Ωk0, ωX, α, H0) are free parameters fit to external data. The QSO analysis uses the LX–LUV relation of eq. (12) to predict X-ray flux via eq. (13), with luminosity distance from eqs. (14)–(15); the relation's parameters β, γ, and the dispersion δ are fitted simultaneously with the cosmological parameters (Sec. 4), and the paper reports them as fitted values, never as predictions. There is no instance of a fitted parameter being renamed as a prediction. The LX–LUV relation is an external ansatz from Risaliti & Lusso (2015), and Sec. 5.2 explicitly states the analysis is 'based on the assumed validity' of that relation, tested by the external reference; this is a systematic/assumption caveat, not a circular reduction. The model equations in Sec. 2 are standard results from the literature, and the BAO and H(z) data are taken from external tables. Citations to prior work by the same group (e.g., Ryan et al. 2019, Park & Ratra 2018d) provide context for the closed-curvature preference, but the paper computes its own contours from the data, so these citations are not load-bearing self-citations. No circular step can be exhibited from the paper's own equations or self-citations.

Assumptions & free parameters 9 free parameters · 4 assumptions · 0 invented entities

No new physical entities are introduced. The free parameters are standard cosmological parameters plus the QSO LX-LUV nuisance parameters beta, gamma, and delta. The main assumption to watch is the redshift-independent LX-LUV relation; if it is wrong, all QSO-only cosmological constraints shift. The phiCDM potential choice is an assumption, but it is not needed for the standard-model consistency result.

free parameters (9)
  • beta (LX-LUV intercept) = About 8.2 to 9.0 across models and priors
    Nuisance intercept in eq. (12), fitted jointly with cosmological parameters in the QSO likelihood eq. (16).
  • gamma (LX-LUV slope) = About 0.53 to 0.59
    Slope of the log LX-log LUV relation; fitted simultaneously with cosmology and other nuisance parameters.
  • delta (global intrinsic dispersion) = About 0.31 to 0.33
    Extra scatter added in quadrature in eq. (16); fitted and large, which makes QSO constraints weak and reduced chi-squared less than 1.
  • H0 (Hubble constant) = About 66.7 to 73.5 depending on prior and model
    Constrained with Gaussian priors H0 = 68 +/- 2.8 or 73.24 +/- 1.74 km/s/Mpc; central to all distance calculations.
  • Omega_m0 = About 0.24 to 0.34
    Current non-relativistic matter density parameter, free in all six models.
  • Omega_Lambda = About 0.69 to 1.13
    Cosmological constant density parameter; free in the non-flat LambdaCDM model and derived in the flat model.
  • Omega_k0 = About -0.30 to 0.11
    Spatial curvature density parameter, free in the non-flat models with prior -0.7 <= k <= 0.7.
  • omega_X = About -2.49 to -0.67
    Dark energy equation-of-state parameter, free in the XCDM parametrization.
  • alpha = About 0.03 to 1.20
    Slope parameter of the inverse-power-law scalar field potential in phiCDM models.
assumptions (4)
  • domain assumption FLRW metric and Friedmann equations describe the expansion history, eqs. (1)-(11).
    All six models are built on these equations; the paper does not derive them.
  • domain assumption The QSO LX-LUV relation log LX = beta + gamma log LUV holds with constant beta and gamma over the full redshift range, with no evolution or selection effects beyond one dispersion delta.
    This is the central calibrating relation, eq. (12), used to turn QSO fluxes into distance indicators; if it evolves or is selection-biased, the QSO constraints are biased.
  • domain assumption BAO and H(z) measurements are independent and Gaussian, with only the first six BAO points correlated through the covariance matrix in eq. (19).
    The likelihoods in eqs. (16)-(18) assume this; uncorrected correlations or non-Gaussian tails would change the constraints.
  • ad hoc to paper The phiCDM inverse-power-law potential in eq. (5) is a representative dynamical dark energy model and the numerical solutions of eqs. (7)-(9) are accurate.
    The model is chosen for study; the paper relies on numerical integration of the scalar field equations but provides no code or convergence tests.

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Cite this review

Pith. "Pith review of Quasar X-ray and UV flux, baryon acoustic oscillation, and Hubble parameter measurement constraints on cosmological model parameters." pith.science (2026). https://pith.science/paper/T77ZSD56

@misc{pith2026190901400,
  author       = {Pith},
  title        = {Pith review of: Quasar X-ray and UV flux, baryon acoustic oscillation, and Hubble parameter measurement constraints on cosmological model parameters},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/T77ZSD56}},
  note         = {Machine review of arXiv:1909.01400}
}
abstract

We use the Risaliti & Lusso (2015) compilation of 808 X-ray and UV flux measurements of quasars (QSOs) in the redshift range $0.061 \leq z \leq 6.28$, alone and in conjuction with baryon acoustic oscillation (BAO) and Hubble parameter [$H(z)$] measurements, to constrain cosmological parameters in six cosmological models. The QSO data constraints are significantly weaker than, but consistent with, those from the $H(z)$ + BAO data. A joint analysis of the QSO + $H(z)$ + BAO data is consistent with the current standard model, spatially-flat $\Lambda$CDM, but mildly favors closed spatial hypersurfaces and dynamical dark energy.

Figures

Figures reproduced from arXiv: 1909.01400 by the authors.

Figure 1
Figure 1. Flat ΛCDM model constraints from QSO (grey), H(z) + BAO (red), and QSO + H(z) + BAO (blue) data. Left panel shows 1, 2, and 3σ confidence contours and one-dimensional likelihoods for all free parameters. Right panel shows magnified plots for only cosmological parameters Ωm0 and H0, without the QSO-only constraints. These plots are for the H0 = 68 ± 2.8 km s−1Mpc−1 prior. 69 72 75 78 H0 0.3 0.33 0.52 0.56 0.6 0.64 7 … view at source ↗
Figure 2
Figure 2. Flat ΛCDM model constraints from QSO (grey), H(z) + BAO (red), and QSO + H(z) + BAO (blue) data. Left panel shows 1, 2, and 3σ confidence contours and one-dimensional likelihoods for all free parameters. Right panel shows magnified plots for only cosmological parameters Ωm0 and H0, without the QSO-only constraints. These plots are for the H0 = 73.24 ± 1.74 km s−1Mpc−1 prior. MNRAS 000, 1–8 (2019) [PITH_FULL_IMAGE:f… view at source ↗
Figure 3
Figure 3. Non-flat ΛCDM model constraints from QSO (grey), H(z) + BAO (red), and QSO + H(z) + BAO (blue) data. Left panel shows 1, 2, and 3σ confidence contours and one-dimensional likelihoods for all free parameters. Right panel shows magnified plots for cosmological parameters Ωm0, ΩΛ, and H0, without the QSO-only constraints. These plots are for the H0 = 68 ± 2.8 km s−1Mpc−1 prior. The black dotted straight lines correspon… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Non-flat ΛCDM model constraints from QSO (grey), H(z) + BAO (red), and QSO + H(z) + BAO (blue) data. Left panel shows 1, 2, and 3σ confidence contours and one-dimensional likelihoods for all free parameters. Right panel shows magnified plots for only cosmological param…
Figure 5
Figure 5. Figure 5: Flat XCDM model constraints from QSO (grey), H(z) + BAO (red), and QSO + H(z) + BAO (blue) data. Left panel shows 1, 2, and 3σ confidence contours and one-dimensional likelihoods for all free parameters. Right panel shows magnified plots for only cosmological parameter…
Figure 6
Figure 6. Figure 6: Flat XCDM model constraints from QSO (grey), H(z) + BAO (red), and QSO + H(z) + BAO (blue) data. Left panel shows 1, 2, and 3σ confidence contours and one-dimensional likelihoods for all free parameters. Right panel shows magnified plots for only cosmological parameter…
Figure 7
Figure 7. Figure 7: Non-flat XCDM model constraints from QSO (grey), H(z) + BAO (red), and QSO + H(z) + BAO (blue) data. Left panel shows 1, 2, and 3σ confidence contours and one-dimensional likelihoods for all free parameters. Right panel shows magnified plots for only cosmological param…
Figure 8
Figure 8. Figure 8: Non-flat XCDM model constraints from QSO (grey), H(z) + BAO (red), and QSO + H(z) + BAO (blue) data. Left pnnel shows 1, 2, and 3σ confidence contours and one-dimensional likelihoods for all free parameters. Right panel shows magnified plots for only cosmological param…
Figure 9
Figure 9. Figure 9: Flat φCDM model constraints from QSO (grey), H(z) + BAO (red), and QSO + H(z) + BAO (blue) data. Left panel shows 1, 2, and 3σ confidence contours and one-dimensional likelihoods for all free parameters. Right panel shows magnified plots for only cosmological parameter…
Figure 10
Figure 10. Figure 10: Flat φCDM model constraints from QSO (grey), H(z) + BAO (red), and QSO + H(z) + BAO (blue) data. Left panel shows 1, 2, and 3σ confidence contours and one-dimensional likelihoods for all free parameters. Right panel shows magnified plots for only cosmological paramete…
Figure 11
Figure 11. Figure 11: Non-flat φCDM model constraints from QSO (grey), H(z) + BAO (red), and QSO + H(z) + BAO (blue) data. Left panel shows 1, 2, and 3σ confidence contours and one-dimensional likelihoods for all free parameters. Right panel shows magnified plots for only cosmological para…
Figure 12
Figure 12. Figure 12: Non-Flat φCDM model constraints from QSO (grey), H(z) + BAO (red), and QSO + H(z) + BAO (blue) data. Left panel shows 1, 2, and 3σ confidence contours and one-dimensional likelihoods for all free parameters. Right panel shows magnified plots for only cosmological para…

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Reviewed August 14, 2026 · model on record in the stance chip above.