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 →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
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.
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
- 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.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
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)
- [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.
- [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)
- [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.
- [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.
- [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.
- [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.
- [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
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
free parameters (9)
- beta (LX-LUV intercept) =
About 8.2 to 9.0 across models and priors
- gamma (LX-LUV slope) =
About 0.53 to 0.59
- delta (global intrinsic dispersion) =
About 0.31 to 0.33
- H0 (Hubble constant) =
About 66.7 to 73.5 depending on prior and model
- Omega_m0 =
About 0.24 to 0.34
- Omega_Lambda =
About 0.69 to 1.13
- Omega_k0 =
About -0.30 to 0.11
- omega_X =
About -2.49 to -0.67
- alpha =
About 0.03 to 1.20
assumptions (4)
- domain assumption FLRW metric and Friedmann equations describe the expansion history, eqs. (1)-(11).
- 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.
- 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).
- 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.
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
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Reference graph
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Reviewed August 14, 2026 · model on record in the stance chip above.
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