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Distance duality can't save late-time fixes to Hubble tension

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2026-07-10 03:33 UTC pith:HF2DCYR4

load-bearing objection Clean algebraic argument that CDDR violation cannot save late-time Hubble tension solutions; new geometric reciprocity constraint is a genuine addition but not load-bearing for the main conclusion.

arxiv 2607.08654 v1 pith:HF2DCYR4 submitted 2026-07-09 astro-ph.CO

Can Distance Duality Violation Save Late-time Solutions to the Hubble Tension?

Yashi Tiwari , Ujjwal Upadhyay , Shao-Jiang Wang , Vivian Poulin This is my paper
classification astro-ph.CO
keywords Hubble tensioncosmic distance duality relationEtherington reciprocitybaryon acoustic oscillationsType Ia supernovaephoton number conservationlate-time cosmology
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The Hubble tension—the disagreement between early- and late-Universe measurements of the expansion rate—has motivated many proposals that modify only the late-time expansion history. This paper shows that such attempts face a fundamental obstacle: a relation called the cosmic distance duality relation (CDDR), which links luminosity distances from supernovae to angular-diameter distances from baryon acoustic oscillations (BAO). When the sound-horizon scale and supernova calibration are held fixed, the CDDR, combined with uncalibrated BAO and supernova data, fixes the Hubble constant at 66.6 ± 0.7 km/s/Mpc regardless of what the late-time expansion does. Reconciling this with the locally measured value near 73 would require an 8–10% violation of distance duality. The paper then decomposes a CDDR violation into its two independent ingredients—violation of Etherington reciprocity (which distorts angular distances) and photon number non-conservation (which alters luminosity distances)—and confronts each with data. A new geometric constraint from transverse and radial BAO combined with cosmic-chronometer measurements limits reciprocity violation to the sub-percent level (α = 0.99 ± 0.008), while existing thermal Sunyaev–Zel'dovich measurements constrain photon non-conservation to the percent level. Both are far below the 8–10% departure needed, ruling out late-time CDDR violation as a viable path.

Core claim

The central result is an equation (Eq. 8) showing that, for a fixed sound-horizon calibration, the Hubble constant is determined entirely by the distance-duality parameter η, the supernova intercept M, and the sound horizon r_d—none of which depend on the late-time expansion history. This means no modification to late-time expansion alone can shift H_0 unless it also breaks distance duality. The paper then shows that the required ~8–10% duality violation is excluded because its two components are independently constrained to sub-percent and percent levels by current BAO, cosmic-chronometer, and CMB-temperature data.

What carries the argument

The argument hinges on the CDDR parameter η = d_L / [(1+z)² d_A], which is decomposed as η = α·β, where α quantifies Etherington reciprocity violation (constrained geometrically from transverse vs. radial BAO) and β quantifies photon number non-conservation (constrained from CMB temperature–redshift scaling). The combination A = M_B + 5 log₁₀(r_d · η) is shown to be tightly fixed by uncalibrated BAO+supernova data alone, creating a calibration degeneracy that no late-time expansion modification can break without violating duality.

Load-bearing premise

The new geometric constraint on reciprocity violation assumes that any reciprocity-breaking effect distorts only the transverse (angular) distance while leaving the radial BAO distance c/H unchanged. If reciprocity violation also distorts the radial distance or modifies the expansion rate H(z), this particular geometric probe would not apply—though conventional CDDR tests combining luminosity and angular-diameter distances would still constrain such scenarios.

What would settle it

A detection of reciprocity violation or photon non-conservation at the 8–10% level from BAO, cosmic-chronometer, or CMB-temperature data would falsify the claim that the required CDDR violation is excluded. Conversely, a late-time expansion model that achieves H_0 ≈ 73 while preserving both α = 1 and β = 1 would falsify the claim that CDDR fixes H_0 independently of late-time physics.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Late-time modified-gravity and dynamical dark-energy models that preserve the CDDR cannot resolve the Hubble tension when confronted with combined CMB, BAO, and supernova data.
  • Future BAO surveys with improved transverse and radial measurements at multiple redshifts can tighten the geometric reciprocity constraint further, potentially pushing below the 0.5% level.
  • The decomposition η = α·β provides a template for testing any future proposal that invokes distance-duality violation: it must specify which ingredient is broken and survive the corresponding independent constraint.
  • The result narrows the solution space toward early-Universe modifications that reduce the sound horizon or toward unresolved local systematics in the supernova calibration.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If future CMB experiments (e.g., CMB-S4) further tighten the sound-horizon calibration, the CDDR-based H_0 determination of 66.6 ± 0.7 would sharpen, increasing the pressure on any late-time solution even if a modest CDDR violation were allowed.
  • The geometric reciprocity probe (Eq. 15) could be extended to anisotropic BAO measurements across multiple redshift bins to test whether α(z) shows any redshift-dependent trend, which might reveal subtler violations invisible to a single-redshift constraint.
  • If the Hubble tension persists with next-generation data and all CDDR components remain constrained below the percent level, the tension would effectively become a binary diagnostic: either the sound horizon is wrong or a local systematic exists, with no remaining late-time escape.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 6 minor

Summary. This paper recasts the Hubble tension as a calibration mismatch in the $r_d$–$M_B$ plane and shows, via a clean algebraic argument (Eqs. 1–8), that the CDDR combined with BAO and uncalibrated SNIa data fixes $H_0$ independently of the late-time expansion history, provided $r_d$ and $M_B$ calibrations are held fixed. Resolving the tension then requires an $O(8{-}10%)$ violation of distance duality ($eta ≈ 0.92$). The authors test this by separately constraining the two ingredients of the CDDR: Etherington reciprocity ($alpha$) and photon number conservation ($beta$). They derive a new geometric constraint on $alpha$ from transverse and radial BAO combined with cosmic chronometers ($alpha = 0.99 ± 0.008$ at $z sim 1$), and combine it with existing percent-level bounds on $beta$ from tSZ measurements of $T_{rm CMB}(z)$. The conclusion is that the required level of CDDR violation is strongly disfavoured by current data, ruling out late-time CDDR violation as a viable solution.

Significance. The paper provides a transparent, model-independent restatement of why late-time expansion-history modifications fail to resolve the Hubble tension, and makes the role of the CDDR explicit. The new BAO+CC constraint on reciprocity-violating distortions of angular-diameter distances (Eq. 15) is a useful complementary probe that does not rely on luminosity-distance information. The $alpha$–$beta$ decomposition in Fig. 3 is pedagogically effective and clearly delineates which mechanisms are constrained by which observations. The algebraic derivation is parameter-free and the GPR methodology is standard and well-implemented.

minor comments (6)
  1. §II, Eq. (8) and surrounding text: The quantity $eta$ is described as 'an effective redshift-averaged distance-duality parameter $bar{eta}$' when $eta(z)$ is not constant, but the notation is then simplified to $eta$ throughout. The connection between this effective $bar{eta}$ and the constraints evaluated at $z simeq 1$ in Fig. 3 could be made more explicit. In particular, a CDDR violation concentrated at very low redshifts ($z < 0.1$) could in principle affect the supernova intercept $mathcal{M}$ while leaving the BAO+SNIa matching at $z > 0.1$ consistent with $eta = 1$. The paper does discuss ultra-low-redshift $M_B$ evolution as a separate possibility (point 2 in 'Possible ways forward'), but it would strengthen the presentation to note explicitly that such a scenario falls under the 'local systematics' category rather than a late-time expansion-history modification, and is therefore
  2. §III, Eq. (15): The assumption that reciprocity violations affect only the transverse distance sector while leaving $D_H = c/H$ unchanged is clearly stated, but the physical motivation for this specific ansatz could be briefly elaborated. Which classes of non-metric gravity or non-standard photon propagation naturally produce purely transverse distortions? A sentence or two would help the reader assess the scope of the new constraint.
  3. Fig. 1: The arrows indicating the three principal directions in parameter space are helpful, but the arrow for 'CDDR violation ($eta < 1$)' is described as shifting the green band 'upward-rightward' in the text (§II, point 3), while the figure caption says 'upward-rightward shift of the green band.' It would aid clarity to label the arrows directly in the figure or to state in the caption which arrow corresponds to which direction.
  4. §III, discussion of $beta$ constraints: The statement that the tSZ bounds 'apply directly to microwave photons' and that 'extending them to the optical wavelengths relevant for SNIa requires the photon-number-violating mechanism to be approximately achromatic' is important but brief. A citation to specific tests of chromaticity (e.g., supernova colour measurements) would help the reader verify this claim. References [21, 50, 54–56] are cited in the subsequent paragraph but not directly linked to the achromaticity requirement.
  5. Appendix A: The choice of Matérn $nu = 3/2$ kernel is stated but not motivated. A brief remark on why this kernel was preferred over, e.g., the squared-exponential kernel, and whether the results are robust to this choice, would be welcome.
  6. Typographical: In §II, the sentence beginning 'A key strength of this CDDR-based constraint...' has no space after the colon: 'minimal theoretical input:it is essentially independent...'

Circularity Check

0 steps flagged

No significant circularity; derivation chain is algebraic and self-contained

full rationale

The paper's central derivation (Eqs. 1-8, 11) is straightforward algebra from standard definitions of d_L, d_A, and η. The H_0 = 66.6 ± 0.7 result is explicitly identified as the standard inverse distance ladder (Ref. [40]), not presented as a novel prediction. The new α constraint (Eq. 15) is derived from actual BAO+CC observational data through a geometric relation, with the transverse-only assumption explicitly stated and caveated. Self-citations exist (Refs. [14, 15, 16] share authors with the present paper) but are methodological and framing citations, not load-bearing mathematical theorems. The claim that late-time resolution requires CDDR violation follows algebraically from Eq. (8) within this paper itself, not from the cited works. The conclusion that η ≈ 0.92 is excluded has independent support from the external cosmographic η test (Ref. [52], no author overlap), so it does not depend on any self-cited result. No step in the derivation chain reduces to its own inputs by construction, and no 'prediction' is a renamed fit. The minor score of 1 reflects the presence of self-citations for methodology that, while not load-bearing, frame the paper's approach.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The paper introduces no new particles, forces, or fields. It works entirely within the existing framework of distance duality, reciprocity, and photon conservation, using standard cosmological probes (BAO, SNIa, CMB, cosmic chronometers). The parameters eta, alpha, beta are standard in the CDDR literature.

free parameters (4)
  • eta (distance duality parameter) = 1 (assumed); ~0.92 required for tension resolution
    Treated as a constant free parameter in Eq. (5); the paper shows the tension requires eta ~ 0.92, then constrains it.
  • alpha (reciprocity parameter) = 0.99 ± 0.008 (from BAO+CC)
    Constrained from data in Eq. (15); not fitted to resolve the tension but derived from observations.
  • beta (photon conservation parameter) = ~1.01 ± 0.013 at z=1 (from tSZ)
    Parameterized via epsilon in Eq. (17); constrained from external tSZ data [51].
  • GPR hyperparameters (sigma_f, ell) = Optimized by marginal likelihood
    Matern 3/2 kernel hyperparameters for luminosity distance and H(z) reconstructions; standard practice but introduces fitting freedom.
axioms (5)
  • domain assumption Cosmic distance duality relation: d_L = (1+z)^2 d_A holds in metric gravity with null geodesics and photon conservation
    Invoked throughout as the baseline; Eq. (1). Standard result from Etherington (1933) and Ellis (2007).
  • domain assumption BAO measurements provide model-independent angular-diameter distance information via d_A = r_d / (theta_BAO * (1+z))
    Eq. (3); standard BAO methodology assuming the sound horizon r_d as a standard ruler.
  • ad hoc to paper Reciprocity violations affect only the transverse distance sector, leaving radial BAO (D_H = c/H) unchanged
    Stated in Section III when deriving Eq. (15): 'Assuming that reciprocity violations affect only the transverse (angular) distance sector, while leaving the background expansion history and therefore the radial BAO distance D_H = c/H unchanged.' This is the key assumption enabling the geometric probe.
  • domain assumption Photon number non-conservation is adiabatic and approximately achromatic
    Section III, Eq. (17); required to connect tSZ temperature constraints to optical-wavelength supernova observations. The paper acknowledges this limitation.
  • domain assumption The sound horizon r_d = 147 ± 0.3 Mpc from Planck-LCDM is the correct calibration for BAO+CC reconstruction
    Used in Section III to convert D_H/r_d into H(z) for the alpha reconstruction. The BAO-only relation is calibration-independent, but the BAO+CC combination is conditional on this value.

pith-pipeline@v1.1.0-glm · 18527 in / 2911 out tokens · 509133 ms · 2026-07-10T03:33:11.411714+00:00 · methodology

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read the original abstract

The discrepancy between early- and late-Universe determinations of the Hubble constant may point to physics beyond $\Lambda$CDM or to unaccounted-for systematics. Numerous late-time modifications to the expansion history have been proposed to alleviate this discrepancy, with limited success. Recent works have shown that, when the sound-horizon and supernova calibrations are held fixed, any purely late-time resolution requires a violation of the cosmic distance duality relation (CDDR). Recasting the tension in the $r_d$-$M_B$ plane, we show explicitly that distance duality, together with BAO and uncalibrated supernova data and a fixed sound-horizon calibration, determines $H_0$ independently of the late-time expansion history. We then test the viability of the required CDDR violation by separately constraining reciprocity violation and photon number non-conservation, deriving a new constraint on reciprocity-violating distortions of angular-diameter distances from BAO and cosmic-chronometer data. Combining this result with existing photon-number-conservation constraints, we find that the level of distance-duality violation needed to resolve the tension is strongly disfavoured by current data. We therefore conclude that, for fixed sound-horizon and supernova calibrations, no modification confined to the late-time expansion history -- even one violating distance duality -- can resolve the Hubble tension, pointing instead toward early-Universe physics or unresolved local systematics.

Figures

Figures reproduced from arXiv: 2607.08654 by Shao-Jiang Wang, Ujjwal Upadhyay, Vivian Poulin, Yashi Tiwari.

Figure 1
Figure 1. Figure 1: Constraint in the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Constraints on reciprocity violations modifying the [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Constraints on departures from the cosmic distance [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Gaussian Process reconstruction of the luminosity [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Gaussian-process reconstruction of H(z) from radial BAO and CC measurements. [1] Rong-Gen Cai and Shao-Jiang Wang, “The Hubble ten￾sion: A decade review,” (2026) arXiv:2606.20434 [astro￾ph.CO]. [2] Ali Rida Khalife, Maryam Bahrami Zanjani, Silvia Galli, Sven Günther, Julien Lesgourgues, and Karim Benabed, “Review of Hubble tension solutions with new SH0ES and SPT-3G data,” JCAP 04, 059 (2024), arXiv:2312.0… view at source ↗

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Reference graph

Works this paper leans on

62 extracted references · 62 canonical work pages · 44 internal anchors

  1. [1]

    1 sug- gests that reducing the sound horizon (i.e., shifting the yellow band leftward) remains a viable route to alleviate the Hubble tension while remaining consis- tent with CDDR

    Early-universe physics: The analysis of Fig. 1 sug- gests that reducing the sound horizon (i.e., shifting the yellow band leftward) remains a viable route to alleviate the Hubble tension while remaining consis- tent with CDDR. Therefore, the resolution of the Hubble tension may ultimately involve at least some modifications to the early Universe [42]. How...

    work page

  2. [2]

    Z z 0 DH(z′) rd ∥ dz′ #

    Violation of CDDR: A more radical possibility is a genuine breakdown of the CDDR itself, cor- responding to an upward-rightward shift of the green band in Fig. 1. We discuss this scenario in detail in the next section, particularly exploring the observational implications of distance-duality violation. III. VIABILITY OF DIST ANCE DUALITY VIOLA TION? The p...

    work page 2022

  3. [3]

    The Hubble tension: A decade review

    Rong-Gen Cai and Shao-Jiang Wang, “The Hubble ten- sion: A decade review,” (2026) arXiv:2606.20434 [astro- ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  4. [4]

    Review of Hubble tension solutions with new SH0ES and SPT-3G data

    Ali Rida Khalife, Maryam Bahrami Zanjani, Silvia Galli, Sven Günther, Julien Lesgourgues, and Karim Benabed, “Review of Hubble tension solutions with new SH0ES and SPT-3G data,” JCAP04, 059 (2024), arXiv:2312.09814 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  5. [5]

    Hubble Tension: The Evidence of New Physics

    Jian-Ping Hu and Fa-Yin Wang, “Hubble Tension: The Evidence of New Physics,” Universe9, 94 (2023), arXiv:2302.05709 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  6. [6]

    Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies

    Elcio Abdallaet al., “Cosmology intertwined: A re- view of the particle physics, astrophysics, and cosmol- ogy associated with the cosmological tensions and anoma- lies,” JHEAp34, 49–211 (2022), arXiv:2203.06142 [astro- ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  7. [7]

    The $H_0$ Olympics: A fair ranking of proposed models

    Nils Schöneberg, Guillermo Franco Abellán, Andrea Pérez Sánchez, Samuel J. Witte, Vivian Poulin, and Julien Lesgourgues, “The H0 Olympics: A fair rank- ing of proposed models,” Phys. Rept.984, 1–55 (2022), 9 arXiv:2107.10291 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  8. [8]

    The Hubble Hunter's Guide

    Lloyd Knox and Marius Millea, “Hubble constant hunter’s guide,” Phys. Rev. D101, 043533 (2020), arXiv:1908.03663 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  9. [9]

    In the Realm of the Hubble tension $-$ a Review of Solutions

    Eleonora Di Valentino, Olga Mena, Supriya Pan, Luca Visinelli, Weiqiang Yang, Alessandro Melchiorri, David F. Mota, Adam G. Riess, and Joseph Silk, “In the realm of the Hubble tension—a review of solutions,” Class. Quant. Grav.38, 153001 (2021), arXiv:2103.01183 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  10. [10]

    Tensions between the Early and the Late Universe

    L. Verde, T. Treu, and A. G. Riess, “Tensions between the Early and the Late Universe,” Nature Astron.3, 891 (2019), arXiv:1907.10625 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  11. [11]

    Sounds Discordant: Classical Distance Ladder & $\Lambda$CDM -based Determinations of the Cosmological Sound Horizon

    Kevin Aylor, Mackenzie Joy, Lloyd Knox, Marius Millea, Srinivasan Raghunathan, and W. L. Kimmy Wu, “Sounds Discordant: Classical Distance Ladder andΛCDM-based Determinations of the Cosmological Sound Horizon,” As- trophys. J.874, 4 (2019), arXiv:1811.00537 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  12. [12]

    A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team

    Adam G. Riesset al., “A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s−1 Mpc−1 Uncertainty from the Hubble Space Telescope and the SH0ES Team,” Astrophys. J. Lett.934, L7 (2022), arXiv:2112.04510 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  13. [13]

    Planck 2018 results. VI. Cosmological parameters

    N. Aghanimet al.(Planck), “Planck 2018 results. VI. Cosmological parameters,” Astron. Astrophys.641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  14. [14]

    The tension in the absolute magnitude of type ia supernovae,

    David Camarena and Valerio Marra, “The tension in the absolute magnitude of type ia supernovae,” inThe Hubble Constant Tension, edited by Eleonora Di Valentino and Dillon Brout (Springer NatureSingapore, Singapore, 2024) pp. 661–674

    work page 2024

  15. [15]

    To H0 or not to H0?

    George Efstathiou, “To H0 or not to H0?” Mon. Not. Roy. Astron. Soc.505, 3866–3872 (2021), arXiv:2103.08723 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  16. [16]

    On the implications of the `cosmic calibration tension' beyond $H_0$ and the synergy between early- and late-time new physics

    Vivian Poulin, Tristan L. Smith, Rodrigo Calderón, and Théo Simon, “Implications of the cosmic calibration ten- sion beyond H0 and the synergy between early- and late- time new physics,” Phys. Rev. D111, 083552 (2025), arXiv:2407.18292 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  17. [17]

    Implications of distance duality violation for the $H_0$ tension and evolving dark energy

    Elsa M. Teixeira, William Giarè, Natalie B. Hogg, Thomas Montandon, Adèle Poudou, and Vivian Poulin, “Implica- tions of distance duality violation for the H0 tension and evolving dark energy,” Phys. Rev. D112, 023515 (2025), arXiv:2504.10464 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  18. [18]

    Revisiting cosmic distance duality with megamasers and DESI DR2 observations: Model-independent constraints on early-late calibration,

    Brijesh Kanodia, Ujjwal Upadhyay, and Yashi Tiwari, “Revisiting cosmic distance duality with megamasers and DESI DR2 observations: Model-independent constraints on early-late calibration,” Phys. Rev. D113, 023505 (2026), arXiv:2507.11518 [astro-ph.CO]

    work page arXiv 2026

  19. [19]

    On the Difficulties with Late-Time Solutions for the Hubble Tension,

    Prakhar Bansal and Dragan Huterer, “On the Difficulties with Late-Time Solutions for the Hubble Tension,” (2026), arXiv:2602.06293 [astro-ph.CO]

    work page arXiv 2026

  20. [20]

    Hint to- ward an inconsistency between BAO and supernovae datasets: The evidence of redshift evolving dark energy from DESI DR2 is absent,

    Samsuzzaman Afroz and Suvodip Mukherjee, “Hint to- ward an inconsistency between BAO and supernovae datasets: The evidence of redshift evolving dark energy from DESI DR2 is absent,” Phys. Rev. D113, 083514 (2026), arXiv:2504.16868 [astro-ph.CO]

    work page arXiv 2026

  21. [21]

    Lx. on the definition of distance in general relativity,

    IMH Etherington, “Lx. on the definition of distance in general relativity,” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science15, 761– 773 (1933)

    work page 1933

  22. [22]

    On the definition of distance in general relativity: I. M. H. Etherington (Philosophical Magazine ser. 7, vol. 15, 761 (1933)),

    George F. R. Ellis, “On the definition of distance in general relativity: I. M. H. Etherington (Philosophical Magazine ser. 7, vol. 15, 761 (1933)),” General Relativity and Grav- itation39, 1047–1052 (2007)

    work page 1933

  23. [23]

    Cosmic distance-duality as probe of exotic physics and acceleration

    Bruce A. Bassett and Martin Kunz, “Cosmic distance- duality as a probe of exotic physics and acceleration,” Phys. Rev. D69, 101305 (2004), arXiv:astro-ph/0312443

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  24. [24]

    The distance duality relation from X-ray and SZ observations of clusters

    Jean-Philippe Uzan, Nabila Aghanim, and Yannick Mel- lier, “The Distance duality relation from x-ray and SZ ob- servations of clusters,” Phys. Rev. D70, 083533 (2004), arXiv:astro-ph/0405620

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  25. [25]

    Constraints on the CMB temperature redshift dependence from SZ and distance measurements

    A. Avgoustidis, G. Luzzi, C. J. A. P. Martins, and A. M. R. V. L. Monteiro, “Constraints on the CMB temperature redshift dependence from SZ and distance measurements,” JCAP02, 013 (2012), arXiv:1112.1862 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  26. [26]

    Constraints on Distance Duality Relation from Sunyaev Zel'dovich Effect and Chandra X-ray measurements

    Francesco De Bernardis, Elena Giusarma, and Alessan- dro Melchiorri, “Constraints on dark energy and distance duality from Sunyaev Zel’dovich effect and Chandra X-ray measurements,” Int. J. Mod. Phys. D15, 759–766 (2006), arXiv:gr-qc/0606029

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  27. [27]

    Comparison of Standard Ruler and Standard Candle constraints on Dark Energy Models

    R. Lazkoz, S. Nesseris, and L. Perivolaropoulos, “Com- parison of Standard Ruler and Standard Candle con- straints on Dark Energy Models,” JCAP07, 012 (2008), arXiv:0712.1232 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  28. [28]

    The blackness of the cosmic microwave background spectrum as a probe of the distance-duality relation

    GeorgeF.R.Ellis, RobertPoltis, Jean-PhilippeUzan, and Amanda Weltman, “Blackness of the cosmic microwave background spectrum as a probe of the distance-duality re- lation,” Phys. Rev. D87, 103530 (2013), arXiv:1301.1312 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  29. [29]

    Cosmic distance duality relation and the shape of galaxy clusters,

    R. F. L. Holanda, J. A. S. Lima, and M. B. Ribeiro, “Cosmic distance duality relation and the shape of galaxy clusters,” Astronomy & Astrophysics528, L14 (2011)

    work page 2011

  30. [30]

    Deformed Distance Duality Relations and Supernovae Dimming

    J. A. S. Lima, J. V. Cunha, and V. T. Zanchin, “Deformed DistanceDualityRelationsandSupernovaeDimming,” As- trophys. J. Lett.742, L26 (2011), arXiv:1110.5065 [astro- ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  31. [31]

    Testing the distance–duality relation with galaxy clusters and type ia supernovae,

    R. F. L. Holanda, J. A. S. Lima, and M. B. Ribeiro, “Testing the distance–duality relation with galaxy clusters and type ia supernovae,” The Astrophysical Journal722, L233–L237 (2010)

    work page 2010

  32. [32]

    Cosmological-model-independent tests for the distance-duality relation from Galaxy Clusters and Type Ia Supernova

    Zhengxiang Li, Puxun Wu, and Hong Wei Yu, “Cosmological-model-independent tests for the distance- duality relation from Galaxy Clusters and Type Ia Supernova,” Astrophys. J. Lett.729, L14 (2011), arXiv:1101.5255 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  33. [33]

    A new Tolman test of a cosmic distance duality relation at 21 cm

    Satej Khedekar and Sayan Chakraborti, “A new Tolman test of a cosmic distance duality relation at 21 cm,” Phys. Rev. Lett.106, 221301 (2011), arXiv:1105.1138 [astro- ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  34. [34]

    The cosmic distance duality relation in light of the time-delayed strong gravitational lensing

    Li Tang, Hai-Nan Lin, and Ying Wu, “Cosmic dis- tance duality relation in light of time-delayed strong grav- itational lensing*,” Chin. Phys. C49, 015104 (2025), arXiv:2410.08595 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  35. [35]

    Testing the Cosmic Distance Duality Relation Using Strong Gravitational Lensing Time Delays and Type Ia Supernovae

    Jing-Zhao Qi, Yi-Fan Jiang, Wan-Ting Hou, and Xin Zhang, “Testing the Cosmic Distance Duality Relation Using Strong Gravitational Lensing Time Delays and Type Ia Supernovae,” Astrophys. J.979, 2 (2025), arXiv:2407.07336 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  36. [36]

    Testing the cosmic distance duality relation using Type Ia supernovae and radio quasars through model-independent methods

    Fan Yang, Xiangyun Fu, Bing Xu, Kaituo Zhang, Yang Huang, and Ying Yang, “Testing the cosmic distance duality relation using Type Ia supernovae and radio quasars through model-independent methods,” (2024), arXiv:2407.05559 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  37. [37]

    The cosmic tetrarchy: four estimators breaking the assumption degeneracy in cosmological distance tensions

    Matteo Martinelli and Domenico Sapone, “The cosmic tetrarchy: four estimators breaking the assumption de- generacy in cosmological distance tensions,” (2026), arXiv:2606.16844 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  38. [38]

    Redshift-dependent 10 Distance Duality Violation in Resolving Multidimen- sional Cosmic Tensions,

    Zhihuan Zhou, Zhuang Miao, Rong Zhang, Hanbing Yang, Penghao Fu, and Chaoqian Ai, “Redshift-dependent 10 Distance Duality Violation in Resolving Multidimen- sional Cosmic Tensions,” (2025), arXiv:2511.02357 [astro- ph.CO]

    work page arXiv 2025

  39. [39]

    The Pantheon+ Analysis: The Full Dataset and Light-Curve Release

    Dan Scolnicet al., “The Pantheon+ Analysis: The Full Data Set and Light-curve Release,” Astrophys. J.938, 113 (2022), arXiv:2112.03863 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  40. [40]

    DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints

    M. Abdul Karimet al.(DESI), “DESI DR2 results. II. Measurements of baryon acoustic oscillations and cosmo- logical constraints,” Phys. Rev. D112, 083515 (2025), arXiv:2503.14738 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  41. [41]

    Why reducing the cosmic sound horizon alone can not fully resolve the Hubble tension

    Karsten Jedamzik, Levon Pogosian, and Gong-Bo Zhao, “Why reducing the cosmic sound horizon alone can not fully resolve the Hubble tension,” Commun. in Phys.4, 123 (2021), arXiv:2010.04158 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  42. [42]

    A new method to build the (inverse) distance ladder

    David Camarena and Valerio Marra, “A new method to build the (inverse) distance ladder,” Mon. Not. Roy. As- tron. Soc.495, 2630–2644 (2020), arXiv:1910.14125 [astro- ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  43. [43]

    A 2.4% Determination of the Local Value of the Hubble Constant

    Adam G. Riesset al., “A 2.4% Determination of the Lo- cal Value of the Hubble Constant,” Astrophys. J.826, 56 (2016), arXiv:1604.01424 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  44. [44]

    Seven hints that early-time new physics alone is not sufficient to solve the Hubble tension

    Sunny Vagnozzi, “Seven Hints That Early-Time New Physics Alone Is Not Sufficient to Solve the Hubble Ten- sion,” Universe9, 393 (2023), arXiv:2308.16628 [astro- ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  45. [45]

    A rapid transition of $G_{\rm eff}$ at $z_t \simeq 0.01$ as a solution of the Hubble and growth tensions

    Valerio Marra and Leandros Perivolaropoulos, “Rapid transition of Geff at zt≃0.01 as a possible solution of the Hubble and growth tensions,” Phys. Rev. D104, L021303 (2021), arXiv:2102.06012 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  46. [46]

    A gravitational constant transition within cepheids as supernovae calibrators can solve the Hubble tension,

    Ruchika, Himansh Rathore, Shouvik Roy Choudhury, and Vikram Rentala, “A gravitational constant transition within cepheids as supernovae calibrators can solve the Hubble tension,” JCAP06, 056 (2024), arXiv:2306.05450 [astro-ph.CO]

    work page arXiv 2024

  47. [47]

    Effects of a local physics change on the SH0ES determination of H0,

    Ruchika, Leandros Perivolaropoulos, and Alessandro Mel- chiorri, “Effects of a local physics change on the SH0ES determination of H0,” Phys. Rev. D111, 123526 (2025), arXiv:2408.03875 [astro-ph.CO]

    work page arXiv 2025

  48. [48]

    Challenges to a sharp change in $G$ as a solution to the Hubble tension

    Indranil Banik, Harry Desmond, and Nick Samaras, “Challenges to a sharp change in G as a solution to the Hubble tension,” Mon. Not. Roy. Astron. Soc.539, 1553– 1561 (2025), arXiv:2411.15301 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  49. [49]

    Cosmology-Independent Constraints on the Etherington Relation and SNeIa Absolute Magnitude Evolution from DESI-DR2

    Sourav Das, Surhud More, and Shadab Alam, “Cosmology-Independent Constraints on the Etherington Relation and SNeIa Absolute Magnitude Evolution from DESI-DR2,” (2026), arXiv:2604.02433 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  50. [50]

    Hubble Tension and the G-step Model: Re-examination of Recent Constraints on Modified Local Physics

    Leandros Perivolaropoulos and Ruchika, “Hubble tension and the G-step model: Reexamination of recent con- straints on modified local physics,” Phys. Rev. D113, 023501 (2026), arXiv:2508.04395 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  51. [51]

    Unveiling the Universe with Emerging Cosmological Probes

    Michele Morescoet al., “Unveiling the Universe with emerging cosmological probes,” Living Rev. Rel.25, 6 (2022), arXiv:2201.07241 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  52. [52]

    Sub-percent constraints on cosmological temperature evolution

    A. Avgoustidis, R. T. Génova-Santos, G. Luzzi, and C. J. A. P. Martins, “Subpercent constraints on the cosmological temperature evolution,” Phys. Rev. D93, 043521 (2016), arXiv:1511.04335 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  53. [53]

    Resilience and implications of adi- abatic CMB cooling,

    M. Ruchika, William Giarè, Elsa M. Teixeira, and Alessandro Melchiorri, “Resilience and implications of adi- abatic CMB cooling,” Phys. Dark Univ.49, 101999 (2025), arXiv:2505.02909 [astro-ph.CO]

    work page arXiv 2025

  54. [54]

    High-redshift cosmography with a possible cosmic distance duality relation violation

    José F. Jesus, Mikael J. S. Gomes, Rodrigo F. L. Holanda, and Rafael C. Nunes, “High-redshift cosmography with a possible cosmic distance duality relation violation,” JCAP 01, 088 (2025), arXiv:2408.13390 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  55. [55]

    Testing the cosmic distance duality relation using Type Ia supernovae and BAO observations

    Fan Yang, Xiangyun Fu, Bing Xu, Kaituo Zhang, Yang Huang, and Ying Yang, “Testing the cosmic distance du- ality relation using Type Ia supernovae and BAO observa- tions,” Eur. Phys. J. C85, 186 (2025), arXiv:2502.05417 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  56. [56]

    On the impact of intergalactic dust on cosmology with type ia supernovae: Cosmicdustandcosmologywithsupernovae,

    Brice Ménard, Martin Kilbinger, and Ryan Scranton, “On the impact of intergalactic dust on cosmology with type ia supernovae: Cosmicdustandcosmologywithsupernovae,” MonthlyNoticesoftheRoyalAstronomicalSociety,no–no (2010)

    work page 2010

  57. [57]

    Constraints on cosmic opacity and beyond the standard model physics from cosmological distance measurements

    Anastasios Avgoustidis, Clare Burrage, Javier Redondo, Licia Verde, and Raul Jimenez, “Constraints on cosmic opacity and beyond the standard model physics from cos- mological distance measurements,” JCAP10, 024 (2010), arXiv:1004.2053 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  58. [58]

    Model-independent constraints on the cosmic opacity

    R. F. L. Holanda, J. C. Carvalho, and J. S. Alcaniz, “Model-independent constraints on the cosmic opacity,” JCAP04, 027 (2013), arXiv:1207.1694 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  59. [59]

    An Intuitive Tutorial to Gaussian Process Regression

    Jie Wang, “An Intuitive Tutorial to Gaussian Process Regression,” arXiv e-prints , arXiv:2009.10862 (2020), arXiv:2009.10862 [stat.ML]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  60. [60]

    Bishop,Pattern Recognition and Machine Learning (Information Science and Statistics)(Springer- Verlag, Berlin, Heidelberg, 2006)

    Christopher M. Bishop,Pattern Recognition and Machine Learning (Information Science and Statistics)(Springer- Verlag, Berlin, Heidelberg, 2006)

    work page 2006

  61. [61]

    Carl Edward Rasmussen and Christopher K. I. Williams, Gaussian processes for machine learning, Vol. 2 (MIT Press, United States, 2006)

    work page 2006

  62. [62]

    Stein,Interpolation of Spatial Data: Some Theory for Kriging, 1st ed., Springer Series in Statistics (Springer Science+Business Media, New York, 1999)

    Michael L. Stein,Interpolation of Spatial Data: Some Theory for Kriging, 1st ed., Springer Series in Statistics (Springer Science+Business Media, New York, 1999)

    work page 1999