pith. sign in

arxiv: 2606.31324 · v1 · pith:JCOWIW57new · submitted 2026-06-30 · 🌌 astro-ph.CO · gr-qc

Cosmological Viability of Exponential Infrared f(T) Gravity

Mahmoud Hashim , Eleonora Di Valentino , Jackson Levi Said , Waleed El Hanafy This is my paper

Pith reviewed 2026-07-01 04:36 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc
keywords f(T) gravityteleparallel gravityHubble tensioncosmological constraintsCMB observationsdark energymodified gravityBAO
0
0 comments X

The pith

Exponential infrared f(T) gravity produces two acceleration branches, but data rule out both over standard cosmology.

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

The paper tests whether a specific exponential form of f(T) teleparallel gravity can explain late-time cosmic acceleration while using exactly the same six parameters as flat Lambda CDM. It identifies two distinct solution branches: one phantom-like and one that transitions from negative to positive effective torsional dark energy density. Constraints from Planck, ACT, SPT, DESI BAO and Pantheon+ supernovae show the first branch eases the Hubble tension yet remains statistically disfavoured, while the second branch is ruled out entirely. The failure arises because late-time distance data fix the expansion history so tightly that the required shifts in matter density, scalar amplitude, spectral index and reionization optical depth ruin the fit to CMB perturbations.

Core claim

The exponential infrared f(T) model admits two distinct solution branches. Model I behaves like phantom dark energy and reduces the Hubble tension relative to Lambda CDM but is still disfavoured by the combined dataset. Model II produces a negative-to-positive transition in the effective torsional dark-energy density and is decisively ruled out. This exclusion stems from the interplay between background and perturbation constraints: once distance measurements fix the expansion, the model forces correlated parameter shifts that degrade the CMB damping tail fit and drive the optical depth to unphysical values.

What carries the argument

The two distinct solution branches of the exponential infrared f(T) model, each fixing a different evolution for the effective torsional dark-energy density without extra free parameters.

If this is right

  • Model I reduces the Hubble tension without enlarging the parameter space.
  • Neither branch improves the fit to the combined dataset over Lambda CDM.
  • Perturbation observables supply independent tests that can eliminate models allowed by background expansion alone.
  • The failure of Model II shows that background and perturbation constraints must be applied jointly for teleparallel gravity models.

Where Pith is reading between the lines

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

  • Similar torsional modifications may need explicit mechanisms to keep perturbation parameters within physical ranges once background data are fixed.
  • Full Boltzmann solvers that include both background and linear perturbations will be required for any future f(T) viability tests.
  • Tighter future constraints on the reionization optical depth could provide an independent way to test whether the required parameter shifts are viable.

Load-bearing premise

The exponential infrared f(T) form produces exactly two solution branches whose effective torsional dark-energy density evolves exactly as described, with no additional free parameters.

What would settle it

A high-precision measurement of the CMB damping tail and optical depth that remains consistent with the background-constrained shifts in Omega_m h^2, A_s, n_s and tau_reio required by Model II.

Figures

Figures reproduced from arXiv: 2606.31324 by Eleonora Di Valentino, Jackson Levi Said, Mahmoud Hashim, Waleed El Hanafy.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The TT, TE, and EE angular power spectra of the three models compared with the CMB measurements from [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Observational constraints on the ΛCDM model. Marginalized 68% and 95% confidence regions for the cosmological [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Observational constraints on Model I. Marginalized 68% and 95% confidence regions for the cosmological parameters [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Observational constraints on Model II: 2D joint marginalized constraints at 68% and 95% CL for the cosmological [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Purely late-Universe constraints (PP/PPS+DESI) for ΛCDM, [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Purely early-Universe constraints (CMB-SPA) for ΛCDM, [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Combined early- and late-Universe constraints (CMB-SPA+PP+DESI) for ΛCDM, [PITH_FULL_IMAGE:figures/full_fig_p025_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Combined early- and late-Universe constraints (CMB-SPA+PPS+DESI) for ΛCDM, [PITH_FULL_IMAGE:figures/full_fig_p026_11.png] view at source ↗
read the original abstract

We investigate the cosmological viability of exponential infrared $f(T)$ teleparallel gravity using current cosmological observations. This framework realizes late-time cosmic acceleration through torsional modifications of gravity without enlarging the six-parameter cosmological parameter space of spatially flat $\Lambda$CDM, and admits two distinct solution branches: a phantom-like model (Model I) and a model featuring a negative-to-positive transition in the effective torsional dark-energy density (Model II). We constrain both branches using CMB observations from Planck, ACT, and SPT together with DESI BAO and Pantheon+ Type Ia supernovae. We find that the principal branch (Model I) alleviates the Hubble tension relative to $\Lambda$CDM, but remains statistically disfavoured by the combined dataset. The secondary branch (Model II) is decisively ruled out. We show that the failure of Model II originates from the interplay between background and perturbation constraints: once late-time distance measurements constrain the expansion history, the model becomes overconstrained, forcing correlated shifts in $\Omega_{\rm m}h^2$, $A_s$, $n_s$, and $\tau_{\rm reio}$, degrading the fit to the CMB damping tail and driving the optical depth to unphysical values. Our results demonstrate that perturbation observables provide stringent and complementary tests of teleparallel gravity beyond the background expansion history.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates exponential infrared f(T) teleparallel gravity, which realizes late-time acceleration without enlarging the six-parameter space of flat ΛCDM and admits two solution branches: a phantom-like Model I and Model II with a negative-to-positive transition in effective torsional dark-energy density. Using Planck, ACT, SPT CMB data combined with DESI BAO and Pantheon+ supernovae, it finds Model I mildly alleviates the Hubble tension but is statistically disfavoured, while Model II is ruled out by the interplay of background and perturbation constraints that force unphysical shifts in Ω_m h², A_s, n_s, and τ_reio, degrading the CMB damping tail fit. The work emphasizes that perturbation observables provide stringent tests beyond background expansion.

Significance. If the derivations of the two branches and the effective-DE mapping hold, the results demonstrate that current multi-probe datasets can decisively test and exclude branches of teleparallel gravity even when background expansion appears viable, underscoring the complementary role of perturbation constraints in modified gravity viability studies. The parameter-space equivalence to ΛCDM is a notable strength if confirmed.

major comments (2)
  1. [model definition and branch derivation] The central viability conclusions rest on the assertion (abstract) that the exponential infrared f(T) form yields precisely two solution branches with effective torsional DE density evolving exactly as stated and with zero extra free parameters or degrees of freedom. The modified Friedmann and perturbation equations must be shown to admit no additional solutions or hidden parameter dependence; otherwise the statistical disfavor of Model I and the specific overconstraint mechanism for Model II (shifts in Ω_m h², A_s, n_s, τ_reio) would not follow.
  2. [perturbation equations and constraints] The explanation that Model II fails due to background-perturbation interplay (abstract) requires explicit confirmation that the perturbation equations for each branch contain no non-standard slip or growth terms beyond the effective-DE mapping; if such terms exist, the claimed degradation of the CMB damping tail fit and the unphysical τ_reio values would need re-derivation.
minor comments (2)
  1. [model section] Clarify the exact functional form of f(T) and the infrared cutoff scale in the model section to aid reproducibility.
  2. [data and methodology] Ensure all dataset combinations and priors are tabulated for direct comparison with ΛCDM results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and valuable comments. We address each major comment below with clarifications on the model derivations and perturbation structure. These responses confirm the robustness of our conclusions while incorporating explicit statements where helpful.

read point-by-point responses

  1. Referee: [model definition and branch derivation] The central viability conclusions rest on the assertion (abstract) that the exponential infrared f(T) form yields precisely two solution branches with effective torsional DE density evolving exactly as stated and with zero extra free parameters or degrees of freedom. The modified Friedmann and perturbation equations must be shown to admit no additional solutions or hidden parameter dependence; otherwise the statistical disfavor of Model I and the specific overconstraint mechanism for Model II (shifts in Ω_m h², A_s, n_s, τ_reio) would not follow.

    Authors: We appreciate the referee's focus on uniqueness. Section II derives the modified Friedmann equation from the exponential IR f(T) action, reducing it to a first-order ODE for the torsional DE density ρ_T with boundary conditions of matter domination at high z and late-time acceleration. This ODE admits exactly two analytic solutions: the always-positive phantom branch (Model I) and the sign-transition branch (Model II). No other solutions satisfy the asymptotic conditions, and the f(T) form introduces no extra parameters or degrees of freedom. Numerical checks of the ODE confirm no additional branches in the relevant range. We will add an explicit paragraph in Section II stating this uniqueness to strengthen the presentation. revision: yes

  2. Referee: [perturbation equations and constraints] The explanation that Model II fails due to background-perturbation interplay (abstract) requires explicit confirmation that the perturbation equations for each branch contain no non-standard slip or growth terms beyond the effective-DE mapping; if such terms exist, the claimed degradation of the CMB damping tail fit and the unphysical τ_reio values would need re-derivation.

    Authors: Section III presents the linear perturbation equations in Newtonian gauge. For both branches the torsional modifications map exactly to an effective perfect fluid with equation-of-state w_T taken from the background solution; no additional slip parameter, anisotropic stress, or non-standard growth terms appear. The perturbation sector is therefore standard once the background expansion is fixed. The overconstraint on Model II (shifts in Ω_m h², A_s, n_s, τ_reio and damping-tail mismatch) follows directly from this structure. We will insert a clarifying sentence in Section III confirming the absence of non-standard terms. revision: yes

Circularity Check

0 steps flagged

No significant circularity; statistical results data-driven from external datasets

full rationale

The paper defines the exponential infrared f(T) form and its two solution branches (phantom-like Model I; negative-to-positive transition in effective torsional DE for Model II) as part of the model setup, then constrains both using external public datasets (Planck, ACT, SPT, DESI BAO, Pantheon+). No equation reduces a claimed prediction or viability result to a fitted parameter by construction, nor does any central claim rest solely on a self-citation chain whose content is unverified. The statistical conclusions (Model I mildly alleviates H0 tension but disfavored; Model II ruled out via background-perturbation interplay) are obtained by fitting the six-parameter space identical to flat ΛCDM. Minor self-citations for the functional form or prior f(T) results are present but not load-bearing for the data-driven viability assessment.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the chosen exponential infrared f(T) functional form, the existence of exactly two late-time solution branches, and the applicability of standard cosmological perturbation theory to teleparallel gravity without additional free parameters.

axioms (2)
  • domain assumption The exponential infrared f(T) form realizes late-time acceleration while preserving the six-parameter flat Lambda CDM space.
    Invoked in the abstract to define the model class under test.
  • domain assumption Standard linear perturbation equations in teleparallel gravity correctly describe the CMB damping tail and growth observables for these models.
    Required for the claim that perturbation constraints overconstrain Model II.

pith-pipeline@v0.9.1-grok · 5775 in / 1569 out tokens · 60123 ms · 2026-07-01T04:36:58.466298+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

232 extracted references · 24 canonical work pages · 8 internal anchors

  1. [1]

    Xjenza Malta

    Model II: Negative-to-positive dark energy density transition We note that this branch retains the same minimal six-parameter space as the spatially flat ΛCDM model. How- ever, the effective torsional (dark-energy) density undergoes a transition from negative to positive values during the cosmological evolution. Similar to Model I, the effective torsional...

    2018

  2. [2]

    8, we show the observational constraints obtained from the purely late-Universe dataset PP+DESI

    Constraints from purely late universe data In the left panel of Fig. 8, we show the observational constraints obtained from the purely late-Universe dataset PP+DESI. Since both SNIa and BAO measurements are uncalibrated, they do not determine the absolute distance scale and therefore cannot tightly constrain the Hubble constant. This freedom propagates th...

  3. [3]

    9, we compare the constraints obtained using the purely early-Universe dataset CMB-SPA

    Constraints from purely early universe data In Fig. 9, we compare the constraints obtained using the purely early-Universe dataset CMB-SPA. For the primary cosmological parameters, Ωbh2, Ωch2,A s,n s, andτ reio, Model I remains in excellent agreement with ΛCDM, reflecting the fact that the modifications are confined to the late Universe. The main differen...

  4. [4]

    10 and 11, we compare the three models using the combined early- and late-Universe datasets

    Constraints from both early and late universe data In Figs. 10 and 11, we compare the three models using the combined early- and late-Universe datasets. Within the ΛCDM framework, the inclusion of DESI BAO and Type Ia supernovae data shifts several independent cosmological parameters towards larger values, reflecting the well-known tension between CMB and...

  5. [5]

    R. A. Hulse and J. H. Taylor, Astrophys. J. Lett.195, L51 (1975)

    1975

  6. [6]

    B. P. Abbottet al.(LIGO Scientific, Virgo), Phys. Rev. Lett.116, 061102 (2016), arXiv:1602.03837 [gr-qc]

    Pith/arXiv arXiv 2016

  7. [7]

    First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole

    K. Akiyamaet al.(Event Horizon Telescope), Astrophys. J. Lett.875(2019), 10.3847/2041-8213/ab0ec7, arXiv:1906.11238 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/2041-8213/ab0ec7 2019

  8. [8]

    First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring

    K. Akiyamaet al.(Event Horizon Telescope), Astrophys. J. Lett.875(2019), 10.3847/2041-8213/ab0f43, arXiv:1906.11242 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/2041-8213/ab0f43 2019

  9. [9]

    A. G. Riesset al.(Supernova Search Team), Astron. J.116, 1009 (1998), arXiv:astro-ph/9805201

    Pith/arXiv arXiv 1998

  10. [10]

    Perlmutteret al.(Supernova Cosmology Project), Astrophys

    S. Perlmutteret al.(Supernova Cosmology Project), Astrophys. J.517, 565 (1999), arXiv:astro-ph/9812133

    Pith/arXiv arXiv 1999

  11. [11]

    Scolnicet al., Astrophys

    D. Scolnicet al., Astrophys. J.938, 113 (2022), arXiv:2112.03863 [astro-ph.CO]

    Pith/arXiv arXiv 2022

  12. [12]

    Popovicet al.(DES), Mon

    B. Popovicet al.(DES), Mon. Not. Roy. Astron. Soc.548, stag632 (2026), arXiv:2511.07517 [astro-ph.CO]

    Pith/arXiv arXiv 2026

  13. [13]

    T. J. Hoyt, D. Rubin, G. Aldering, S. Perlmutter, A. Cuceu, and R. Gupta, (2026), arXiv:2601.19424 [astro-ph.CO]

    arXiv 2026

  14. [14]

    Planck 2018 results. VI. Cosmological parameters

    N. Aghanimet al.(Planck), Astron. Astrophys.641(2020), 10.1051/0004-6361/201833910, [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201833910 2020

  15. [15]

    Planck 2018 results. I. Overview and the cosmological legacy of Planck

    N. Aghanimet al.(Planck), Astron. Astrophys.641(2020), 10.1051/0004-6361/201833880, arXiv:1807.06205 [astro- ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201833880 2020

  16. [16]

    Louiset al.(Atacama Cosmology Telescope), JCAP11, 062 (2025), arXiv:2503.14452 [astro-ph.CO]

    T. Louiset al.(Atacama Cosmology Telescope), JCAP11, 062 (2025), arXiv:2503.14452 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  17. [17]

    Camphuiset al.(SPT-3G), Phys

    E. Camphuiset al.(SPT-3G), Phys. Rev. D113, 083504 (2026), arXiv:2506.20707 [astro-ph.CO]

    Pith/arXiv arXiv 2026

  18. [18]

    Jungman, M

    G. Jungman, M. Kamionkowski, and K. Griest, Phys. Rept.267, 195 (1996), arXiv:hep-ph/9506380

    Pith/arXiv arXiv 1996

  19. [19]

    Craig, inBeyond the Standard Model after the first run of the LHC(2013) arXiv:1309.0528 [hep-ph]

    N. Craig, inBeyond the Standard Model after the first run of the LHC(2013) arXiv:1309.0528 [hep-ph]

    Pith/arXiv arXiv 2013

  20. [20]

    Adhikariet al.(COSINE-100), Sci

    G. Adhikariet al.(COSINE-100), Sci. Adv.7, abk2699 (2021), arXiv:2104.03537 [hep-ex]

    arXiv 2021

  21. [21]

    W. L. Freedman, B. F. Madore, T. Hoyt, I. S. Jang, R. Beaton, M. G. Lee, A. Monson, J. Neeley, and J. Rich, Astrophys. J.891, 57 (2020), arXiv:2002.01550 [astro-ph.GA]

    arXiv 2020

  22. [22]

    Birreret al., Astron

    S. Birreret al., Astron. Astrophys.643(2020), 10.1051/0004-6361/202038861, arXiv:2007.02941 [astro-ph.CO]

    work page doi:10.1051/0004-6361/202038861 2020

  23. [23]

    A. G. Riesset al., Astrophys. J. Lett.934(2022), 10.3847/2041-8213/ac5c5b, arXiv:2112.04510 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/2041-8213/ac5c5b 2022

  24. [24]

    R. I. Anderson, N. W. Koblischke, and L. Eyer, Astrophys. J. Lett.963(2024), 10.3847/2041-8213/ad284d, arXiv:2303.04790 [astro-ph.CO]

    work page doi:10.3847/2041-8213/ad284d 2024

  25. [25]

    Scolnic, A

    D. Scolnic, A. G. Riess, J. Wu, S. Li, G. S. Anand, R. Beaton, S. Casertano, R. I. Anderson, S. Dhawan, and X. Ke, Astrophys. J. Lett.954(2023), 10.3847/2041-8213/ace978, arXiv:2304.06693 [astro-ph.CO]

    work page doi:10.3847/2041-8213/ace978 2023

  26. [26]

    D. O. Joneset al., Astrophys. J.933, 172 (2022), arXiv:2201.07801 [astro-ph.CO]

    arXiv 2022

  27. [27]

    G. S. Anand, R. B. Tully, L. Rizzi, A. G. Riess, and W. Yuan, Astrophys. J.932, 15 (2022), arXiv:2108.00007 [astro- ph.CO]

    arXiv 2022

  28. [28]

    W. L. Freedman, Astrophys. J.919, 16 (2021), arXiv:2106.15656 [astro-ph.CO]

    arXiv 2021

  29. [29]

    S. A. Uddinet al., Astrophys. J.970, 72 (2024), arXiv:2308.01875 [astro-ph.CO]

    arXiv 2024

  30. [30]

    C. D. Huanget al., Astrophys. J.963, 83 (2024), arXiv:2312.08423 [astro-ph.CO]

    arXiv 2024

  31. [31]

    S. Li, A. G. Riess, S. Casertano, G. S. Anand, D. M. Scolnic, W. Yuan, L. Breuval, and C. D. Huang, Astrophys. J.966, 20 (2024), arXiv:2401.04777 [astro-ph.CO]

    arXiv 2024

  32. [32]

    D. W. Pesceet al., Astrophys. J. Lett.891(2020), 10.3847/2041-8213/ab75f0, arXiv:2001.09213 [astro-ph.CO]

    work page doi:10.3847/2041-8213/ab75f0 2020

  33. [33]

    Kourkchi, R

    E. Kourkchi, R. B. Tully, G. S. Anand, H. M. Courtois, A. Dupuy, J. D. Neill, L. Rizzi, and M. Seibert, Astrophys. J. 896, 3 (2020), arXiv:2004.14499 [astro-ph.GA]

    arXiv 2020

  34. [34]

    Schombert, S

    J. Schombert, S. McGaugh, and F. Lelli, Astron. J.160, 71 (2020), arXiv:2006.08615 [astro-ph.CO]

    arXiv 2020

  35. [35]

    J. P. Blakeslee, J. B. Jensen, C.-P. Ma, P. A. Milne, and J. E. Greene, Astrophys. J.911, 65 (2021), arXiv:2101.02221 [astro-ph.CO]

    arXiv 2021

  36. [36]

    de Jaeger, L

    T. de Jaeger, L. Galbany, A. G. Riess, B. E. Stahl, B. J. Shappee, A. V. Filippenko, and W. Zheng, Mon. Not. Roy. Astron. Soc.514, 4620 (2022), arXiv:2203.08974 [astro-ph.CO]

    arXiv 2022

  37. [37]

    Y. S. Murakami, A. G. Riess, B. E. Stahl, W. D. Kenworthy, D.-M. A. Pluck, A. Macoretta, D. Brout, D. O. Jones, D. M. Scolnic, and A. V. Filippenko, JCAP11, 046 (2023), arXiv:2306.00070 [astro-ph.CO]

    arXiv 2023

  38. [38]

    Breuval, A

    L. Breuval, A. G. Riess, S. Casertano, W. Yuan, L. M. Macri, M. Romaniello, Y. S. Murakami, D. Scolnic, G. S. Anand, and I. Soszy´ nski, Astrophys. J.973, 30 (2024), arXiv:2404.08038 [astro-ph.CO]

    arXiv 2024

  39. [39]

    W. L. Freedman, B. F. Madore, T. J. Hoyt, I. S. Jang, A. J. Lee, and K. A. Owens, Astrophys. J.985, 203 (2025), [Erratum: Astrophys.J. 993, 252 (2025)], arXiv:2408.06153 [astro-ph.CO]

    arXiv 2025

  40. [40]

    A. G. Riesset al., Astrophys. J.977, 120 (2024), arXiv:2408.11770 [astro-ph.CO]

    arXiv 2024

  41. [41]

    Voglet al., Astron

    C. Voglet al., Astron. Astrophys.702(2025), 10.1051/0004-6361/202452910, arXiv:2411.04968 [astro-ph.CO]

    work page doi:10.1051/0004-6361/202452910 2025

  42. [42]

    Scolnicet al., Astrophys

    D. Scolnicet al., Astrophys. J. Lett.979(2025), 10.3847/2041-8213/ada0bd, arXiv:2409.14546 [astro-ph.CO]

    work page doi:10.3847/2041-8213/ada0bd 2025

  43. [43]

    Saidet al., Mon

    K. Saidet al., Mon. Not. Roy. Astron. Soc.539, 3627 (2025), arXiv:2408.13842 [astro-ph.CO]

    arXiv 2025

  44. [44]

    Boubel, M

    P. Boubel, M. Colless, K. Said, and L. Staveley-Smith, Mon. Not. Roy. Astron. Soc.533, 1550 (2024), arXiv:2408.03660 [astro-ph.CO]

    arXiv 2024

  45. [45]

    Scolnic, P

    D. Scolnic, P. Boubel, J. Byrne, A. G. Riess, and G. S. Anand, (2024), arXiv:2412.08449 [astro-ph.CO]

    arXiv 2024

  46. [46]

    S. Li, A. G. Riess, D. Scolnic, S. Casertano, and G. S. Anand, Astrophys. J.988, 97 (2025), arXiv:2502.05259 [astro- ph.CO]

    arXiv 2025

  47. [47]

    J. B. Jensen, J. P. Blakeslee, M. Cantiello, M. Cowles, G. S. Anand, R. B. Tully, E. Kourkchi, and G. Raimondo, (2025), 10.3847/1538-4357/addfd6, arXiv:2502.15935 [astro-ph.CO]. 28

    work page doi:10.3847/1538-4357/addfd6 2025

  48. [48]

    A. G. Riesset al., Astrophys. J. Lett.992(2025), 10.3847/2041-8213/ae0ad6, arXiv:2509.01667 [astro-ph.CO]

    work page doi:10.3847/2041-8213/ae0ad6 2025

  49. [49]

    Benisty, J

    D. Benisty, J. Wagner, S. Haridasu, and P. Salucci, JCAP06, 005 (2026), arXiv:2504.04135 [astro-ph.CO]

    Pith/arXiv arXiv 2026

  50. [50]

    M. J. B. Newmanet al., (2025), arXiv:2508.20023 [astro-ph.CO]

    arXiv 2025

  51. [51]

    Stiskalek, H

    R. Stiskalek, H. Desmond, E. Tsaprazi, A. Heavens, G. Lavaux, S. McAlpine, and J. Jasche, Mon. Not. Roy. Astron. Soc.546, staf2260 (2026), arXiv:2509.09665 [astro-ph.CO]

    Pith/arXiv arXiv 2026

  52. [52]

    The Local Distance Network: a community consensus report on the measurement of the Hubble constant at 1% precision

    S. Casertanoet al.(H0DN), Astron. Astrophys.708(2026), 10.1051/0004-6361/202557993, arXiv:2510.23823 [astro- ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/202557993 2026

  53. [53]

    Agrawalet al., Astrophys

    A. Agrawalet al., Astrophys. J.1002, 187 (2026), arXiv:2510.07637 [astro-ph.CO]

    Pith/arXiv arXiv 2026

  54. [54]

    Bhardwaj, N

    A. Bhardwaj, N. Matsunaga, C. D. Huang, A. G. Riess, and M. Rejkuba, Astrophys. J.990, 63 (2025), arXiv:2507.10658 [astro-ph.GA]

    arXiv 2025

  55. [55]

    Verde, T

    L. Verde, T. Treu, and A. G. Riess, Nature Astron.3, 891 (2019), arXiv:1907.10625 [astro-ph.CO]

    Pith/arXiv arXiv 2019

  56. [56]

    Di Valentinoet al., Astropart

    E. Di Valentinoet al., Astropart. Phys.131, 102605 (2021), arXiv:2008.11284 [astro-ph.CO]

    arXiv 2021

  57. [57]

    Di Valentino, O

    E. Di Valentino, O. Mena, S. Pan, L. Visinelli, W. Yang, A. Melchiorri, D. F. Mota, A. G. Riess, and J. Silk, Class. Quant. Grav.38, 153001 (2021), arXiv:2103.01183 [astro-ph.CO]

    Pith/arXiv arXiv 2021

  58. [58]

    Perivolaropoulos and F

    L. Perivolaropoulos and F. Skara, New Astron. Rev.95, 101659 (2022), arXiv:2105.05208 [astro-ph.CO]

    Pith/arXiv arXiv 2022

  59. [59]

    Abdallaet al., JHEAp34, 49 (2022), arXiv:2203.06142 [astro-ph.CO]

    E. Abdallaet al., JHEAp34, 49 (2022), arXiv:2203.06142 [astro-ph.CO]

    Pith/arXiv arXiv 2022

  60. [60]

    Di Valentino, Universe8, 399 (2022)

    E. Di Valentino, Universe8, 399 (2022)

    2022

  61. [61]

    Kamionkowski and A

    M. Kamionkowski and A. G. Riess, Ann. Rev. Nucl. Part. Sci.73, 153 (2023), arXiv:2211.04492 [astro-ph.CO]

    Pith/arXiv arXiv 2023

  62. [62]

    Hu and F.-Y

    J.-P. Hu and F.-Y. Wang, Universe9, 94 (2023), arXiv:2302.05709 [astro-ph.CO]

    arXiv 2023

  63. [63]

    Verde, N

    L. Verde, N. Sch¨ oneberg, and H. Gil-Mar´ ın, Ann. Rev. Astron. Astrophys.62, 287 (2024), arXiv:2311.13305 [astro- ph.CO]

    arXiv 2024

  64. [64]

    Di Valentino and D

    E. Di Valentino and D. Brout, eds.,The Hubble Constant Tension, Springer Series in Astrophysics and Cosmology (Springer, 2024)

    2024

  65. [65]

    Di Valentinoet al.(CosmoVerse Network), Phys

    E. Di Valentinoet al.(CosmoVerse Network), Phys. Dark Univ.49, 101965 (2025), arXiv:2504.01669 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  66. [66]

    Abdul Karimet al.(DESI), Phys

    M. Abdul Karimet al.(DESI), Phys. Rev. D112, 083515 (2025), arXiv:2503.14738 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  67. [67]

    Lodhaet al.(DESI), Phys

    K. Lodhaet al.(DESI), Phys. Rev. D112, 083511 (2025), arXiv:2503.14743 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  68. [68]

    A. G. Adameet al.(DESI), JCAP02, 021 (2025), arXiv:2404.03002 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  69. [69]

    Lodhaet al.(DESI), Phys

    K. Lodhaet al.(DESI), Phys. Rev. D111, 023532 (2025), arXiv:2405.13588 [astro-ph.CO]

    arXiv 2025

  70. [70]

    Cortˆ es and A

    M. Cortˆ es and A. R. Liddle, JCAP12, 007 (2024), arXiv:2404.08056 [astro-ph.CO]

    arXiv 2024

  71. [71]

    Shlivko and P

    D. Shlivko and P. J. Steinhardt, Phys. Lett. B855, 138826 (2024), arXiv:2405.03933 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  72. [72]

    Luongo and M

    O. Luongo and M. Muccino, Astron. Astrophys.690(2024), 10.1051/0004-6361/202450512, arXiv:2404.07070 [astro- ph.CO]

    work page doi:10.1051/0004-6361/202450512 2024

  73. [73]

    I. D. Gialamas, G. H¨ utsi, K. Kannike, A. Racioppi, M. Raidal, M. Vasar, and H. Veerm¨ ae, Phys. Rev. D111, 043540 (2025), arXiv:2406.07533 [astro-ph.CO]

    arXiv 2025

  74. [74]

    Wang and Y.-S

    H. Wang and Y.-S. Piao, Phys. Lett. B873, 140180 (2026), arXiv:2404.18579 [astro-ph.CO]

    arXiv 2026

  75. [75]

    G. Ye, M. Martinelli, B. Hu, and A. Silvestri, Phys. Rev. Lett.134, 181002 (2025), arXiv:2407.15832 [astro-ph.CO]

    arXiv 2025

  76. [76]

    Tada and T

    Y. Tada and T. Terada, Phys. Rev. D109(2024), 10.1103/PhysRevD.109.L121305, arXiv:2404.05722 [astro-ph.CO]

    work page doi:10.1103/physrevd.109.l121305 2024

  77. [77]

    Carloni, O

    Y. Carloni, O. Luongo, and M. Muccino, Phys. Rev. D111, 023512 (2025), arXiv:2404.12068 [astro-ph.CO]

    arXiv 2025

  78. [78]

    C.-G. Park, J. de Cruz P´ erez, and B. Ratra, Phys. Rev. D110, 123533 (2024), arXiv:2405.00502 [astro-ph.CO]

    arXiv 2024

  79. [79]

    Bhattacharya, G

    S. Bhattacharya, G. Borghetto, A. Malhotra, S. Parameswaran, G. Tasinato, and I. Zavala, JCAP09, 073 (2024), arXiv:2405.17396 [astro-ph.CO]

    arXiv 2024

  80. [80]

    Rebou¸ cas, D

    J. Rebou¸ cas, D. H. F. de Souza, K. Zhong, V. Miranda, and R. Rosenfeld, JCAP02, 024 (2025), arXiv:2408.14628 [astro-ph.CO]

    arXiv 2025

Showing first 80 references.