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REVIEW 4 major objections 7 minor 86 references

k-essence dark energy cuts the Planck–late-Universe Hubble tension from nearly 6σ in ΛCDM to under 1σ without retuning parameters across datasets.

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2026-07-12 01:29 UTC pith:7NKDI522

load-bearing objection Clean direct-test numbers showing k-essence can drop Planck–late H0 tension to <1σ with stable parameters; the compressed Planck likelihood is the real soft spot. the 4 major comments →

arxiv 2607.03569 v1 pith:7NKDI522 submitted 2026-07-03 astro-ph.CO

Hubble tension in k-essence: Evidence for robust tension alleviation

Isaac Opio (BIUST) , Didam Duniya (BIUST) , Bishop Mongwane (Cape Town) , Hassan Abdalla (NWU , Omdurman) This is my paper
classification astro-ph.CO PACS 98.80.Es95.36.+x98.80.-k
keywords Hubble tensionk-essencedilatontachyondark energyPlanckPantheon+SH0ESDESI
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 paper argues that the long-standing mismatch between the expansion rate inferred from the cosmic microwave background and the rate measured by local supernovae and other late-time probes is not an inevitable feature of the data. It is largely an artifact of assuming a cosmological-constant dark energy. Replacing that constant with two concrete k-essence scalar-field models (dilaton and tachyon) lets the same Planck data prefer a higher present-day Hubble constant while the late-Universe data remain essentially unchanged or move only modestly. When every late-time probe is combined, the residual offsets drop to 0.14σ (dilaton) and 0.69σ (tachyon) versus 5.89σ in the standard model. The model parameters themselves stay fixed across every data combination, so the authors conclude the relief is an intrinsic dynamical consequence of the non-canonical kinetic terms rather than fine-tuning.

Core claim

In two physically motivated k-essence cosmologies the Planck–late-Universe Hubble tension falls from 5.89σ in ΛCDM to 0.14σ (dilaton) and 0.69σ (tachyon) once all late-time probes are combined; the reduction is stable across every independent late-time combination and occurs without dataset-dependent retuning of the k-essence parameters.

What carries the argument

k-essence scalar fields whose Lagrangians depend non-linearly on the kinetic term X; the resulting non-canonical self-interactions modify the post-recombination expansion history, shift the sound horizon, and thereby raise the Planck-inferred H0 while leaving the baryon density essentially untouched.

Load-bearing premise

The analysis treats three compressed Planck numbers (acoustic scale, shift parameter, and baryon density) derived under standard recombination as still valid once k-essence alters the expansion after last scattering.

What would settle it

A full Boltzmann-code analysis of the same dilaton and tachyon models against the complete Planck likelihood (including early integrated Sachs–Wolfe and polarisation) that either restores a multi-sigma H0 tension or forces the k-essence parameters to run strongly with dataset would falsify the claim of robust, parameter-stable alleviation.

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

If this is right

  • The severity of the Hubble tension is model-dependent and can be reduced by changing only the dark-energy sector.
  • Late-time supernova, chronometer and BAO data need not be in conflict with CMB data once dark energy carries non-canonical kinetics.
  • Future early-Universe probes (ACT, SPT, next-generation CMB) can be used as decisive tests of whether the same k-essence dynamics continue to reconcile H0.
  • The two models offer distinct pathways—one-sided early-Universe shift (dilaton) versus two-sided early-and-late shift (tachyon)—that can be distinguished by precision growth or BAO measurements.

Where Pith is reading between the lines

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

  • If the compressed-likelihood approximation holds, k-essence becomes a concrete, observationally viable alternative to early dark energy or modified gravity for the H0 problem.
  • The same non-canonical kinetic structure may also leave imprints on the growth of structure or the late-time integrated Sachs–Wolfe effect that can be hunted in upcoming large-scale structure surveys.
  • Because the model parameters remain stable, the mechanism is in principle predictive rather than merely accommodating; forecasts for DESI Year 5 or Roman supernovae can therefore be made without further tuning.

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

4 major / 7 minor

Summary. The paper performs a direct (independent early- vs late-Universe) test of the Hubble tension in two k-essence models—dilatonic ghost condensate and tachyon—against ΛCDM. Using a compressed Planck likelihood (ℓA, R, Ωb0h²) and late-Universe combinations of Pantheon+SH0ES, Union3, DESY5, CC and DESI, it reports that the Planck–late H0 offset falls from 5.89σ in ΛCDM to 0.14σ (dilaton) and 0.69σ (tachyon) for the joint late-Universe set, with intermediate combinations also showing substantial reduction. The authors attribute the alleviation to modified expansion history (via non-canonical kinetics affecting rs and/or DM) and argue it is intrinsic rather than fine-tuned because the k-essence parameters remain stable across datasets.

Significance. If the reported direct-test alleviation survives a more complete early-Universe treatment, the result would be a meaningful contribution to the Hubble-tension literature: it cleanly separates early and late inferences within the same model (unlike joint fits that can mask residual tension), tests robustness across several independent late-time probes, and uses two standard, physically motivated k-essence Lagrangians rather than ad-hoc H0 extensions. The tabulated multi-dataset comparison and the explicit emphasis on parameter stability as a fine-tuning check are useful methodological strengths. The work would strengthen the case that the apparent tension is model-dependent and that non-canonical dark energy is a viable pathway, while the authors already correctly flag that other early-Universe probes remain necessary for a general resolution.

major comments (4)
  1. §III.B, Eqs. (24)–(30) and (28), (32): The Planck constraints are obtained from a three-parameter compressed likelihood (ℓA, R, Ωb0h²) whose means/covariance come from a ΛCDM Planck chain, together with Hu–Sugiyama fitting formulae for z* and zd. The central claim is that k-essence modifies the expansion so as to change rs (Eq. 27) and raise the Planck H0 (Tables II–IV). That claim is load-bearing for every reported ΔH0 (including the headline 0.14σ/0.69σ). The compression and fitting formulae assume standard recombination and that residual early effects (early ISW, damping, shifted recombination) are negligible. The paper does not validate the compressed likelihood at the reported best-fit points (higher Ωc0h², AD0/AT0∼1.25). Without a Boltzmann-code check or an explicit demonstration that E(a) for a≲a* and the recombination history remain within the domain of the compression, the Planc
  2. Table I and §IV.B: The priors on the k-essence parameters are extremely narrow (λ∈[0.01,0.02], α∈[0.02,0.03]). The abstract and §IV–V repeatedly use the observation that “model parameters remain unchanged across datasets” as evidence that alleviation is “intrinsic… rather than of model fine tuning.” With such tight priors the parameters cannot move appreciably; stability is then largely prior-enforced and does not constitute an independent check against fine-tuning. The prior ranges should be substantially widened (or carefully justified from theory) and the MCMC re-run so that the stability claim is data-driven.
  3. Abstract vs Table IV (dilaton ALL row) and §IV.B: For the strongest result (ALL → 0.14σ), the dilaton parameters do change: AD0 moves from 1.25±0.14 (Planck) to 0.71+0.39−0.22 (ALL), and λ from 0.015±0.003 to 0.011+0.004−0.001. The text acknowledges a “slightly weaker” contribution, but the abstract’s unqualified statement that parameters “remain unchanged across datasets” is not accurate for this case. The claim should be restricted to the tachyon (where stability holds) and to dilaton combinations other than ALL, or the ALL result should be presented as requiring a re-tuned amplitude.
  4. §I–II and Eq. (27): The abstract and introduction state that k-essence modifies expansion “beyond recombination; thereby impacting the sound horizon.” Post-recombination modifications change DM(z*), not rs; only a non-negligible pre-recombination contribution to E(a) alters rs. The paper never shows ρϕ(z) or E(a) near z* at the best-fit points, nor clarifies whether the H0 shift is driven by rs, by DM(z*), or by the Ωc0h² compensation. A short background-evolution figure (or table of rs and DM at the best fits relative to ΛCDM) is needed to make the physical mechanism precise and consistent with the wording.
minor comments (7)
  1. Throughout: “beyond recombination” is ambiguous (after vs. in addition to). Prefer “pre- and/or post-recombination” once the mechanism is clarified.
  2. Table I: Prior edges for λ and α sit essentially on top of the reported posteriors; even after widening, state whether posteriors are prior-bounded.
  3. §III.A, Eq. (22): θ lists both AD0 and AT0 in a single vector; clarify that only one is active per model to avoid implying a joint dilaton+tachyon fit.
  4. Figs. 1–5: Contours are useful but dense; consider marking the SH0ES/Planck H0 bands or adding a one-panel H0 summary across datasets for readability.
  5. §IV.A: “reductions of about 50% and 70%” in tension (σ units) is informal; prefer absolute Δσ or a clear definition of the percentage.
  6. Typos/notation: “desnsity” (p.2), “T achyon” spacing in headings, and occasional “wρ = Pϕ/ρρ” (Eq. after (2)).
  7. References: The deferred full early-Universe study is noted; a sentence on why WMAP/ACT/SPT are omitted (beyond “Planck is gold-standard”) would help scope the claim.

Circularity Check

0 steps flagged

No significant circularity: independent early/late MCMC fits produce the reported H0 offsets and parameter stability as emergent numerical results, not by construction.

full rationale

The paper's central claim (robust Planck–late-Universe H0 tension reduction to 0.14σ/0.69σ in dilaton/tachyon versus 5.89σ in ΛCDM, with model parameters stable across datasets) is obtained by separate MCMC inferences of the free parameters (H0, Ωb0h², Ωc0h², AD0/AT0, λ/α, MB) on the compressed Planck likelihood (ℓA, R, Ωb0h²) versus each late-Universe combination (PP, PP+CC, PP+Union3, PP+DESY5, PP+DESI, ALL). The Friedmann equation, sound-horizon integral, and model-specific wϕ are written explicitly and solved numerically; H0_early and H0_late are not defined in terms of each other or of the k-essence parameters. Parameter stability is an a-posteriori observation from the chains, not an input that forces the ΔH0 values. The single self-citation (arXiv:2604.20989) supplies only background-evolution details already derivable from the Lagrangians given in the text and is not load-bearing for the tension numbers. Compressed-likelihood validity under modified E(a) is a modelling-assumption issue outside the circularity criteria. The derivation chain is therefore self-contained against the paper's own equations and data.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The central claim rests on standard FLRW cosmology plus two specific non-canonical Lagrangians whose free parameters are fitted but shown to be stable. No new particles or forces are invented; the only non-standard ingredients are the dilatonic and tachyonic kinetic structures already present in the literature.

free parameters (5)
  • λ (dilaton potential slope) = ≈0.015
    Dimensionless free parameter in U(ϕ)=M⁴ exp(λ κ ϕ); prior [0.01,0.02]; remains ≈0.015 across most data sets.
  • α (tachyon potential index) = ≈0.025
    Dimensionless free parameter in U(ϕ)=M^{4+α}/ϕ^α; prior [0.02,0.03]; remains ≈0.025 across all data sets.
  • A_D0 (dilaton amplitude) = ≈1.25
    Present-day dimensionless amplitude κ² M⁴/(3 H0²); prior [0.5,1.5]; stable near 1.25 except for the full ALL combination.
  • A_T0 (tachyon amplitude) = ≈1.25
    Present-day dimensionless amplitude κ² M⁴/(3 H0²); prior [0.8,2.0]; stable near 1.25.
  • M_B (SNIa absolute magnitude) = ≈−19.25 to −19.36
    Calibration nuisance for Pantheon+SH0ES and Union3; fitted jointly with cosmology.
axioms (5)
  • domain assumption Spatially flat FLRW metric and standard continuity equations for radiation, baryons, CDM and k-essence.
    Stated at the opening of §II; used to derive the Friedmann equation (5).
  • domain assumption Dilatonic ghost-condensate Lagrangian P = −X + (X²/M⁸) U(ϕ) with exponential potential.
    Eq. (10)–(11); taken from the existing literature (Piazza & Tsujikawa).
  • domain assumption Tachyon Lagrangian P = −U(ϕ) √(1−2X/M⁴) with inverse-power potential.
    Eq. (13)–(14); standard tachyon form.
  • ad hoc to paper Compressed Planck likelihood (ℓA, R, Ωb0h²) remains an adequate summary statistic when the post-recombination expansion is modified by k-essence.
    §III.B; the three numbers and their covariance are taken from ΛCDM-derived chains and applied unchanged to the k-essence models.
  • ad hoc to paper ΛCDM-like initial conditions for the background evolution of the scalar field.
    Explicitly stated before Table I.

pith-pipeline@v1.1.0-grok45 · 29844 in / 3301 out tokens · 30427 ms · 2026-07-12T01:29:25.680687+00:00 · methodology

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read the original abstract

The Hubble tension has come to stay as a major problem in modern cosmology as it continues to plague the standard cosmological model ($\Lambda$CDM). As one of the viable, self-consistent dark energy theories, k-essence involves nontrivial self-interactions that can modify the background expansion beyond recombination; thereby impacting the sound horizon to last scattering, and hence, the inferred value of the Hubble constant. We examine this tension in two physically motivated k-essence models, dilaton and tachyon, using datasets from Planck and late-Universe probes including Pantheon+SH0ES, cosmic chronometer (CC), Supernova Cosmology Project Union compilation (Union3), Dark Energy Survey Year~5 (DESY5), and Dark Energy Spectroscopic Instrument (DESI) measurements. While $\Lambda$CDM exhibits inconsistent tension inferences, both k-essence models exhibit a substantial tension alleviation that is robust against the inclusion of the independent late-Universe cosmological datasets, giving consistent tension reduction irrespective of whether the observations are supernovae (Pantheon+SH0ES, Union3, DESY5) alone or in combination with cosmic chronometers (CC) and baryon acoustic oscillation measurements (DESI). The combined late-Universe dataset leads to only $0.14\sigma$ and $0.69\sigma$ offsets from the Planck prediction in the dilaton and tachyon models, respectively, compared to $5.89\sigma$ tension in $\Lambda$CDM. Both models demonstrate that the inferred tension alleviation is a stable, intrinsic consequence of the underlying k-essence dynamics rather than of model fine tuning: model parameters remain unchanged across datasets. The results establish that the apparent Hubble tension is not an unavoidable feature of late-Universe cosmology but depends critically on the description of dark energy.

Figures

Figures reproduced from arXiv: 2607.03569 by Bishop Mongwane (Cape Town), Didam Duniya (BIUST), Hassan Abdalla (NWU, Isaac Opio (BIUST), Omdurman).

Figure 1
Figure 1. Figure 1: Dilaton: The contour plots of cosmological parameter estimates with Pantheon+SH0ES and Planck 2018 datasets, for the dilaton and cosmological-constant models. The associated probability density functions are given in the outer panels. to ΛCDM), in Table II. In the dilaton model, the Planck best-fit value moves upward in H0 (+2.30 kms−1Mpc−1 ) and that of Pantheon+SH0ES moves slightly downward (< 1 kms−1Mpc… view at source ↗
Figure 2
Figure 2. Figure 2: Tachyon: The contour plots of cosmological parameter estimates with Pantheon+SH0ES and Planck 2018 datasets, for the tachyon and cosmological-constant models. The associated probability density functions are given in the outer panels. ers, between the datasets, therefore implies that the shift in the Planck-preferred H0 in the dilaton model is owing to changes in the dark matter sector rather than modific￾… view at source ↗
Figure 3
Figure 3. Figure 3: ΛCDM: Contour plots of cosmological constraints for ΛCDM derived from Planck 2018, Pantheon+SH0ES, and [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Dilaton: Contour plots of cosmological constraints for the dilaton model derived from Planck 2018, Pantheon+SH0ES, and different combinations of complementary late-Universe measurements with Pantheon+SH0ES. the preferred late-Universe toward lower H0 and adjus￾ted matter density. The persistence of these behaviours across complementary probes strengthens the interpret￾ation that the inferred cosmological-p… view at source ↗
Figure 5
Figure 5. Figure 5: Tachyon: Contour plots of cosmological constraints for the tachyon model derived from Planck 2018, Pan￾theon+SH0ES, and different combinations of complementary late-Universe measurements with Pantheon+SH0ES. [1] N. Aghanim et 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]. [2] A. … view at source ↗

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Reference graph

Works this paper leans on

86 extracted references · 72 linked inside Pith

  1. [1]

    Planck),H early 0 , and •late-time data (e.g

    Estimating two independent constraints within the same model from •early-time data (e.g. Planck),H early 0 , and •late-time data (e.g. SH0ES),H late 0

  2. [2]

    gold stand- ard

    Explicitly computing ∆H 0 =|H late 0 −H early 0 |, the discrepancy between the two in-model inferences. Essentially, a direct test involves independent parameter inference from early- and late-Universe probes within the same model, followed by assessment of direct discrepancy. This matters because the Hubble tension is fundament- ally a disagreement betwe...

  3. [3]

    dilaton,

    are the present-day values of energy density parameters for the cosmic speciesA, κ≡ √ 8πGwithGbeing the Newton’s gravitational con- stant,H 0 is the Hubble constant (present-day value of the Hubble parameter),f ϕ is as in (4), and Ωr0 = Ωm0 1 +z eq , z eq = 2.5×10 4 (TCMB/2.7K)4 Ωm0h2,(6) with Ω m0 being the matter (baryons plus cold dark matter) density ...

  4. [4]

    (dimensionless) for dilaton (I=D) and tachyon (I=T);λandαare as in (11) and (14). For DESY5 we fit the observed distance modulusµ, with the chi-square statistic given by χ2 DESY5 = (µ−µ Cosmo(θ))T C −1 DESY5 (µ−µ Cosmo(θ)), (23) whereµ Cosmo andθare as given by (17) and (22), re- spectively, andC −1 DESY5 is the inverse of the full DESY5 covariance matrix...

    2018

  5. [5]

    Aghanimet al.(Planck), Planck 2018 results

    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]

    Pith/arXiv arXiv 2018

  6. [6]

    A. 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]

    Pith/arXiv arXiv 2022

  7. [7]

    J. A. Braatz, M. J. Reid, E. M. L. Humphreys, C. Hen- kel, J. J. Condon, and K. Y. Lo, The Megamaser Cosmo- logy Project. II. The Angular-Diameter Distance to UGC 3789, Astrophys. J.718, 657 (2010), arXiv:1005.1955 [astro-ph.CO]

    Pith/arXiv arXiv 2010

  8. [8]

    S. H. Suyuet al.(H0LiCOW), H0LiCOW – I. H0 Lenses in COSMOGRAIL’s Wellspring: program over- view, Mon. Not. Roy. Astron. Soc.468, 2590 (2017), arXiv:1607.00017 [astro-ph.CO]

    Pith/arXiv arXiv 2017

  9. [9]

    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, In the realm of the Hubble tension—a review of solutions, Class. Quant. Grav.38, 153001 (2021), arXiv:2103.01183 [astro-ph.CO]

    Pith/arXiv arXiv 2021

  10. [10]

    Hu and F.-Y

    J.-P. Hu and F.-Y. Wang, Hubble Tension: The Evidence of New Physics, Universe9, 94 (2023), arXiv:2302.05709 [astro-ph.CO]

    Pith/arXiv arXiv 2023

  11. [11]

    Di Valentinoet al.(CosmoVerse Network), The Cos- moVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics, Phys

    E. Di Valentinoet al.(CosmoVerse Network), The Cos- moVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics, Phys. Dark Univ.49, 101965 (2025), arXiv:2504.01669 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  12. [12]

    Cai and S.-J

    R.-G. Cai and S.-J. Wang, The Hubble tension: A decade review (2026) arXiv:2606.20434 [astro-ph.CO]

    Pith/arXiv arXiv 2026

  13. [13]

    J. P. Hu, Y. Y. Wang, J. Hu, and F. Y. Wang, Testing the cosmological principle with the Pantheon+ sample and the region-fitting method, Astron. Astrophys.681, A88 (2024), arXiv:2310.11727 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  14. [14]

    A. G. Riess, The Expansion of the Universe is Faster than Expected, Nature Rev. Phys.2, 10 (2019), arXiv:2001.03624 [astro-ph.CO]

    Pith/arXiv arXiv 2019

  15. [15]

    Verde, T

    L. Verde, T. Treu, and A. G. Riess, Tensions between the Early and the Late Universe, Nature Astron.3, 891 16 (2019), arXiv:1907.10625 [astro-ph.CO]

    Pith/arXiv arXiv 2019

  16. [16]

    A. G. Riesset al., JWST Validates HST Distance Meas- urements: Selection of Supernova Subsample Explains Differences in JWST Estimates of Local H 0, Astrophys. J.977, 120 (2024), arXiv:2408.11770 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  17. [17]

    A. G. Riesset al., The Perfect Host: JWST Cepheid Observations in a Background-free Type Ia Supernova Host Confirm No Bias in Hubble-constant Measurements, Astrophys. J. Lett.992, L34 (2025), arXiv:2509.01667 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  18. [18]

    Pantos and L

    I. Pantos and L. Perivolaropoulos, Dissecting the Hubble tension: Insights from a diverse set of Sound Horizon- free H0 measurements, arXiv preprint arXiv:2601.00650 (2026), arXiv:2601.00650 [astro-ph.CO]

    arXiv 2026

  19. [19]

    Knox and M

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

    Pith/arXiv arXiv 2020

  20. [20]

    Poulin, T

    V. Poulin, T. L. Smith, T. Karwal, and M. Kami- onkowski, Early Dark Energy Can Resolve The Hubble Tension, Phys. Rev. Lett.122, 221301 (2019), arXiv:1811.04083 [astro-ph.CO]

    Pith/arXiv arXiv 2019

  21. [21]

    E. Abdallaet al., Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies, JHEAp 34, 49 (2022), arXiv:2203.06142 [astro-ph.CO]

    Pith/arXiv arXiv 2022

  22. [22]

    E. J. Copeland, A. Moss, S. Sevillano Mu˜ noz, and J. M. M. White, Scaling solutions as Early Dark En- ergy resolutions to the Hubble tension, JCAP05, 078, arXiv:2309.15295 [astro-ph.CO]

    Pith/arXiv arXiv

  23. [23]

    S. A. Hosseini Mansoori and H. Moshafi, Alleviating H 0 and S 8 Tensions Simultaneously in K-essence Cosmology, Astrophys. J.975, 275 (2024), arXiv:2405.05843 [astro- ph.CO]

    Pith/arXiv arXiv 2024

  24. [24]

    Hussain, S

    S. Hussain, S. Nelleri, and K. Bhattacharya, Compre- hensive study of k-essence model: dynamical system analysis and observational constraints from latest Type Ia supernova and BAO observations, JCAP03, 025, arXiv:2406.07179 [astro-ph.CO]

    Pith/arXiv arXiv

  25. [25]

    Doran and G

    M. Doran and G. Robbers, Early dark energy cosmolo- gies, JCAP06, 026, arXiv:astro-ph/0601544

    Pith/arXiv arXiv

  26. [26]

    Niedermann and M

    F. Niedermann and M. S. Sloth, New early dark energy, Phys. Rev. D103, L041303 (2021), arXiv:1910.10739 [astro-ph.CO]

    Pith/arXiv arXiv 2021

  27. [27]

    Agrawal, F.-Y

    P. Agrawal, F.-Y. Cyr-Racine, D. Pinner, and L. Ran- dall, Rock ‘n’ roll solutions to the Hubble tension, Phys. Dark Univ.42, 101347 (2023), arXiv:1904.01016 [astro- ph.CO]

    Pith/arXiv arXiv 2023

  28. [28]

    J. C. Hill, E. McDonough, M. W. Toomey, and S. Al- exander, Early dark energy does not restore cosmolo- gical concordance, Phys. Rev. D102, 043507 (2020), arXiv:2003.07355 [astro-ph.CO]

    Pith/arXiv arXiv 2020

  29. [29]

    W. Yang, S. Pan, E. Di Valentino, R. C. Nunes, S. Vagnozzi, and D. F. Mota, Tale of stable interacting dark energy, observational signatures, and theH 0 ten- sion, JCAP09, 019, arXiv:1805.08252 [astro-ph.CO]

    Pith/arXiv arXiv

  30. [30]

    Bhattacharyya, U

    A. Bhattacharyya, U. Alam, K. L. Pandey, S. Das, and S. Pal, AreH 0 andσ 8 tensions generic to present cosmological data?, Astrophys. J.876, 143 (2019), arXiv:1805.04716 [astro-ph.CO]

    Pith/arXiv arXiv 2019

  31. [31]

    Kumar, R

    S. Kumar, R. C. Nunes, and S. K. Yadav, Dark sec- tor interaction: a remedy of the tensions between CMB and LSS data, Eur. Phys. J. C79, 576 (2019), arXiv:1903.04865 [astro-ph.CO]

    Pith/arXiv arXiv 2019

  32. [32]

    Di Valentino, A

    E. Di Valentino, A. Melchiorri, O. Mena, and S. Vagnozzi, Nonminimal dark sector physics and cos- mological tensions, Phys. Rev. D101, 063502 (2020), arXiv:1910.09853 [astro-ph.CO]

    Pith/arXiv arXiv 2020

  33. [33]

    R. C. Nunes, Structure formation inf(T) gravity and a solution forH 0 tension, JCAP05, 052, arXiv:1802.02281 [gr-qc]

    Pith/arXiv arXiv

  34. [34]

    Escamilla-Rivera and J

    C. Escamilla-Rivera and J. Levi Said, Cosmological viable models inf(T, B) theory as solutions to the H0 tension, Class. Quant. Grav.37, 165002 (2020), arXiv:1909.10328 [gr-qc]

    Pith/arXiv arXiv 2020

  35. [35]

    S. D. Odintsov, D. S´ aez-Chill´ on G´ omez, and G. S. Sharov, Analyzing theH 0 tension inF(R) gravity mod- els, Nucl. Phys. B966, 115377 (2021), arXiv:2011.03957 [gr-qc]

    Pith/arXiv arXiv 2021

  36. [36]

    Braglia, M

    M. Braglia, M. Ballardini, F. Finelli, and K. Koyama, Early modified gravity in light of theH 0 tension and LSS data, Phys. Rev. D103, 043528 (2021), arXiv:2011.12934 [astro-ph.CO]

    Pith/arXiv arXiv 2021

  37. [37]

    Shimon, Possible resolution of the Hubble ten- sion with Weyl invariant gravity, JCAP04(04), 048, arXiv:2012.10879 [astro-ph.CO]

    M. Shimon, Possible resolution of the Hubble ten- sion with Weyl invariant gravity, JCAP04(04), 048, arXiv:2012.10879 [astro-ph.CO]

    Pith/arXiv arXiv 2012

  38. [38]

    M. R. Gangopadhyay, S. K. J. Pacif, M. Sami, and M. K. Sharma, Generic Modification of Gravity, Late Time Ac- celeration and Hubble Tension, Universe9, 83 (2023), arXiv:2211.12041 [gr-qc]

    Pith/arXiv arXiv 2023

  39. [39]

    Mandal, O

    S. Mandal, O. Sokoliuk, S. S. Mishra, and P. K. Sahoo, H0 tension in torsion-based modified gravity, Nucl. Phys. B993, 116285 (2023), arXiv:2301.06328 [astro-ph.CO]

    Pith/arXiv arXiv 2023

  40. [40]

    Petronikolou and E

    M. Petronikolou and E. N. Saridakis, Alleviating the H 0 Tension in Scalar–Tensor and Bi-Scalar–Tensor Theories, Universe9, 397 (2023), arXiv:2308.16044 [gr-qc]

    Pith/arXiv arXiv 2023

  41. [41]

    N. S. Kavya, S. Swagat Mishra, and P. K. Sahoo, f(Q) gravity as a possible resolution of the H0 and S8 tensions with DESI DR2, Sci. Rep.15, 36504 (2025)

    2025

  42. [42]

    Verma, A

    S. Verma, A. Dixit, A. Pradhan, and M. S. Barak, Testing f(T) gravity with cosmological observations: Confront- ing the Hubble tension and implications for the late-time universe, JHEAp49, 100440 (2026), arXiv:2508.20107 [astro-ph.CO]

    Pith/arXiv arXiv 2026

  43. [43]

    Li and A

    X. Li and A. Shafieloo, A Simple Phenomenolo- gical Emergent Dark Energy Model can Resolve the Hubble Tension, Astrophys. J. Lett.883, L3 (2019), arXiv:1906.08275 [astro-ph.CO]

    Pith/arXiv arXiv 2019

  44. [44]

    Di Valentino, A

    E. Di Valentino, A. Mukherjee, and A. A. Sen, Dark En- ergy with Phantom Crossing and theH 0 Tension, En- tropy23, 404 (2021), arXiv:2005.12587 [astro-ph.CO]

    Pith/arXiv arXiv 2021

  45. [45]

    W. Yang, E. Di Valentino, S. Pan, A. Shafieloo, and X. Li, Generalized emergent dark energy model and the Hubble constant tension, Phys. Rev. D104, 063521 (2021), arXiv:2103.03815 [astro-ph.CO]

    Pith/arXiv arXiv 2021

  46. [46]

    Adi, Lowering the Horizon on Dark Energy: A Late-Time Response to Early Solutions for the Hubble Tension, arXiv preprint arXiv:2509.12331 (2025), arXiv:2509.12331 [astro-ph.CO]

    T. Adi, Lowering the Horizon on Dark Energy: A Late-Time Response to Early Solutions for the Hubble Tension, arXiv preprint arXiv:2509.12331 (2025), arXiv:2509.12331 [astro-ph.CO]

    arXiv 2025

  47. [47]

    Zhang, T

    Z. Zhang, T. Xu, and Y. Chen, Dynamical Dark Energy and the Unresolved Hubble Tension: Multi-model Con- straints from DESI 2025 and Other Probes, arXiv pre- print arXiv:2512.07281 (2025), arXiv:2512.07281 [astro- ph.CO]

    Pith/arXiv arXiv 2025

  48. [48]

    K.-F. Lyu, E. Stamou, and L.-T. Wang, Self-interacting neutrinos: Solution to Hubble tension versus experi- mental constraints, Phys. Rev. D103, 015004 (2021), arXiv:2004.10868 [hep-ph]

    Pith/arXiv arXiv 2021

  49. [49]

    Di Valentino, S

    E. Di Valentino, S. Gariazzo, C. Giunti, O. Mena, S. Pan, 17 and W. Yang, Minimal dark energy: Key to sterile neut- rino and Hubble constant tensions?, Phys. Rev. D105, 103511 (2022), arXiv:2110.03990 [astro-ph.CO]

    Pith/arXiv arXiv 2022

  50. [50]

    Yarahmadi, A

    M. Yarahmadi, A. Salehi, and A. Tohidi, Coupled non- canonical scalar field to neutrinos could alleviate the Hubble tension and cross the phantom barrier, Commun. Theor. Phys.78, 035402 (2026), arXiv:2509.22306 [astro- ph.CO]

    arXiv 2026

  51. [51]

    Armendariz-Picon, T

    C. Armendariz-Picon, T. Damour, and V. F. Mukhanov, k-inflation, Phys. Lett. B458, 209 (1999), arXiv:hep- th/9904075

    arXiv 1999

  52. [52]

    Armendariz-Picon, V

    C. Armendariz-Picon, V. F. Mukhanov, and P. J. Stein- hardt, A Dynamical solution to the problem of a small cosmological constant and late time cosmic accelera- tion, Phys. Rev. Lett.85, 4438 (2000), arXiv:astro- ph/0004134

    arXiv 2000

  53. [53]

    Chiba, T

    T. Chiba, T. Okabe, and M. Yamaguchi, Kinetically driven quintessence, Phys. Rev. D62, 023511 (2000), arXiv:astro-ph/9912463

    Pith/arXiv arXiv 2000

  54. [54]

    Armendariz-Picon, V

    C. Armendariz-Picon, V. F. Mukhanov, and P. J. Stein- hardt, Essentials of k essence, Phys. Rev. D63, 103510 (2001), arXiv:astro-ph/0006373

    Pith/arXiv arXiv 2001

  55. [55]

    Piazza and S

    F. Piazza and S. Tsujikawa, Dilatonic ghost condensate as dark energy, JCAP07, 004, arXiv:hep-th/0405054

    Pith/arXiv arXiv

  56. [56]

    Amendola and S

    L. Amendola and S. Tsujikawa,Dark Energy: Theory and Observations(Cambridge University Press, 2010)

    2010

  57. [57]

    Duniya, I

    D. Duniya, I. Opio, B. Mongwane, and H. Ab- dalla, Relativistic effects in k-essence, arXiv pre- print arXiv:2604.20989 (2026), arXiv:2604.20989 [astro- ph.CO]

    Pith/arXiv arXiv 2026

  58. [58]

    J. S. Bagla, H. K. Jassal, and T. Padmanabhan, Cosmo- logy with tachyon field as dark energy, Phys. Rev. D67, 063504 (2003), arXiv:astro-ph/0212198

    Pith/arXiv arXiv 2003

  59. [59]

    L. P. Chimento, Extended tachyon field, Chaplygin gas and solvable k-essence cosmologies, Phys. Rev. D69, 123517 (2004), arXiv:astro-ph/0311613

    Pith/arXiv arXiv 2004

  60. [60]

    P. J. E. Peebles and B. Ratra, Cosmology with a Time Variable Cosmological Constant, Astrophys. J. Lett.325, L17 (1988)

    1988

  61. [61]

    Brax and J

    P. Brax and J. Martin, Quintessence and supergravity, Phys. Lett. B468, 40 (1999), arXiv:astro-ph/9905040

    Pith/arXiv arXiv 1999

  62. [62]

    Barreiro, E

    T. Barreiro, E. J. Copeland, and N. J. Nunes, Quint- essence arising from exponential potentials, Phys. Rev. D61, 127301 (2000), arXiv:astro-ph/9910214

    Pith/arXiv arXiv 2000

  63. [63]

    Tsujikawa, Quintessence: A Review, Class

    S. Tsujikawa, Quintessence: A Review, Class. Quant. Grav.30, 214003 (2013), arXiv:1304.1961 [gr-qc]

    Pith/arXiv arXiv 2013

  64. [64]

    Chen, Q.-G

    L. Chen, Q.-G. Huang, and K. Wang, Distance Priors from Planck Final Release, JCAP02, 028, arXiv:1808.05724 [astro-ph.CO]

    Pith/arXiv arXiv

  65. [65]

    Scolnicet al., The Pantheon+ Analysis: The Full Data Set and Light-curve Release, Astrophys

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

    Pith/arXiv arXiv 2022

  66. [66]

    Broutet al., The Pantheon+ Analysis: Cosmo- logical Constraints, Astrophys

    D. Broutet al., The Pantheon+ Analysis: Cosmo- logical Constraints, Astrophys. J.938, 110 (2022), arXiv:2202.04077 [astro-ph.CO]

    Pith/arXiv arXiv 2022

  67. [67]

    com/PantheonPlusSH0ES/DataRelease

    PantheonPlusSH0ES Data Release,https://github. com/PantheonPlusSH0ES/DataRelease

  68. [68]

    Rubinet al., Union Through UNITY: Cosmology with 2,000 SNe Using a Unified Bayesian Framework, Astrophys

    D. Rubinet al., Union Through UNITY: Cosmology with 2,000 SNe Using a Unified Bayesian Framework, Astrophys. J.986, 231 (2025), arXiv:2311.12098 [astro- ph.CO]

    Pith/arXiv arXiv 2025

  69. [69]

    T. M. C. Abbottet al.(DES), The Dark Energy Survey: Cosmology Results with∼1500 New High-redshift Type Ia Supernovae Using the Full 5 yr Data Set, Astrophys. J. Lett.973, L14 (2024), arXiv:2401.02929 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  70. [70]

    Perivolaropoulos and F

    L. Perivolaropoulos and F. Skara, On the homogeneity of SnIa absolute magnitude in the Pantheon+ sample, Mon. Not. Roy. Astron. Soc.520, 5110 (2023), arXiv:2301.01024 [astro-ph.CO]

    Pith/arXiv arXiv 2023

  71. [71]

    Zhai and Y

    Z. Zhai and Y. Wang, Robust and model-independent cosmological constraints from distance measurements, JCAP07, 005, arXiv:1811.07425 [astro-ph.CO]

    Pith/arXiv arXiv

  72. [72]

    Y. Yang, Y. Wang, and X. Dai, Cosmological constraints on two vacuum decay models, Eur. Phys. J. C85, 224 (2025), arXiv:2502.17792 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  73. [73]

    Yang, Constraining deviations fromΛCDM in the Hubble expansion rate, Eur

    Y. Yang, Constraining deviations fromΛCDM in the Hubble expansion rate, Eur. Phys. J. C85, 1350 (2025), arXiv:2508.17848 [astro-ph.CO]

    arXiv 2025

  74. [74]

    Wang and S

    Y. Wang and S. Wang, Distance Priors from Planck and Dark Energy Constraints from Current Data, Phys. Rev. D88, 043522 (2013), [Erratum: Phys.Rev.D 88, 069903 (2013)], arXiv:1304.4514 [astro-ph.CO]

    Pith/arXiv arXiv 2013

  75. [75]

    Cai, Z.-K

    R.-G. Cai, Z.-K. Guo, and B. Tang, Updated reduced CMB data and constraints on cosmological parameters, Int. J. Mod. Phys. D24, 1550071 (2015), arXiv:1409.0223 [astro-ph.CO]

    Pith/arXiv arXiv 2015

  76. [76]

    Hu and N

    W. Hu and N. Sugiyama, Small scale cosmological per- turbations: An Analytic approach, Astrophys. J.471, 542 (1996), arXiv:astro-ph/9510117

    Pith/arXiv arXiv 1996

  77. [77]

    A. G. Adameet al.(DESI), DESI 2024 VI: cosmolo- gical constraints from the measurements of baryon acous- tic oscillations, JCAP02, 021, arXiv:2404.03002 [astro- ph.CO]

    Pith/arXiv arXiv 2024

  78. [78]

    Abdul Karimet al.(DESI), DESI DR2 results

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

    Pith/arXiv arXiv 2025

  79. [79]

    D. J. Eisenstein and W. Hu, Baryonic features in the matter transfer function, Astrophys. J.496, 605 (1998), arXiv:astro-ph/9709112

    Pith/arXiv arXiv 1998

  80. [80]

    H. Yu, B. Ratra, and F.-Y. Wang, Hubble Parameter and Baryon Acoustic Oscillation Measurement Constraints on the Hubble Constant, the Deviation from the Spa- tially Flat ΛCDM Model, the Deceleration–Acceleration Transition Redshift, and Spatial Curvature, Astrophys. J.856, 3 (2018), arXiv:1711.03437 [astro-ph.CO]

    Pith/arXiv arXiv 2018

Showing first 80 references.