Pith. sign in

REVIEW 4 major objections 5 minor 5 cited by

Data rule out early non-phantom scaling as a fix for the Hubble tension.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-03 14:32 UTC pith:MSCIFUUM

load-bearing objection Useful λ2 bounds on early scaling dark energy, but the paper overreads them: without a direct Ωφ(zeq) posterior, the blanket no-EDE conclusion isn't established. the 4 major comments →

arxiv 2512.19888 v2 pith:MSCIFUUM submitted 2025-12-22 astro-ph.CO gr-qc

Observational constraints on early time non-phantom behaviour of dynamical dark energy

Sk. Sohail , Sonej Alam , Md. Wali Hossain This is my paper
classification astro-ph.CO gr-qc
keywords dark energyquintessenceearly dark energyHubble tensionscaling solutionsCPL parametrizationcosmological parameter constraintsphantom behaviour
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.

This paper asks whether dark energy could have been non-phantom — with an equation of state above −1 — in the early universe, as in scaling and tracker-type quintessence models, and still fit current cosmological observations. Analysing CMB distance priors, baryon acoustic oscillations, supernovae, Hubble-parameter measurements and growth-rate data, the authors find that the exponential potential responsible for early scaling must be extremely steep, with steepness λ2 greater than roughly 20–30. At such steepness, the scaling solution keeps the dark-energy fraction below one percent around matter–radiation equality, far too small to alter the expansion history. The paper concludes that early-time non-phantom scaling cannot alleviate the Hubble tension and is disfavoured by model selection, while late-time dynamics like the CPL parametrisation retain a mild (~2σ) preference for evolution away from w = −1.

Core claim

The central claim, stated on the paper's own terms, is that the data force the early-time scaling sector to be inert. For the three models that combine a steep exponential potential with late-time acceleration — scaling-plus-thawing, scaling-plus-Λ, scaling-plus-wCDM — the steepness parameter satisfies λ2 > 30 at 1σ; for the scaling-plus-CPL variant the bound is λ2 > 20. Because an exponential potential's scaling solution has Ωφ = 4/λ2² in radiation domination and 3/λ2² in matter domination, these bounds place the early dark-energy density below one percent at matter–radiation equality. The paper extends the same reasoning to tracker-type dynamics, arguing that they closely resemble scaling

What carries the argument

The central object is the double-exponential potential V(ϕ) = V1 e^{−λ1ϕ/MPl} + V2 e^{−λ2ϕ/MPl} with V2 > V1 and λ2 > λ1 > 0. The steeper exponential term drives a scaling attractor at early times, while the shallower term (or, in the fluid variants, a constant or CPL dark-energy component) supplies late-time acceleration. The load-bearing identity is the scaling solution Ωφ = 3(1+w_b)/λ2² (so 4/λ2² during radiation, 3/λ2² during matter), which converts the fitted lower bound on λ2 into an upper bound on the early dark-energy fraction. The paper also uses the pair {λ(ϕ), Γ(ϕ)} to classify thawing, scaling and tracker phases, with Γ = 1 for exponential potentials.

Load-bearing premise

The translation of the fitted λ2 lower bound into a statement about early dark-energy density assumes the field sits exactly on the exponential scaling attractor, with Ωφ ≈ 3/λ2²–4/λ2², during radiation and matter domination; off-attractor or non-exponential early evolution could evade the bound.

What would settle it

A measurement that pins the dark-energy density at z ≳ 1000 to values above roughly 1.5% of the critical density — for example from the CMB damping tail or primordial helium abundance — would contradict the paper's λ2 ≳ 20 bound for an exponential scaling field. Alternatively, a fit to the same data that returned λ2 < 10 would directly falsify the claim that early non-phantom scaling is excluded.

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

If this is right

  • If λ2 is indeed ≳20–30, any exponential-potential early scaling solution must keep dark energy below roughly one percent of the critical density at matter–radiation equality, so the early component is cosmologically inert.
  • Early-time scaling models within the canonical scalar-field class cannot be used to raise H0; resolving the Hubble tension would require phantom fields, more general tracker potentials with time-varying λ, or additional physics beyond a single canonical scalar field.
  • The mild (~2σ) preference for CPL-style late-time evolution survives the addition of early-time scaling, but the early component itself is not preferred by the combined data.
  • Model-selection criteria (AIC and BIC) penalise the added complexity of early scaling, so within this model class the combined-data best fit remains close to ΛCDM with at most mild late-time evolution.
  • The constraints on the standard background parameters (Ωm0, h, ωb, rdh, σ8) are stable across all models, meaning early-time non-phantom dynamics do not alter the late-time expansion history.

Where Pith is reading between the lines

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

  • Because the scaling-attractor identity Ωφ ≈ 3/λ2²–4/λ2² is what converts the λ2 bound into a statement about early dark energy, a model that starts off the attractor — e.g., with kinetic domination or a frozen phase ending closer to equality — could in principle hold a transient early component without violating the bound. The paper's own Fig. 1 shows such phases before the scaling regime, so this
  • The SC+w and SC+CPL variants add a background fluid that is not derived from a scalar-field action; the λ2 > 20 bound in those cases is therefore a constraint on a hybrid model. A fully covariant two-field realisation might evade the bound, so the exclusion of 'effective fluid extensions' is narrower than it appears.
  • The argument that trackers inherit the bound assumes trackers behave like scaling solutions at matter–radiation equality; potentials with Γ > 1 that make λ decay slowly could produce a larger early component while still satisfying the late-time constraints, so the paper's tracker exclusion is an extrapolation, not a direct fit.
  • One direct test the paper leaves implicit: if early dark energy were exactly at the percent level around equality, it would show up in CMB damping and lensing as a slight change in the sound horizon. Re-fitting the same data with a free early-dark-energy density that is not tied to the scaling identity would isolate the assumption being tested.

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 / 5 minor

Summary. The paper studies dark-energy models that allow non-phantom behavior at early times: thawing, scaling+thawing, scaling+ΛCDM, scaling+wCDM, and scaling+CPL. It constrains these models with Planck CMB distance priors, DESI DR2 BAO, Pantheon+ SNe, H(z), and RSD data using MCMC, and reports background parameters, dark-energy parameters, and model-selection criteria. The central claims are that late-time background parameters are stable across models; CPL-like dynamics mildly prefer phantom evolution; and early-time exponential scaling is strongly constrained, with λ2 ≳ 20–30, implying Ωφ < 1% at matter–radiation equality, so that this class of early dark energy cannot alleviate the Hubble tension.

Significance. If correct, the λ2 lower bounds would constitute a useful no-go result for simple exponential scaling/early-dark-energy resolutions of the Hubble tension. The paper uses a standard, reproducible MCMC pipeline (emcee+GetDist) and a current combination of cosmological data, which is a strength. However, the key inference from the fitted λ2 to Ωφ at equality relies on an attractor relation that is not directly verified with the chains, and the effective fluid models are not pure scalar-field potentials. The late-time CPL preference is also only demonstrated for the SC+CPL hybrid, not for CPL alone.

major comments (4)
  1. [Sec. VI, Table I] The central conclusion 'λ2>20–30 forces Ωφ<1% at matter–radiation equality' uses the exponential attractor relations 4/λ2^2 and 3/λ2^2 [90]. But the constrained models are double exponentials (Eq. 5) or hybrid constructions (Eqs. 16–20), and Fig. 1 explicitly shows frozen (CC-like) and kinetic-dominated phases before the scaling regime. In those phases Ωφ is not given by the attractor formula and depends on initial φ, dφ/dN, and V2. The manuscript never reports the initial conditions used in the MCMC integration, nor the posterior distribution of Ωφ(z_eq) computed from the full background equations. The one-sentence extension to 'tracker dynamics' is also unsupported. Please add direct constraints on Ωφ(z_eq) from the chains and state/justify the initial conditions.
  2. [Abstract, Sec. III.E/VI] The abstract and conclusions state that time-dependent parametrizations such as CPL show a ~2σ preference for phantom evolution. However, no standalone CPL or wCDM model is fitted; only SC+CPL is analyzed. The preference therefore cannot be attributed to the CPL parametrization in general. In addition, the SC+CPL values are inconsistent: Table I gives w0=-0.864±0.060, wa=-0.61±0.23, while Sec. VI states w0=-0.873±0.069, wa=-0.62±0.32. This needs to be reconciled and the claim restricted to the fitted hybrid model.
  3. [Sec. II, Eq. (8)] The discussion of the 'frozen' phase appears to invert the standard criterion. Eq. (8) defines m_phi^2 ≡ V'' > H^2 and the text says the field remains frozen when m_phi exceeds H, with Hubble friction weakening when m_phi ~ H. For a canonical scalar, strong Hubble damping and freezing occur when m_phi^2 << H^2; m_phi^2 >> H^2 leads to rapid field oscillations. This affects the interpretation of the early-time transient shown in Fig. 1 and should be corrected.
  4. [Sec. III.D, III.E, Eqs. (16)-(20)] The objects V_w(a) and V_CPL(a) are called potentials, but they are functions of scale factor, not of φ, so they do not enter V'(φ) in the Klein-Gordon equation (1). If these terms are intended as additional dark-energy fluids, the field equations and the two-fluid conservation laws should be stated explicitly. This matters for the scaling-attractor mapping: the presence of an additional early-time fluid with w(a)≠1/3 or w(a)≠0 modifies the effective background and the scalar-field attractor relation used in Sec. VI.
minor comments (5)
  1. [Table I] The σ8 entry for SC+TH appears as 0.75±0.29; this is likely a typo for 0.750±0.029. Please check all table entries for missing leading zeros.
  2. [Sec. II, Eq. (8)] The sentence 'm_phi exceeds the Hubble scale, H(t)' is dimensionally inconsistent with Eq. (8) (m_phi^2 compared to H^2); rephrase for clarity even after correcting the inequality direction.
  3. [Table I/V] The λ2 limits are reported as '>30' and '>20' at the 1σ level. Since the priors for SC+Λ and SC+w are [0,50], it should be stated explicitly whether these are one-sided credible limits and whether the upper prior boundary affects the marginalized posterior.
  4. [Fig. 1 and Sec. II] The labels 'CC like', 'Scaling', 'Thawing like' and the narrative in the bullet list are difficult to follow, especially regarding the order of kinetic, frozen, and scaling phases. A clearer schematic or a description with explicit initial conditions would help.
  5. [Model naming] The model is called both SC+Λ and SC+ΛCDM at different points; unify the notation for consistency.

Circularity Check

0 steps flagged

No constructional circularity: the λ2 constraints are MCMC fits to external data and the Ωφ conversion uses an external parameter-free attractor result; self-citations are background and non-load-bearing.

full rationale

The central derivation chain is: (1) define canonical scalar field models with steep exponential / double-exponential potentials, (2) fit λ2 to CMB distance priors + DESI BAO + PantheonPlus + H(z) + RSD via MCMC, obtaining lower bounds λ2 > 20–30, and (3) convert this into Ωφ < 0.01 at matter–radiation equality using the standard scaling-attractor relation Ωφ ≈ 4/λ2^2 (radiation) and 3/λ2^2 (matter), citing ref. [90] (Copeland, Liddle, Wands), which is external and parameter-free. No target quantity is defined through a fitted parameter: λ2 is a potential slope fitted to data, and Ωφ is a derived parameter computed from an independent dynamical-systems result. The paper also reports standard model-selection penalties, which are independent of the Ωφ conversion. The self-citations present (refs. 40, 57, 58, 100) support background model classification and the double-exponential framework, but the double-exponential construction is anchored to external refs. [104] and [90]; none of these self-citations is doing the load-bearing work of the central claim. A robustness caveat: the paper assumes the field sits on the scaling attractor around z_eq, while its own Fig. 1 shows frozen and kinetic-dominated phases before the scaling regime, and the extension to 'tracker dynamics' in Sec. VI is asserted rather than derived. That is a correctness/over-claim concern, not a circular reduction: the paper does not fit Ωφ and then rename it, nor does it smuggle the attractor formula in via self-citation. The score of 2 reflects only the presence of minor, non-load-bearing self-citations, not any constructional circularity.

Axiom & Free-Parameter Ledger

6 free parameters · 5 axioms · 0 invented entities

No new entities or forces are introduced; all parameters are fitted to existing data or fixed by flatness. The main burden is the mapping from fitted λ2 to early dark-energy fraction via the scaling-attractor relation, and the hybrid fluid-in-potential construction in SC+w/SC+CPL.

free parameters (6)
  • λ2 (early scaling steepness) = >20–30 (1σ lower bound, model-dependent)
    Central fitted parameter; lower bound directly drives the early-DE fraction claim.
  • λ1 (thawing steepness) = <0.8 (1σ, Thaw model)
    Constrains late-time thawing; less central to the main claim.
  • w0 (SC+CPL present EoS) = -0.864 ± 0.060 (Table I) / -0.873 ± 0.069 (Sec. VI)
    Drives the claimed ~2σ late-time deviation; values are inconsistent between Table I and the text.
  • wa (SC+CPL EoS evolution) = -0.61 ± 0.23 (Table I) / -0.62 ± 0.32 (Sec. VI)
    Drives the claimed ~2σ late-time deviation; values are inconsistent between Table I and the text.
  • V1 (thawing potential amplitude) = unconstrained
    Treated as free in MCMC but largely fixed by flatness rescaling; poorly constrained by data.
  • log10 V2 (scaling potential amplitude) = unconstrained
    Flatness fixes the overall scale; log-amplitude is not constrained by data.
axioms (5)
  • standard math Flat FLRW universe with a canonical scalar field obeying the Klein–Gordon equation (Eq. 1).
    Starting framework for all models in Section II.
  • domain assumption Exponential-potential scaling attractor with energy fraction Ωφ ≈ 4/λ2^2 in radiation and 3/λ2^2 in matter (Copeland et al. 1998).
    Used in Section VI to turn the λ2>20 bound into Ωφ<0.01 at matter–radiation equality; requires the field to be on the attractor.
  • domain assumption Double-exponential potential with V2>V1, λ2>λ1 gives early scaling followed by late thawing (Eqs. 5–7, Fig. 1).
    Model-building assumption from refs [104–107].
  • domain assumption Tracker dynamics resemble scaling solutions with mild deviations, so scaling bounds are extended to trackers.
    Stated in Section VI; no explicit tracker potential is integrated.
  • ad hoc to paper For SC+w and SC+CPL, the late-time component can be represented as a scale-factor-dependent term V_w(a) or V_CPL(a) added to the scalar-field potential (Eqs. 16–20).
    This is not derived from a scalar-field Lagrangian; the potential becomes explicitly a-dependent, so Eq. (1) is not the full combined dynamics.

pith-pipeline@v1.3.0-alltime-deepseek · 15756 in / 18079 out tokens · 173514 ms · 2026-08-03T14:32:45.932366+00:00 · methodology

0 comments
read the original abstract

We investigate dynamical dark energy models that admit non-phantom behaviour at early times, including thawing, scaling--thawing, and effective fluid extensions. Using current cosmological observations, we find that late-time background parameters remain stable across all models. Time-dependent parametrizations such as CPL show a $\sim2\sigma$ preference for phantom evolution at low redshift. Imposing non-phantom scaling dynamics at early times leads to strong lower bounds on the potential steepness, $\lambda \gtrsim 20$--$30$, constraining the early dark energy density to below the percent level at matter--radiation equality. Consequently, early scaling behaviour does not alleviate the Hubble tension and is penalised by Bayesian model selection. Our results indicate that while late-time dynamics can mildly improve the fit, early non-phantom scaling is strongly disfavoured by current data.

Figures

Figures reproduced from arXiv: 2512.19888 by Md. Wali Hossain, Sk. Sohail, Sonej Alam.

Figure 1
Figure 1. Figure 1: FIG. 1. Evolution of the energy densities of matter (long-dashed green), radiation (short-dashed red), and the scalar field (solid [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The 1 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

discussion (0)

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

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Exploring the interplay of late-time dynamical dark energy and new physics before recombination

    astro-ph.CO 2026-03 conditional novelty 5.5

    Under standard recombination, phantom-crossing dynamical dark energy is preferred at ~97–98.5% probability; early-time fixes to the Hubble tension erase that preference while creating severe ω_m tension with CMB.

  2. Exploring the interplay of late-time dynamical dark energy and new physics before recombination

    astro-ph.CO 2026-03 unverdicted novelty 5.0

    Model-independent reconstruction finds 96.7-98.5% probability of phantom crossing if recombination is standard, but early new physics to ease Hubble tension weakens this preference while requiring unrealistically high...

  3. Joint Constraints on Neutrinos and Dynamical Dark Energy in Minimally Modified Gravity

    astro-ph.CO 2026-01 unverdicted novelty 5.0

    The w†VCDM model shows a statistically significant preference for late-time quintessence-phantom crossing dark energy, raises the Hubble constant, and satisfies neutrino mass and Neff constraints from current cosmolog...

  4. Probing late-time deviations from $\Lambda$CDM with a quadratic dark energy expansion

    astro-ph.CO 2026-05 unverdicted novelty 4.0

    The QDEE model fits combined cosmological datasets better than Lambda CDM, shifts the Hubble constant higher, and shows strong Bayesian evidence in its favor.

  5. Dissipative Cosmology and the Nature of Dark Energy: Insights from Bulk Viscosity with DESI DR2 observations

    astro-ph.CO 2026-06 unverdicted novelty 3.0

    Bulk viscous fluid models for dark energy yield improved fits to supernova, BAO, and CMB data over LambdaCDM, especially in the interacting non-minimal case.

Reference graph

Works this paper leans on

117 extracted references · 86 linked inside Pith · cited by 4 Pith papers

  1. [1]

    Scaling+Thawing

    Imposing flatness condition and FixingV 1 in numerical code Numerically, the flatness condition is imposed atz= 0 by ensuring that the total energy density equals the critical density of the Universe, with Ω DE0 = Ω ϕ0, the present value of the scalar field density parameter: Ωm0 + Ωr0 + Ωϕ0 = 1.(11) The scalar field energy density parameter Ω ϕ(z) is giv...

    2018

  2. [2]

    This demonstrates that the early dark energy fraction is tightly constrained to be very small for scaling-type dynamics, which therefore appear unable to alleviate theH 0 tension

    For the weakest lower bound,λ 2 >20, this implies Ω ϕ <0.01 at matter– radiation equality. This demonstrates that the early dark energy fraction is tightly constrained to be very small for scaling-type dynamics, which therefore appear unable to alleviate theH 0 tension. This argument can be extended to tracker dynamics, which closely resemble scaling solu...

    2021

  3. [3]

    prevents early scalar field 3 -2 0 2 4 6 8 -10 0 10 20 30 Log10 (1+z) Log10 (ρϕ /ρc0) ρm ρr ρϕ ρϕ~a -6 CC like CC=Cosmological Constant ScalingThawing like FIG. 1. Evolution of the energy densities of matter (long-dashed green), radiation (short-dashed red), and the scalar field (solid blue) normalised by the present critical densityρ c0 for the potential...

  4. [4]

    E. J. Copeland, M. Sami, and S. Tsujikawa, Int. J. Mod. Phys. D15, 1753 (2006), arXiv:hep-th/0603057

    Pith/arXiv arXiv 2006

  5. [5]

    Martin, Comptes Rendus Physique13, 566 (2012), arXiv:1205.3365 [astro-ph.CO]

    J. Martin, Comptes Rendus Physique13, 566 (2012), arXiv:1205.3365 [astro-ph.CO]

    Pith/arXiv arXiv 2012

  6. [6]

    Sahni and A

    V. Sahni and A. A. Starobinsky, Int. J. Mod. Phys. D 9, 373 (2000), arXiv:astro-ph/9904398

    Pith/arXiv arXiv 2000

  7. [7]

    Aghanimet al.(Planck), Astron

    N. Aghanimet al.(Planck), Astron. Astrophys.641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

    Pith/arXiv arXiv 2020

  8. [8]

    A. G. Riesset al., Astrophys. J. Lett.934, L7 (2022), arXiv:2112.04510 [astro-ph.CO]

    Pith/arXiv arXiv 2022

  9. [9]

    Perivolaropoulos and F

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

    Pith/arXiv arXiv 2022

  10. [10]

    T. M. C. Abbottet al.(Kilo-Degree Survey, Dark En- ergy Survey), Open J. Astrophys.6, 2305.17173 (2023), arXiv:2305.17173 [astro-ph.CO]

    Pith/arXiv arXiv 2023

  11. [11]

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

    Pith/arXiv arXiv

  12. [12]

    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

  13. [13]

    Guet al.(DESI), Nature Astron.9, 1879 (2025), arXiv:2504.06118 [astro-ph.CO]

    G. Guet al.(DESI), Nature Astron.9, 1879 (2025), arXiv:2504.06118 [astro-ph.CO]

    arXiv 2025

  14. [14]

    Calderonet al.(DESI), JCAP10, 048, arXiv:2405.04216 [astro-ph.CO]

    R. Calderonet al.(DESI), JCAP10, 048, arXiv:2405.04216 [astro-ph.CO]

    Pith/arXiv arXiv

  15. [15]

    Lodhaet al.(DESI), Phys

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

    Pith/arXiv arXiv 2025

  16. [16]

    Giar` e, M

    W. Giar` e, M. A. Sabogal, R. C. Nunes, and E. Di Valentino, Phys. Rev. Lett.133, 251003 (2024), arXiv:2404.15232 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  17. [17]

    K. V. Berghaus, J. A. Kable, and V. Miranda, Phys. Rev. D110, 103524 (2024), arXiv:2404.14341 [astro- ph.CO]

    Pith/arXiv arXiv 2024

  18. [18]

    W. J. Wolf, C. Garc ´ ıa-Garc ´ ıa, and P. G. Ferreira, JCAP 05, 034, arXiv:2502.04929 [astro-ph.CO]

    Pith/arXiv arXiv

  19. [19]

    D. H. Lee, W. Yang, E. Di Valentino, S. Pan, and C. van de Bruck (2025), arXiv:2507.11432 [astro- ph.CO]

    arXiv 2025

  20. [20]

    Zhong and B

    K. Zhong and B. Jain (2025), arXiv:2509.26480 [astro- ph.CO]

    arXiv 2025

  21. [21]

    Z. Yao, G. Ye, and A. Silvestri (2025), arXiv:2508.01378 [gr-qc]

    Pith/arXiv arXiv 2025

  22. [22]

    F. J. Qu, K. M. Surrao, B. Bolliet, J. C. Hill, B. D. Sherwin, H. T. Jense, and A. La Posta, Phys. Rev. D 111, 123507 (2025), arXiv:2404.16805 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  23. [23]

    Wang and Y.-S

    H. Wang and Y.-S. Piao (2024), arXiv:2404.18579 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  24. [24]

    Giar` e, M

    W. Giar` e, M. Najafi, S. Pan, E. Di Valentino, and J. T. Firouzjaee, JCAP10, 035, arXiv:2407.16689 [astro- ph.CO]

    Pith/arXiv arXiv

  25. [25]

    I. D. Gialamas, G. H¨ utsi, K. Kannike, A. Racioppi, M. Raidal, M. Vasar, and H. Veerm¨ ae, Phys. Rev. D 111, 043540 (2025), arXiv:2406.07533 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  26. [26]

    Shlivko and P

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

    Pith/arXiv arXiv 2024

  27. [27]

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

    Pith/arXiv arXiv 2025

  28. [28]

    Bhattacharya, G

    S. Bhattacharya, G. Borghetto, A. Malhotra, S. Parameswaran, G. Tasinato, and I. Zavala, JCAP 09, 073, arXiv:2405.17396 [astro-ph.CO]

    Pith/arXiv arXiv

  29. [29]

    O. F. Ramadan, J. Sakstein, and D. Rubin, Phys. Rev. D110, L041303 (2024), arXiv:2405.18747 [astro- ph.CO]

    Pith/arXiv arXiv 2024

  30. [30]

    Jiang, D

    J.-Q. Jiang, D. Pedrotti, S. S. da Costa, and S. Vagnozzi, Phys. Rev. D110, 123519 (2024), arXiv:2408.02365 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  31. [31]

    Payeur, E

    G. Payeur, E. McDonough, and R. Brandenberger, Phys. Rev. D111, 123541 (2025), arXiv:2411.13637 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  32. [32]

    Malekjani, Z

    M. Malekjani, Z. Davari, and S. Pourojaghi (DESI), Phys. Rev. D111, 083547 (2025), arXiv:2407.09767 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  33. [33]

    W. J. Wolf and P. G. Ferreira, Phys. Rev. D108, 103519 (2023), arXiv:2310.07482 [astro-ph.CO]

    Pith/arXiv arXiv 2023

  34. [34]

    W. J. Wolf, C. Garc ´ ıa-Garc ´ ıa, D. J. Bartlett, and P. G. Ferreira, Phys. Rev. D110, 083528 (2024), arXiv:2408.17318 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  35. [35]

    W. J. Wolf, P. G. Ferreira, and C. Garc ´ ıa-Garc ´ ıa, Phys. Rev. D111, L041303 (2025), arXiv:2409.17019 [astro- ph.CO]

    Pith/arXiv arXiv 2025

  36. [37]

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

    Pith/arXiv arXiv 2024

  37. [38]

    B. R. Dinda, JCAP09, 062, arXiv:2405.06618 [astro- ph.CO]

    Pith/arXiv arXiv

  38. [39]

    B. R. Dinda and R. Maartens, JCAP01, 120, arXiv:2407.17252 [astro-ph.CO]

    Pith/arXiv arXiv

  39. [40]

    Jiang, W

    J.-Q. Jiang, W. Giar` e, S. Gariazzo, M. G. Dainotti, E. Di Valentino, O. Mena, D. Pedrotti, S. S. da Costa, and S. Vagnozzi, JCAP01, 153, arXiv:2407.18047 [astro-ph.CO]

    Pith/arXiv arXiv

  40. [41]

    E. O. Colg´ ain, M. G. Dainotti, S. Capozziello, S. Pouro- jaghi, M. M. Sheikh-Jabbari, and D. Stojkovic (2024), arXiv:2404.08633 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  41. [42]

    Bhattacharya, G

    S. Bhattacharya, G. Borghetto, A. Malhotra, S. Parameswaran, G. Tasinato, and I. Zavala, JCAP 04, 086, arXiv:2410.21243 [astro-ph.CO]

    arXiv

  42. [43]

    Akthar and M

    S. Akthar and M. W. Hossain, JCAP04, 024, arXiv:2411.15892 [astro-ph.CO]

    Pith/arXiv arXiv

  43. [44]

    Park and B

    C.-G. Park and B. Ratra (2025), arXiv:2501.03480 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  44. [45]

    A. G. Ferrari, M. Ballardini, F. Finelli, and D. Paoletti, Phys. Rev. D111, 083523 (2025), arXiv:2501.15298 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  45. [46]

    Peng and Y.-S

    Z.-Y. Peng and Y.-S. Piao, Phys. Rev. D112, 023502 (2025), arXiv:2502.04641 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  46. [47]

    E. ´O. Colg´ ain and M. M. Sheikh-Jabbari, Mon. Not. Roy. Astron. Soc.542, L24 (2025), arXiv:2412.12905 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  47. [48]

    Mukherjee and A

    P. Mukherjee and A. A. Sen, Phys. Rev. D110, 123502 (2024), arXiv:2405.19178 [astro-ph.CO]

    arXiv 2024

  48. [49]

    Mukherjee, D

    P. Mukherjee, D. Kumar, and A. A. Sen (2025), arXiv:2501.18335 [astro-ph.CO]

    arXiv 2025

  49. [50]

    Mukherjee and A

    P. Mukherjee and A. A. Sen, Rept. Prog. Phys.88, 098401 (2025), arXiv:2505.19083 [astro-ph.CO]

    arXiv 2025

  50. [51]

    Berbig, JCAP03, 015, arXiv:2412.07418 [astro- ph.CO]

    M. Berbig, JCAP03, 015, arXiv:2412.07418 [astro- ph.CO]

    Pith/arXiv arXiv

  51. [52]

    Li, P.-J

    T.-N. Li, P.-J. Wu, G.-H. Du, S.-J. Jin, H.-L. Li, J.- F. Zhang, and X. Zhang, Astrophys. J.976, 1 (2024), arXiv:2407.14934 [astro-ph.CO]. 10

    Pith/arXiv arXiv 2024

  52. [53]

    Li, Y.-H

    T.-N. Li, Y.-H. Li, G.-H. Du, P.-J. Wu, L. Feng, J.-F. Zhang, and X. Zhang, Eur. Phys. J. C85, 608 (2025), arXiv:2411.08639 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  53. [54]

    Li, G.-H

    T.-N. Li, G.-H. Du, Y.-H. Li, P.-J. Wu, S.-J. Jin, J.-F. Zhang, and X. Zhang, Sci. China Phys. Mech. Astron. 69, 210413 (2026), arXiv:2501.07361 [astro-ph.CO]

    arXiv 2026

  54. [55]

    Borghetto, A

    G. Borghetto, A. Malhotra, G. Tasinato, and I. Zavala, Phys. Rev. D112, 023521 (2025), arXiv:2503.11628 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  55. [56]

    Carloni, O

    Y. Carloni, O. Luongo, and M. Muccino, Phys. Rev. D 111, 023512 (2025), arXiv:2404.12068 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  56. [57]

    T. Liu, X. Li, and J. Wang, Astrophys. J.988, 243 (2025), arXiv:2504.21373 [astro-ph.CO]

    arXiv 2025

  57. [58]

    W. J. Wolf, C. Garc ´ ıa-Garc ´ ıa, T. Anton, and P. G. Ferreira, Phys. Rev. Lett.135, 081001 (2025), arXiv:2504.07679 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  58. [59]

    Chudaykin and M

    A. Chudaykin and M. Kunz, Phys. Rev. D110, 123524 (2024), arXiv:2407.02558 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  59. [60]

    Sohail, S

    S. Sohail, S. Alam, S. Akthar, and M. W. Hossain, Phys. Dark Univ.48, 101948 (2025), arXiv:2408.03229 [astro- ph.CO]

    Pith/arXiv arXiv 2025

  60. [61]

    M. W. Hossain and A. Maqsood, Phys. Rev. D112, 083504 (2025), arXiv:2502.19274 [astro-ph.CO]

    arXiv 2025

  61. [62]

    Cheng, E

    H. Cheng, E. Di Valentino, L. A. Escamilla, A. A. Sen, and L. Visinelli, JCAP09, 031, arXiv:2505.02932 [astro- ph.CO]

    arXiv

  62. [63]

    Scherer, M

    M. Scherer, M. A. Sabogal, R. C. Nunes, and A. De Fe- lice, Phys. Rev. D112, 043513 (2025), arXiv:2504.20664 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  63. [64]

    Pedrotti, L

    D. Pedrotti, L. A. Escamilla, V. Marra, L. Perivolaropoulos, and S. Vagnozzi (2025), arXiv:2510.01974 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  64. [65]

    L. A. Escamilla, W. Giar` e, E. Di Valentino, R. C. Nunes, and S. Vagnozzi, JCAP05, 091, arXiv:2307.14802 [astro-ph.CO]

    Pith/arXiv arXiv

  65. [66]

    T. Liu, X. Li, T. Xu, M. Biesiada, and J. Wang, Eur. Phys. J. C85, 1351 (2025), arXiv:2507.04265 [astro- ph.CO]

    arXiv 2025

  66. [67]

    Z. Lu, T. Simon, and P. Zhang (2025), arXiv:2503.04602 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  67. [68]

    W. J. Wolf, P. G. Ferreira, and C. Garc ´ ıa-Garc ´ ıa (2025), arXiv:2509.17586 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  68. [69]

    J. M. Cline and V. Muralidharan, Phys. Rev. D112, 063539 (2025), arXiv:2506.13047 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  69. [70]

    Wang and Y.-S

    H. Wang and Y.-S. Piao, Phys. Rev. D112, 083553 (2025), arXiv:2506.04306 [gr-qc]

    Pith/arXiv arXiv 2025

  70. [71]

    Van Raamsdonk and C

    M. Van Raamsdonk and C. Waddell (2025), arXiv:2505.10662 [astro-ph.CO]

    arXiv 2025

  71. [72]

    Peng, J.-Q

    Z.-Y. Peng, J.-Q. Jiang, H. Wang, and Y.-S. Piao, Phys. Rev. D112, 123519 (2025), arXiv:2509.11902 [astro- ph.CO]

    arXiv 2025

  72. [73]

    Yang, Eur

    Y. Yang, Eur. Phys. J. C85, 1350 (2025), arXiv:2508.17848 [astro-ph.CO]

    arXiv 2025

  73. [74]

    Jiang, Phys

    J.-Q. Jiang, Phys. Dark Univ.48, 101902 (2025), arXiv:2502.15541 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  74. [75]

    Ishak and L

    M. Ishak and L. Medina-Varela (2025), arXiv:2507.22856 [astro-ph.CO]

    arXiv 2025

  75. [76]

    Shlivko, P

    D. Shlivko, P. J. Steinhardt, and C. L. Steinhardt, JCAP2025(06), 054, arXiv:2504.02028 [astro-ph.CO]

    Pith/arXiv arXiv

  76. [77]

    Silva and R

    E. Silva and R. C. Nunes, JCAP11, 078, arXiv:2507.13989 [astro-ph.CO]

    arXiv

  77. [78]

    I. D. Gialamas, G. H¨ utsi, M. Raidal, J. Urrutia, M. Vasar, and H. Veerm¨ ae, Phys. Rev. D112, 063551 (2025), arXiv:2506.21542 [astro-ph.CO]

    arXiv 2025

  78. [79]

    Cortˆ es and A

    M. Cortˆ es and A. R. Liddle, Mon. Not. Roy. Astron. Soc. L121, L125 (2025), arXiv:2504.15336 [astro-ph.CO]

    arXiv 2025

  79. [80]

    Artola, I

    M. Artola, I. Ayuso, R. Lazkoz, and V. Salzano (2025), arXiv:2510.04191 [astro-ph.CO]

    arXiv 2025

  80. [81]

    B. R. Dinda, R. Maartens, and C. Clarkson, JCAP12, 025, arXiv:2509.19899 [astro-ph.CO]

    arXiv

Showing first 80 references.