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REVIEW 3 major objections 4 minor 161 references

Two-fluid dynamical dark energy supports sound waves that imprint a detectable scale dependence on matter growth and galaxy bias.

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2026-07-15 14:49 UTC pith:VX6FQZLH

load-bearing objection Solid multi-tracer P+B forecast for DESI-calibrated two-fluid DDE sound modes; SNRs optimistic without neutrino marginalization, but qualitative need for bispectrum holds. the 3 major comments →

arxiv 2603.05049 v2 pith:VX6FQZLH submitted 2026-03-05 astro-ph.CO

Sound Mode and Scale-Dependent Growth in Two-Fluid Dynamical Dark Energy

Frans van Die , Vincent Desjacques This is my paper
classification astro-ph.CO
keywords dynamical dark energytwo-fluid modelsound modescale-dependent biasmulti-tracerbispectrumphantom dividegravitational drag
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 dynamical dark energy, if real, can be tested not only through its background expansion but through its own fluctuations. It models dark energy as two effective fluids so the total equation of state can cross the phantom divide smoothly, in line with recent DESI-type results. Those fluids support sound-like modes that change how matter grows on different scales and how halos and galaxies are biased. A multi-tracer Fisher forecast shows that combining the galaxy power spectrum with the bispectrum is essential: for a survey of volume about 10 cubic gigaparsecs at redshift 0.5 to 1, the scale dependence is detectable when the fluid sound speeds squared lie between roughly 10^{-2} and 10^{-4}. Still lower sound speeds would drag cluster-sized halos enough to shift growth-rate measurements at the 10 percent level. The result therefore supplies a concrete observational path to confirm or limit dynamical dark energy at the level of its fluctuations.

Core claim

In an effective two-fluid description of dynamical dark energy that allows a smooth phantom crossing, the dark-energy components support propagating sound modes. These modes induce a scale dependence in the linear growth of matter fluctuations and in halo bias, with an amplitude for cluster-sized halos comparable to that from massless neutrinos in ΛCDM. A Fisher forecast for a two-tracer analysis of the power spectrum and bispectrum shows that bispectrum information is essential; for a survey volume V ~ 10 h^{-3} Gpc^{3} at z = 0.5–1 the scale dependence is detectable when the sound speeds satisfy c_s^{2} ~ 10^{-2}–10^{-4}. Lower sound speeds produce a gravitational drag that can alter growt

What carries the argument

The two-fluid dynamical dark energy model: two effective fluids with constant equations of state w± and rest-frame sound speeds ĉ± whose combination yields a total equation of state that crosses w = −1 without singularities. Their Jeans scales set the scale-dependent growth D(k) and the separate-universe / local-Lagrangian scale-dependent bias that enter the multi-tracer P+B Fisher forecast.

Load-bearing premise

Dark energy is treated as two fluids with fixed equations of state and fixed sound speeds, plus non-adiabatic pressure terms chosen only to keep those speeds positive and allow phantom crossing.

What would settle it

A two-tracer power-spectrum plus bispectrum analysis of a ~10 h^{-3} Gpc^{3} galaxy survey at z ≈ 0.5–1 that finds no residual scale-dependent bias (after neutrinos) at the amplitude predicted for c_s^{2} ~ 10^{-3}, or cluster peculiar-velocity data that show no mass-dependent ~10% shift in fσ₈ when one sound speed approaches 10^{-5}.

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

If this is right

  • Bispectrum measurements of multiple tracers become essential for detecting dark-energy sound modes in forthcoming surveys of this volume.
  • Cluster-sized samples with number density ~10^{-4} h^{3} Mpc^{-3} and bias ~3–3.5 can reach SNR of a few for c_s^{2} in the 10^{-2}–10^{-4} window.
  • Sound speeds as low as ~10^{-5} would produce a ~10% shift in fσ₈ inferred from cluster peculiar velocities.
  • Optimal mass weighting of tracers can extend sensitivity to larger sound speeds (c_s^{2} > 10^{-2}).
  • The sign of the scale dependence distinguishes thawing (phantom) from freezing (quintom) crossing directions.

Where Pith is reading between the lines

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

  • If DESI-like background evidence holds, a null result on scale-dependent bias at the forecasted level would push the model toward high sound speeds or non-negligible anisotropic stress not included here.
  • Degeneracy with neutrino-induced scale dependence can be partially broken by multi-redshift measurements, because the dark-energy effect peaks near the phantom-crossing epoch.
  • The same multi-tracer P+B pipeline is a practical search for any sub-horizon sound horizon in the dark sector, independent of the two-fluid microphysics.

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

3 major / 4 minor

Summary. The paper models dynamical dark energy that can cross the phantom divide with two effective fluids of constant equations of state w± and constant rest-frame sound speeds ĉ±. It solves the linear growth equations and spherical-collapse dynamics to obtain a scale-dependent growth factor D(k) and halo bias b1(k) around the Jeans scales k± = H/ĉ±. Separate-universe and local-Lagrangian calculations are compared; the latter overestimates the former by ~50 %. A tree-level multi-tracer Fisher forecast for the power spectrum and bispectrum of two galaxy samples (volume ~10 h^{-3} Gpc^{3} at z = 0.5–1) is used to claim that the scale dependence is detectable for ĉ^{2} ~ 10^{-2}–10^{-4} once bispectrum information is included. A secondary calculation estimates the dynamical-friction drag exerted by the sound wakes on cluster-mass halos and shows that it can shift f_eff σ_{8} by ~10 % only for extremely low sound speeds ~10^{-5}.

Significance. If the quantitative forecasts hold, the work supplies a concrete, observationally accessible signature of dark-energy fluctuations that is complementary to background equation-of-state constraints from DESI. The demonstration that bispectrum information is essential, the explicit comparison of separate-universe versus local-Lagrangian bias, and the order-of-magnitude estimate of gravitational drag are useful additions to the literature on clustering dark energy. The two-fluid construction itself is an effective description rather than a fundamental model, but it is sufficient to illustrate the phenomenology in a largely model-independent way.

major comments (3)
  1. §III.D.2 (Eqs. 44–46 and the three-parameter set {b1↓^a, b1↓^b, A}): the Fisher matrix freezes the shape and amplitude of the reference power spectrum PL(k) and does not marginalize over parameters that produce similar scale-dependent growth (most notably Σ m u, but also As and Ωm). The paper itself notes that the amplitude of Δb/b for M ~ 10^{14} M⊙/h is comparable to that of massless neutrinos. Consequently the SNRs reported in Figs. 7–8 are optimistic upper bounds; a realistic forecast must enlarge the parameter space or demonstrate that the degeneracy can be broken by the multi-tracer + bispectrum combination.
  2. The same Fisher analysis is performed in real space and omits redshift-space distortion kernels. Because the growth-rate factor f multiplies the same scale-dependent D(k) that enters the bias, RSD will entangle the signal with the very quantity one wishes to measure. At minimum the paper should quantify how the inclusion of the Kaiser factor (or a simple multipole expansion) degrades the SNR for A.
  3. §IV and Fig. 9: the dynamical-friction calculation treats the two fluids as ideal media with constant sound speeds and neglects anisotropic stress. While the order-of-magnitude estimate is useful, the claim that ĉ^{2} ~ 10^{-5} is an “effective lower bound” rests on this idealization; a short discussion of how non-zero anisotropic stress or time-dependent sound speeds would alter the drag force is needed before the bound can be taken at face value.
minor comments (4)
  1. Fig. 5 caption and surrounding text: the local-Lagrangian curves are said to overestimate the SU result by ~50 %, yet the vertical scale of the figure makes the difference appear smaller at high k; a short quantitative statement in the caption would help.
  2. Eq. (15) and Table I: the power-law index p = 0.1 is introduced to suppress higher derivatives of w(a), but no sensitivity test to p is shown. A one-sentence remark on how Δb/b changes when p is varied would strengthen the claim that the results are robust.
  3. Appendix A: the covariance matrices are written for the Gaussian approximation only. A brief note that non-Gaussian contributions are neglected (and that they would further reduce the SNR) would be appropriate.
  4. Several figures (especially Figs. 7–8) use “â” for the sound-speed symbols; consistent LaTeX notation throughout would improve readability.

Circularity Check

0 steps flagged

No circularity: scale-dependent growth/bias and Fisher SNRs are derived from the two-fluid equations and external benchmarks, not forced by construction or self-citation.

full rationale

The two-fluid DDE model (w±, ĉ±, δn, ϵn) is taken from Hu (2005) and calibrated to external DESI+CMB+DESY5 or Planck values (Table I, Eqs. 5–15); sound speeds are free parameters scanned over a motivated range. Linear growth D(k,z) follows from the sub-horizon fluid equations (16)–(20) with adiabatic initial conditions; scale-dependent bias b1(k) is obtained independently via separate-universe spherical collapse (21)–(24) or the local-Lagrangian map (25)–(29). The Fisher forecast freezes the shape/amplitude of a reference PL(k) and varies only {b1↓^a, b1↓^b, A}, where A multiplies the pre-computed functions f1(k), f2(k) derived from those equations; SNR ≡ 1/σ_A therefore measures detectability of an independently calculated scale dependence, not a quantity fitted to the same data. Gravitational-drag estimates use the external Ostriker (1999) subsonic force and EPS mass histories. No self-definitional loop, fitted-input-as-prediction, load-bearing self-citation, uniqueness import, or ansatz smuggling appears in the derivation chain. Forecast optimism (frozen PL, omitted neutrino degeneracies) is a modeling limitation, not circularity.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 1 invented entities

The central claims rest on an effective two-fluid description of DDE, standard linear cosmological perturbation theory, the separate-universe spherical-collapse model, tree-level multi-tracer Fisher forecasting, and a subsonic dynamical-friction formula. Free parameters are the sound speeds and the CPL-like background parameters fixed to DESI/Planck. No new fundamental entities are introduced; the two fluids are an effective bookkeeping device.

free parameters (4)
  • ĉ± (sound speeds of the two DE fluids) = scanned 10^{-5}–10^{-2}
    Scanned over 10^{-5}–10^{-2}; the detection claims and drag amplitude depend directly on their values. Not fixed by data.
  • w0, wa (CPL parameters) = Phantom: w0=-0.752, wa=-0.86; Quintom: w0=-1.15, wa=0.5
    Fixed to DESI+CMB+DESY5 best-fit for the Phantom model and to a representative freezing value for the Quintom model; they set the background expansion and the relative energy densities of the two fluids.
  • an, p (normalization epoch and power-law index for εn) = an=0.75, p=0.1
    Chosen by hand (an=0.75, p=0.1) to satisfy the conditions of Hu (2005) and to mitigate higher derivatives of w(a).
  • survey volume Vs, kmax, number densities, bias values = Vs~10 h^{-3} Gpc^{3}, kmax=0.1 h Mpc^{-1}
    Assumed Vs=10–20 h^{-3} Gpc^{3}, kmax=0.1 h Mpc^{-1}, and threshold samples with b1↓ matched to Tinker mass function; they control the forecasted SNR.
axioms (5)
  • ad hoc to paper Two effective fluids with constant w± and constant rest-frame sound speeds ĉ± can describe a total dark-energy component that smoothly crosses w=−1 without singularities.
    Adopted from Hu (2005) and Fang et al.; used throughout §§II–IV. Not derived from a fundamental Lagrangian.
  • domain assumption Anisotropic stress of both DE fluids is negligible (Π±≈0), so Φ=Ψ on sub-horizon scales.
    Stated in §III.A; closes the system of equations for the gravitational potential.
  • domain assumption Linear theory and tree-level bias expansion remain valid up to kmax=0.1 h Mpc^{-1}; redshift-space distortions and P–B cross-covariance can be neglected for the forecast.
    Explicitly adopted in §III.D for the Fisher calculation.
  • domain assumption Halo mass function and bias follow the Tinker et al. (2010) fitting formulae; quadratic and tidal bias are related to linear bias by the co-evolution and Lazeyras et al. relations.
    Used to convert number density into bias and to close the bispectrum kernels (Eqs. 41–43).
  • domain assumption Subsonic dynamical friction force on a point-mass perturber in an ideal fluid is given by Ostriker’s formula with I±≈(1/3)(v/ĉ±)^{3}.
    Invoked in §IV and Appendix B; finite-size corrections are argued to be negligible.
invented entities (1)
  • Two-fluid effective DDE (Phantom and Quintom realizations) no independent evidence
    purpose: Provide a singularity-free description of phantom-crossing dark energy that supports propagating sound modes.
    The two fluids are bookkeeping devices, not fundamental fields; only the total energy density is required to be positive. No independent collider or laboratory handle is claimed.

pith-pipeline@v1.1.0-grok45 · 35754 in / 3830 out tokens · 34174 ms · 2026-07-15T14:49:52.224990+00:00 · methodology

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read the original abstract

We investigate the effects of dynamical dark energy (DDE) on the growth of cosmic structure using a two-fluid model. This framework allows the dark energy equation of state to smoothly cross the phantom divide, in agreement with recent DESI results. In this effective description, DDE supports propagating perturbations that behave like sound waves. These perturbations induce a scale dependence in the growth of matter fluctuations and in halo bias, which can be exploited to test the dynamical nature of dark energy at the level of its fluctuations. For cluster-sized halos, the amplitude of the scale-dependent halo bias is comparable to that produced by massless neutrinos in $\Lambda$CDM. Using a Fisher forecast for a multi-tracer analysis of the power spectrum (P) and bispectrum (B) of galaxy number counts, we find that bispectrum information is essential to detect the scale dependence induced by the DDE sound mode. For a survey of volume $V\sim 10\, h^{-3}{\rm Gpc}^3$ at redshift $z=0.5 - 1$, a two-tracer P+B analysis could detect this scale dependence if the sound speeds of the dark energy fluids are in the range $c_s^2\sim 10^{-2} - 10^{-4}$. Lower sound speeds cause halos to experience a gravitational drag force through the excitations of sound waves. This effect impacts measurements of the growth rate inferred from cluster-sized halos at the 10\% level if one of the fluids has a very low sound speed $c_s^2\sim 10^{-5}$. Larger sound speeds $c_s^2 > 10^{-2}$ could be probed with optimal weighting schemes that reduce shot noise and increase the effective bias.

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Reference graph

Works this paper leans on

161 extracted references · 113 linked inside Pith

  1. [1]

    so that the gravitational (Bardeen) potentials satisfy Φ = Ψ (e.g. [85]). Furthermore, we shall ignore the metric perturbations induced by the components of the stress-energy tensor other than matter and DE. On the sub-horizon scalesk/H ≫1 of interest here, the equa- 5 tion governing the growth of linear matter perturbation reduces to d2δm d lna2 + � 1 + ...

  2. [2]

    Separate universe approach The separate universe (SU) technique [86–90] can pro- vide accurate predictions for the scale-dependent bias in- duced by the scale-dependent growth of matter fluctua- tions. Following [84, 91], the scale-dependent linear bias of DM halos at the collapse redshiftzis given by b1(z, M, k) = 1−b L 1 (z, M) dδc dδm (21) where the cr...

  3. [3]

    (25) to calculate the scale-dependent bias

    Local Lagrangian bias approximation Alternatively, we follow [82, 83] and assume that the linear order Lagrangian and matter density fields satisfy a scale-independent relation δL h (zi,�) =b L 1 (zi, M)δ m(zi,�) +. . .(25) to calculate the scale-dependent bias. This approxi- mation provides a fast estimate of the late-time scale- dependent bias because t...

  4. [4]

    Theoretical predictions In Fig. 5, we plot the fractional deviation ∆b b = b1(z, M, k) 1 +b L 1 (z, M) −1 (30) from a scale-independent bias predicted by the SU ap- proach (filled circles with a thin interpolating line) and the local Lagrangian approximation (thick curves) for two of the models shown in Fig. 4. We assume a halo massM= 10 14 M⊙/�(correspon...

  5. [5]

    Single tracer We consider first the detectability of the scale- dependence in measurements of the power spectrum of a single galaxy sample. We assume linear theory, ig- nore redshift-space distortions and consider the model (we omit the redshift dependence hereafter to avoid clut- ter) Pg(k)≡b 2 1(k)D2(k)PL(k) + 1 ¯ng (32) whereP L(k) is a reference (ΛCDM...

  6. [6]

    Furthermore, the scale-dependence induced by the sound mode is also present in the bispectrum owing to its dependence on the galaxy bias parameters

    Multiple tracers By comparing differently biased tracers of the same surveyed volume, multi-tracer analyses can partly alle- viate the limitation brought by cosmic variance and im- prove the detection level of scale-dependent features [99– 106]. Furthermore, the scale-dependence induced by the sound mode is also present in the bispectrum owing to its depe...

  7. [7]

    under the assumption that each halo host exactly one surveyed (central) galaxy, whereas the second sam- ple ”�” has number density ¯nb = 0.01� 3Mpc−3 and bias b(b) 1↓ = 1 as in Fig. 7. In this case the plotted range of ¯na corresponds to a range in minimal massM min of 1010.5 −10 13.5 M⊙/�, from right to left. The maxi- mum wavenumber isk max = 0.1�Mpc −1...

  8. [8]

    Finite size effects Since DM halos are extended objects, the point-like approximation for the computation of the friction coeffi- cient may not hold. The correction caused by the finite size of the DM halo enters the Fourier transform of the halo density, ρh(ω,�) = � dη � d3x ρh(η,�)e −i�·�+iωη (B1) = � dη a(η)−3M(η)u(k, η)e −i�·� � (η)+iωη , through the ...

  9. [9]

    Concretely, we assume a redshift-dependent halo mass M(z) =M 0(1 +z) αeβz (B2) whereM 0 is the present-day halo mass

    Mass accretion history We include the average mass accretion history of DM halos following the approach of [136] based on the ex- tended Press-Schechter (EPS) formalism (see also [137– 139]). Concretely, we assume a redshift-dependent halo mass M(z) =M 0(1 +z) αeβz (B2) whereM 0 is the present-day halo mass. The mass ac- cretion over cosmic time is govern...

  10. [10]

    R. R. Caldwell, R. Dave, and P. J. Steinhardt, Cosmo- logical Imprint of an Energy Component with General Equation of State, Phys. Rev. Lett.80, 1582 (1998), arXiv:astro-ph/9708069 [astro-ph]

    Pith/arXiv arXiv 1998

  11. [11]

    Zlatev, L

    I. Zlatev, L. Wang, and P. J. Steinhardt, Quintessence, cosmic coincidence, and the cosmological constant, Phys. Rev. Lett.82, 896 (1999), arXiv:astro- ph/9807002

    arXiv 1999

  12. [12]

    Ratra and P

    B. Ratra and P. J. E. Peebles, Cosmological conse- quences of a rolling homogeneous scalar field, Phys. Rev. D37, 3406 (1988)

    1988

  13. [13]

    J. A. Frieman, C. T. Hill, A. Stebbins, and I. Waga, Cosmology with Ultralight Pseudo Nambu-Goldstone Bosons, Phys. Rev. Lett.75, 2077 (1995), arXiv:astro- ph/9505060 [astro-ph]

    arXiv 2077

  14. [14]

    J. K. Erickson, R. R. Caldwell, P. J. Steinhardt, C. Armendariz-Picon, and V. Mukhanov, Measuring the Speed of Sound of Quintessence, Phys. Rev. Lett.88, 121301 (2002), arXiv:astro-ph/0112438 [astro-ph]

    Pith/arXiv arXiv 2002

  15. [15]

    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

  16. [16]

    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

  17. [17]

    Arkani-Hamed, P

    N. Arkani-Hamed, P. Creminelli, S. Mukohyama, and M. Zaldarriaga, Ghost inflation, JCAP2004, 001 (2004), arXiv:hep-th/0312100 [hep-th]

    Pith/arXiv arXiv 2004

  18. [18]

    E. A. Lim, I. Sawicki, and A. Vikman, Dust of dark en- ergy, JCAP2010, 012 (2010), arXiv:1003.5751 [astro- ph.CO]

    Pith/arXiv arXiv 2010

  19. [19]

    Kunz, The phenomenological approach to model- ing the dark energy, Comptes Rendus Physique13, 539 (2012), arXiv:1204.5482 [astro-ph.CO]

    M. Kunz, The phenomenological approach to model- ing the dark energy, Comptes Rendus Physique13, 539 (2012), arXiv:1204.5482 [astro-ph.CO]

    Pith/arXiv arXiv 2012

  20. [20]

    Tamayo, E

    D. Tamayo, E. Urquilla, and I. G´ omez-Vargas, Equiv- alence of dark energy models: A theoretical and Bayesian perspective, Phys. Dark Univ.48, 101901 (2025), arXiv:2502.12915 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  21. [22]

    M. S. Linton, A. Pourtsidou, R. Crittenden, and R. Maartens, Variable sound speed in interacting dark energy models, JCAP04, 043, arXiv:1711.05196 [astro- ph.CO]

    Pith/arXiv arXiv

  22. [23]

    Hassani, J

    F. Hassani, J. Adamek, M. Kunz, and F. Vernizzi, k-evolution: a relativistic N-body code for clustering dark energy, JCAP2019, 011 (2019), arXiv:1910.01104 [astro-ph.CO]

    Pith/arXiv arXiv 2019

  23. [24]

    Hassani, J

    F. Hassani, J. Adamek, R. Durrer, and M. Kunz, Bi- ased tracers as a probe of beyond-ΛCDM cosmologies, Astron. Astrophys.668, A56 (2022), arXiv:2206.14179 [astro-ph.CO]

    Pith/arXiv arXiv 2022

  24. [25]

    Ishiyama, F

    T. Ishiyama, F. Prada, and A. A. Klypin, Evolu- tion of clustering in cosmological models with time- varying dark energy, Phys. Rev. D112, 043504 (2025), arXiv:2503.19352 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  25. [26]

    R. Neomenko, Constraints on the interaction strength in the model of interacting dynamical dark energy with linear and non-linear interacting terms, (2024), arXiv:2412.20551 [astro-ph.CO]

    arXiv 2024

  26. [27]

    D’Amico, Y

    G. D’Amico, Y. Donath, L. Senatore, and P. Zhang, Limits on clustering and smooth quintessence from the EFTofLSS, JCAP03, 032, arXiv:2012.07554 [astro- ph.CO]

    Pith/arXiv arXiv 2012

  27. [28]

    P. Wu, M. Zhang, and S.-J. Jin, How Dark Sector Equa- tions of State Govern Interaction Signatures, (2025), arXiv:2512.05548 [astro-ph.CO]

    arXiv 2025

  28. [29]

    Y. Zhai, M. de Cesare, C. van de Bruck, E. Di Valentino, and E. Wilson-Ewing, A low-redshift preference for an interacting dark energy model, JCAP11, 010, arXiv:2503.15659 [astro-ph.CO]

    Pith/arXiv arXiv

  29. [30]

    A. G. Adameet al.(DESI), DESI 2024 VII: cosmological constraints from the full-shape modeling of clustering measurements, JCAP07, 028, arXiv:2411.12022 [astro- ph.CO]

    Pith/arXiv arXiv 2024

  30. [31]

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

    Pith/arXiv arXiv 2024

  31. [32]

    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

  32. [33]

    Garcia-Quinteroet al.(DESI), Cosmological impli- cations of DESI DR2 BAO measurements in light of the latest ACT DR6 CMB data, Phys

    C. Garcia-Quinteroet al.(DESI), Cosmological impli- cations of DESI DR2 BAO measurements in light of the latest ACT DR6 CMB data, Phys. Rev. D112, 083529 (2025), arXiv:2504.18464 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  33. [34]

    Wang and D

    D. Wang and D. Mota, Did DESI DR2 truly reveal dy- namical dark energy?, Eur. Phys. J. C85, 1356 (2025), arXiv:2504.15222 [astro-ph.CO]

    arXiv 2025

  34. [35]

    E. M. Teixeira, W. Giar` e, N. B. Hogg, T. Montan- don, A. Poudou, and V. Poulin, Implications of dis- 17 tance duality violation for the H0 tension and evolv- ing dark energy, Phys. Rev. D112, 023515 (2025), arXiv:2504.10464 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  35. [36]

    Capozziello, H

    S. Capozziello, H. Chaudhary, T. Harko, and G. Mustafa, Is dark energy dynamical in the DESI era? A critical review, Phys. Dark Univ.51, 102196 (2026), arXiv:2512.10585 [astro-ph.CO]

    arXiv 2026

  36. [37]

    M. W. Toomey, G. Montefalcone, E. McDonough, and K. Freese, How Theory-Informed Priors Affect DESI Evidence for Evolving Dark Energy, (2025), arXiv:2509.13318 [astro-ph.CO]

    arXiv 2025

  37. [38]

    Chevallier and D

    M. Chevallier and D. Polarski, Accelerating universes with scaling dark matter, Int. J. Mod. Phys. D10, 213 (2001), arXiv:gr-qc/0009008

    Pith/arXiv arXiv 2001

  38. [39]

    E. V. Linder, Exploring the expansion history of the uni- verse, Phys. Rev. Lett.90, 091301 (2003), arXiv:astro- ph/0208512

    arXiv 2003

  39. [40]

    Nesseris, Y

    S. Nesseris, Y. Akrami, and G. D. Starkman, To CPL, or not to CPL? What we have not learned about the dark energy equation of state, (2025), arXiv:2503.22529 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  40. [41]

    A. N. Ormondroyd, W. J. Handley, M. P. Hobson, and A. N. Lasenby, Non-parametric reconstructions of dy- namical dark energy via flexknots, Mon. Not. Roy. As- tron. Soc.541, 3388 (2025), arXiv:2503.08658 [astro- ph.CO]

    Pith/arXiv arXiv 2025

  41. [42]

    Giar` e, T

    W. Giar` e, T. Mahassen, E. Di Valentino, and S. Pan, An overview of what current data can (and cannot yet) say about evolving dark energy, Phys. Dark Univ.48, 101906 (2025), arXiv:2502.10264 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  42. [43]

    Shlivko, P

    D. Shlivko, P. J. Steinhardt, and C. L. Steinhardt, Op- timal parameterizations for observational constraints on thawing dark energy, (2025), arXiv:2504.02028 [astro- ph.CO]

    Pith/arXiv arXiv 2025

  43. [44]

    Artola, I

    M. Artola, I. Ayuso, R. Lazkoz, and V. Salzano, Is Chevallier-Polarski-Linder dark energy a mirage?, Phys. Rev. D113, 023513 (2026), arXiv:2510.04191 [astro- ph.CO]

    arXiv 2026

  44. [45]

    Lodhaet al.(DESI), Extended dark energy analy- sis using DESI DR2 BAO measurements, Phys

    K. Lodhaet al.(DESI), Extended dark energy analy- sis using DESI DR2 BAO measurements, Phys. Rev. D 112, 083511 (2025), arXiv:2503.14743 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  45. [46]

    R. E. Keeley, K. N. Abazajian, M. Kaplinghat, and A. Shafieloo, Preference for evolving dark energy from cosmological distance measurements and possible signa- tures in the growth rate of perturbations, Phys. Rev. D 112, 043501 (2025), arXiv:2502.12667 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  46. [47]

    Roy, Dynamical dark energy in the light of DESI 2024 data, Phys

    N. Roy, Dynamical dark energy in the light of DESI 2024 data, Phys. Dark Univ.48, 101912 (2025), arXiv:2406.00634 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  47. [48]

    Berti, E

    M. Berti, E. Bellini, C. Bonvin, M. Kunz, M. Viel, and M. Zumalacarregui, Reconstructing the dark energy density in light of DESI BAO observations, Phys. Rev. D112, 023518 (2025), arXiv:2503.13198 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  48. [49]

    Bansal and D

    P. Bansal and D. Huterer, Expansion-history prefer- ences of DESI DR2 and external data, Phys. Rev. D 112, 023528 (2025), arXiv:2502.07185 [astro-ph.CO]

    arXiv 2025

  49. [50]

    A. J. Shajib and J. A. Frieman, Scalar-field dark energy models: Current and forecast constraints, Phys. Rev. D 112, 063508 (2025), arXiv:2502.06929 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  50. [51]

    G. Guet al., Dynamical dark energy in light of the DESI DR2 baryonic acoustic oscillations measurements, Nature Astronomy 10.1038/s41550-025-02669-6 (2025), arXiv:2504.06118 [astro-ph.CO]

    doi:10.1038/s41550-025-02669-6 2025

  51. [52]

    T. M. C. Abbottet al.(DES), Dark Energy Survey: implications for cosmological expansion models from the final DES Baryon Acoustic Oscillation and Supernova data, (2025), arXiv:2503.06712 [astro-ph.CO]

    arXiv 2025

  52. [53]

    Mena-Fern´ andezet al.(DES), Dark Energy Sur- vey: DESI-Independent Angular BAO Measurement, (2026), arXiv:2601.14864 [astro-ph.CO]

    J. Mena-Fern´ andezet al.(DES), Dark Energy Sur- vey: DESI-Independent Angular BAO Measurement, (2026), arXiv:2601.14864 [astro-ph.CO]

    arXiv 2026

  53. [54]

    Reischkeet al., KiDS-Legacy: Constraining dark energy, neutrino mass, and curvature, (2025), arXiv:2512.11041 [astro-ph.CO]

    R. Reischkeet al., KiDS-Legacy: Constraining dark energy, neutrino mass, and curvature, (2025), arXiv:2512.11041 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  54. [55]

    S. Chen, M. M. Ivanov, O. H. E. Philcox, and L. Wenzl, Suppression without Thawing: Constraining Structure Formation and Dark Energy with Galaxy Clustering, Phys. Rev. Lett.133, 231001 (2024), arXiv:2406.13388 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  55. [56]

    Chen and M

    S. Chen and M. M. Ivanov, Constraining dynamical dark energy from galaxy clustering with simulation- based priors, Phys. Rev. D112, 083562 (2025)

    2025

  56. [57]

    Silva and R

    E. Silva and R. C. Nunes, Testing signatures of phan- tom crossing through full-shape galaxy clustering anal- ysis, JCAP2025, 078 (2025), arXiv:2507.13989 [astro- ph.CO]

    arXiv 2025

  57. [58]

    B. R. Dinda, R. Maartens, and C. Clarkson, Calibration-independent consistency test of DESI DR2 BAO and SNIa, JCAP12, 025, arXiv:2509.19899 [astro- ph.CO]

    arXiv

  58. [59]

    I. D. Gialamas, G. H¨ utsi, K. Kannike, A. Racioppi, M. Raidal, M. Vasar, and H. Veerm¨ ae, Interpreting DESI 2024 BAO: Late-time dynamical dark energy or a local effect?, Phys. Rev. D111, 043540 (2025), arXiv:2406.07533 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  59. [60]

    J. W. Moffat, Void and Density Walls Inhomo- geneous Cosmic Web And Dark Energy, (2025), arXiv:2503.20912 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  60. [61]

    S. H. Mirpoorian, K. Jedamzik, and L. Pogosian, Is dy- namical dark energy necessary? DESI BAO and mod- ified recombination, JCAP12, 050, arXiv:2504.15274 [astro-ph.CO]

    arXiv

  61. [62]

    Camarena, K

    D. Camarena, K. Greene, J. Houghteling, and F.- Y. Cyr-Racine, Designing concordant distances in the age of precision cosmology: The impact of den- sity fluctuations, Phys. Rev. D112, 083526 (2025), arXiv:2507.17969 [astro-ph.CO]

    arXiv 2025

  62. [63]

    Y. B. Ginat and P. G. Ferreira, Apparent Dark-Energy Evolution from Cosmic Inhomogeneities, (2026), arXiv:2601.20633 [astro-ph.CO]

    arXiv 2026

  63. [64]

    Banik, H

    I. Banik, H. Desmond, V. Kalaitzidis, and S. Mazurenko, The local void model for the Hub- ble and BAO tensions, (2026), arXiv:2602.03928 [astro-ph.CO]

    arXiv 2026

  64. [65]

    R. A. Battye and A. Moss, How isotropic is dark en- ergy?, (2026), arXiv:2601.22351 [astro-ph.CO]

    arXiv 2026

  65. [66]

    F. B. M. d. Santos, J. Morais, S. Pan, W. Yang, and E. Di Valentino, A New Window on Dynamical Dark Energy: Combining DESI-DR2 BAO with future Grav- itational Wave Observations, (2025), arXiv:2504.04646 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  66. [67]

    Garza, B

    D. Garza, B. Robertson, P. Madau, N. Gnedin, M. W. Abruzzo, R. D. Budiardja, R. Caddy, E. Schneider, J. B. White, III, and B. Villasenor, Dynamical Dark Energy Imprints in the Lyman-Alpha Forest, (2026), arXiv:2601.00767 [astro-ph.CO]

    arXiv 2026

  67. [68]

    Guet al.(DESI), Dynamical dark energy in light of the DESI DR2 baryonic acoustic oscillations measure- ments, Nature Astron.9, 1879 (2025), [Erratum: Na- 18 ture Astron

    G. Guet al.(DESI), Dynamical dark energy in light of the DESI DR2 baryonic acoustic oscillations measure- ments, Nature Astron.9, 1879 (2025), [Erratum: Na- 18 ture Astron. 9, 1898 (2025)], arXiv:2504.06118 [astro- ph.CO]

    arXiv 2025

  68. [69]

    W. Fang, W. Hu, and A. Lewis, Crossing the Phantom Divide with Parameterized Post-Friedmann Dark En- ergy, Phys. Rev. D78, 087303 (2008), arXiv:0808.3125 [astro-ph]

    Pith/arXiv arXiv 2008

  69. [70]

    Amendolaet al., Cosmology and fundamental physics with the Euclid satellite, Living Rev

    L. Amendolaet al., Cosmology and fundamental physics with the Euclid satellite, Living Rev. Rel.21, 2 (2018), arXiv:1606.00180 [astro-ph.CO]

    Pith/arXiv arXiv 2018

  70. [71]

    Kunz and D

    M. Kunz and D. Sapone, Crossing the Phantom Di- vide, Phys. Rev. D74, 123503 (2006), arXiv:astro- ph/0609040

    arXiv 2006

  71. [72]

    Perrotta and C

    F. Perrotta and C. Baccigalupi, On the dark energy clustering properties, Phys. Rev. D65, 123505 (2002), arXiv:astro-ph/0201335

    Pith/arXiv arXiv 2002

  72. [73]

    de Putter and E

    R. de Putter and E. V. Linder, Kinetic k-essence and Quintessence, Astropart. Phys.28, 263 (2007), arXiv:0705.0400 [astro-ph]

    Pith/arXiv arXiv 2007

  73. [74]

    de Putter, D

    R. de Putter, D. Huterer, and E. V. Linder, Measuring the Speed of Dark: Detecting Dark Energy Perturba- tions, Phys. Rev. D81, 103513 (2010), arXiv:1002.1311 [astro-ph.CO]

    Pith/arXiv arXiv 2010

  74. [75]

    Calabrese, R

    E. Calabrese, R. de Putter, D. Huterer, E. V. Linder, and A. Melchiorri, Future CMB Constraints on Early, Cold, or Stressed Dark Energy, Phys. Rev. D83, 023011 (2011), arXiv:1010.5612 [astro-ph.CO]

    Pith/arXiv arXiv 2011

  75. [76]

    Gubitosi, F

    G. Gubitosi, F. Piazza, and F. Vernizzi, The Effec- tive Field Theory of Dark Energy, JCAP02, 032, arXiv:1210.0201 [hep-th]

    Pith/arXiv arXiv

  76. [77]

    Gleyzes, D

    J. Gleyzes, D. Langlois, F. Piazza, and F. Vernizzi, Es- sential Building Blocks of Dark Energy, JCAP08, 025, arXiv:1304.4840 [hep-th]

    Pith/arXiv arXiv

  77. [78]

    Hu, Crossing the phantom divide: Dark energy in- ternal degrees of freedom, Phys

    W. Hu, Crossing the phantom divide: Dark energy in- ternal degrees of freedom, Phys. Rev. D71, 047301 (2005), arXiv:astro-ph/0410680 [astro-ph]

    Pith/arXiv arXiv 2005

  78. [79]

    Lodhaet al.(DESI), DESI 2024: Constraints on physics-focused aspects of dark energy using DESI DR1 BAO data, Phys

    K. Lodhaet al.(DESI), DESI 2024: Constraints on physics-focused aspects of dark energy using DESI DR1 BAO data, Phys. Rev. D111, 023532 (2025), arXiv:2405.13588 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  79. [80]

    R. R. Caldwell and E. V. Linder, The Limits of quintessence, Phys. Rev. Lett.95, 141301 (2005), arXiv:astro-ph/0505494

    Pith/arXiv arXiv 2005

  80. [81]

    Mehrabi, S

    A. Mehrabi, S. Basilakos, and F. Pace, How cluster- ing dark energy affects matter perturbations, Mon. Not. Roy. Astron. Soc.452, 2930 (2015), arXiv:1504.01262 [astro-ph.CO]

    Pith/arXiv arXiv 2015

Showing first 80 references.