Uplifting, Depressing, and Tilting Dark Energy

Eric V. Linder

REVIEW 3 major objections 4 minor 6 cited by

Uplifting, Depressing, and Tilting Dark Energy

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read Dark energy must cross w=-1 on its own; interactions can't fix it

desk verdict A clean model-independent argument that generic dark energy interactions can't explain the apparent w=-1 crossing—but the decisive 'bare DE must cross' step relies on an assumed Omega_de(z=1) and no growth calculation. read the letter →

arxiv 2506.02122 v2 pith:ZIR3DMUZ submitted 2025-06-02 astro-ph.CO

Eric V. Linder This is my paper

classification astro-ph.CO

keywords darkenergyequationofstatephantomdividematterinteractionsmodifiedgravityHorndeskidecelerationparametercosmicgrowth

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper takes the current baryon acoustic oscillation, supernova, and cosmic microwave background distance data at face value and asks what the dark energy itself has to be doing to accommodate them. The data prefer stronger-than-$\Lambda$CDM acceleration at $z \approx 0.5$–$1.5$ and weaker-than-$\Lambda$CDM acceleration at $z \lesssim 0.5$, a pattern that lies outside the thawing and freezing behaviors allowed for ordinary scalar fields. The paper shows that adding interactions—decays, couplings to matter, or nonminimal coupling to gravity—does not rescue the fit, because the shifts needed in the coupled sector change the effective dark matter equation of state enough to disturb structure growth. The conclusion is that the bare, uninteracted dark energy must already cross the phantom divide $w=-1$ before any interaction is switched on. The case is made model-independently, so it covers whole classes of interaction models rather than a single Lagrangian.

What carries the argument

The load-bearing identity is $q(z)=\frac{1}{2}[1+3w_{\rm de}\Omega_{\rm de}(z)]$, obtained by summing the continuity equations with an arbitrary interaction $Q$ between dark energy and matter; the interaction cancels out of the deceleration parameter, so an observed $q(z)$ directly constrains the product of the bare equation of state and the effective dark energy density. The companion relation $w^{\rm eff}_{\rm m}=(\Omega_{\rm de}/\Omega_{\rm m})(w_{\rm de}-w^{\rm eff}_{\rm de})$ converts that constraint into a required shift of the dark matter equation of state away from zero, which is what makes most interaction models observationally expensive. Together these identities carry the argument: they show that the crossing of $w=-1$ must be a property of the bare dark energy, not a byproduct of the interaction.

What would settle it

Measure the effective dark matter equation of state at $z=0$ from growth and ISW data: if $|w^{\rm eff}_{\rm m}| < 0.01$ while distance data continue to give $q_0 \approx -0.3$ and $q_1 \approx 0.1$, then uplifting or depressing interactions are excluded and the bare-crossing conclusion is confirmed; if instead $w^{\rm eff}_{\rm m} \approx -0.2$ to $-0.6$ is detected with the same $q$ values, the interaction route remains viable.

Watch

Extended reading notes

Core claim

The central claim is that interaction mechanisms for crossing the phantom divide are effectively moot: to fit both the stronger mid-redshift acceleration and the weaker low-redshift acceleration favored by current distances, the intrinsic dark energy equation of state must itself pass through $w=-1$ before any interaction is included. For phantom dark energy that must be uplifted, the required effective dark matter equation of state is roughly $w^{\rm eff}_{\rm m} \approx w_{\rm de} - w^{\rm eff}_{\rm de}$, numerically about $-0.2$ to $-0.6$, which growth and integrated Sachs-Wolfe observations strongly bound. For thawing dark energy that must be depressed, fitting the high-redshift acceleration forces the effective dark energy density at $z=1$ to be at least $\Omega_{\rm de}(1) \approx 0.27 \pm 0.02$, about twenty percent above the $\Lambda$CDM value, again at the cost of large-scale structure. A sign-changing modified-gravity coupling ("tilting") can soften the tension qualitatively, but the paper concludes it needs several extra parameters and still has no convincing match to growth.

Load-bearing premise

The whole argument takes at face value the Gaussian-process reconstruction of $q(z)$ and $w^{\rm eff}_{\rm de}$ from current BAO, supernova, and CMB distances, with $q_0 \approx -0.3 \pm 0.1$, $q_1 \approx 0.1 \pm 0.03$, $w^{\rm eff}_{\rm de}(0) \approx -0.8 \pm 0.07$, and $\Omega_{\rm de,0} \approx 0.7 \pm 0.1$; if those reconstructed values are biased by survey systematics or the assumed dark energy fraction, the claim that the bare dark energy must cross $w=-1$ loses its quantitative footing.

Editorial extensions

If this is right

If the central claim holds, single-field interaction models—decay, matter coupling, or nonminimal gravity coupling—cannot explain the distance-data pattern without violating growth or integrated Sachs-Wolfe constraints.
The bare dark energy must cross $w=-1$, excluding canonical single-field quintessence and, by the paper's review, noncanonical single-field models that preserve $w \geq -1$.
Uplifting phantom dark energy would require an effective dark matter equation of state of order $-0.2$ to $-0.6$, so future growth and ISW measurements can directly test that branch.
Depressing thawing dark energy requires the effective dark energy density at $z=1$ to be roughly 20% above its $\Lambda$CDM value, a shift that structure-growth data can test independently of distances.
The only route the paper finds worth further study is tilting modified gravity with a running Planck mass that changes sign, at the price of extra parameters and an unproven match to growth.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

An extension the paper leaves implicit: the same identity makes $q(z)$ the cleanest observable to arbitrate the debate, since the interaction is invisible in $q$; a direct, model-independent measurement of $q(z)$ over $0<z<1.5$ would settle whether the crossing requirement is real.
If the bare-crossing conclusion is right, then any viable single-field model must itself be phantom or cross $w=-1$, which pushes model-building toward ghost-like kinetic sectors or phase-transition-like inception; stability at the crossing then becomes the key theoretical test the paper does not run.
One could also turn the argument around: a future detection of $w^{\rm eff}_{\rm m} \approx -0.2$ at $z=0$ would count as evidence for an uplifting interaction rather than for exotic bare dark energy, giving observers a fork in the road.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Read this if you work on coupled dark energy or modified gravity and want a compact argument for why generic interactions won't fix the w=-1 crossing problem. The new content is real: the paper sorts the possibilities into uplifting, depressing, and tilting, and derives a model-independent relation between the dark matter and dark energy equation-of-state shifts (Eq. 12). Equation (9)—where the interaction Q drops out of q(z)—is the cleanest way to see why the bare equation of state, not the effective one, is what the distance data constrain. The tilting discussion with a sign-changing alpha_M in Horndeski is a nice synthesis of known ingredients, and the author is honest that it is not a complete model. Nothing here is machine-checked or accompanied by code; it is a theory note, but a careful one.

The soft spots are where the stress-test note lands. The strong claim in Section III—that the bare dark energy itself must cross w=-1—is only as strong as the assumed value of Omega_de(z≈1). Eq. (9) gives w1 < -1 if Omega_de(1) stays near its LambdaCDM value, but the paper itself notes that forcing w1 ≥ -1 only requires Omega_de(z=1) ≈ 0.27 ± 0.02, about 20% above LambdaCDM. It then says this will affect growth, but no growth or ISW calculation follows. That is a plausibility argument, not a demonstration. The measurement side is also thin: q1 is only about 2 sigma from LambdaCDM. The low-redshift leg is on better footing, but the numbers w0 ≈ -0.76 and Omega_de,0 ≈ 0.7 are point estimates from a GP reconstruction without full error propagation. The paper acknowledges most of this; acknowledging it does not make the conclusion quantitative.

I don't see a circularity problem—the numbers come from an external reconstruction and energy conservation, not from fitting the conclusion. The citation pattern is self-heavy ([5] and the author's earlier modified-gravity papers) but the overlap is explicit and the new derivation stands on its own.

Who should read it: model builders who want a quick, model-insensitive argument against simple interaction mechanisms. It deserves a serious referee, but the referee should ask for at least an order-of-magnitude growth and ISW estimate before the 'must cross' claim is stated as robust, and for error bars on Eq. (10). With those, this becomes a solid conditional result. I would not take the strongest form as established.

Referee Report

3 major / 4 minor

Summary. The manuscript argues that current BAO, supernova, and CMB distance data, as encoded in the Gaussian process reconstruction of [15], prefer a cosmology with stronger acceleration than LambdaCDM at z ~ 0.5-1.5 and weaker acceleration at z < 0.5. The paper derives the deceleration-parameter identity q(z) = (1/2)[1 + 3 w_de Omega_de(z)] in which the interaction Q cancels, and uses this identity to examine three ways of producing an effective dark energy equation of state that crosses w = -1: uplifting an intrinsic phantom, depressing an intrinsic thawing field, and tilting through a sign-changing Horndeski G4 coupling. The central conclusion is that, because interactions shift the coupled dark matter equation of state and hence growth of structure, they generically fail as a viable mechanism for crossing w = -1; the bare dark energy itself must already cross w = -1. A minimal G4(phi) tilt model is presented as a possible but admittedly unproven loophole.

Significance. If the central claim were established with full error propagation and growth calculations, the paper would be significant: it would redirect attempts to explain the DESI DR2 dynamical dark energy signal away from single-field interaction mechanisms and toward intrinsic phantom-crossing behavior. The algebraic steps in Eqs. (3)-(12) are transparent and correct, and the paper is commendably explicit about its limitations, notably at the end of Section IV and in the final paragraph of Section VI. However, the strongest conclusion is conditional on an assumption about the allowed range of Omega_de(z), on a ~2 sigma reconstruction of q1, and on an order-of-magnitude assessment of growth effects; no growth or integrated Sachs-Wolfe calculation is carried out. The paper is therefore best read as a useful framework and plausibility analysis rather than a demonstrated exclusion of interacting dark energy.

major comments (3)

[Section V, q1 estimate] The headline claim that the bare dark energy equation of state must itself cross w = -1 follows from Eq. (9) only if Omega_de(z) is known independently. The paper assumes Omega_de,0 ~ 0.7 +/- 0.1 (Section III) and allows Omega_de(z=1) to deviate by at most 10% from its LambdaCDM value (Section V); when w1 >= -1 is forced, Omega_de(z=1) >= 0.27 +/- 0.02 is dismissed as having 'a concomitant impact on growth of structure' without a growth calculation. Since Eq. (9) can be rewritten as w_de(z) = (2q(z)-1)/(3 Omega_de(z)), a constant bare w near -0.76 with Omega_de(z=1) in the range 0.27-0.35 can reproduce the quoted q(z) values without any phantom crossing. The 'must' claim is therefore conditional on an unquantified prior on Omega_de(z); a concrete growth and ISW calculation for at least one representative interacting model with constant bare w is needed to support the strong form of the conclusion.
[Section V, q1 estimate] The high-redshift side of the argument rests on q(z=1) = 0.1 +/- 0.03 from the Gaussian process reconstruction of [15]. Relative to the LambdaCDM expectation q(z=1) ~ 0.16 (for Omega_m,0 ~ 0.3), this is only a roughly 2 sigma deviation, and Gaussian process priors, systematics, and dataset choices can all affect q1. The paper should show how the inferred w1 and the crossing requirement change when q1 is varied within its 1 sigma and 2 sigma ranges and when alternative reconstructions or distance-only fits are used. Without this robustness check, the statement that 'the data seems to require' intrinsic crossing overstates the statistical support.
[Section IV, Eqs. (10)-(12)] The viability argument against uplifting phantom dark energy uses point estimates q0 ~ -0.3, Omega_de,0 ~ 0.7, and w_eff_de ~ -0.8 without propagating their quoted uncertainties or correlations, and Eq. (12) is derived under the approximation rho_de ~ rho_m. The resulting w_eff_m ~ -0.2 to -0.24 is then compared to observational bounds that vary by orders of magnitude depending on the assumed time dependence of w_eff_m. Since the conclusion is that uplifting is 'quite difficult to make viable,' the paper should either propagate the quoted uncertainties through Eqs. (10)-(12) or explicitly frame the conclusion as an order-of-magnitude plausibility statement rather than a quantitative exclusion.

minor comments (4)

[Section III, after Eq. (9)] The sentence 'the interaction Q does not explicitly appear' could be misread as claiming Q has no effect on q; the next clause does clarify that Q is hidden inside the evolution of Omega_de(z), but the wording should be tightened to avoid an apparent contradiction.
[Section V] The 'up to 10% deviation' in Omega_de(z=1) is introduced without a cited basis or derivation; it should be labeled as an illustrative assumption and, ideally, justified with growth or CMB constraints.
[Section VI, Eqs. (13)-(15) and following] The notation c2s for the scalar sound speed should be written c_s^2, and the proportionality c_s^2 proportional to alpha_M is stated without the coefficient or the conditions beyond the cited references; one sentence specifying the regime of validity would help.
[Section VI, G4 example] For the illustrative G4(phi) = (M_Pl^2/2)[1 + c1 phi - c2 phi^2], the units of c1 and c2 and the conditions on phi/f are not stated; adding a sentence would make the example self-contained.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the crossing inference follows algebraically from Eq. (9) plus external Gaussian-process data and an explicit Omega_de assumption.

full rationale

The paper's central claim is not equivalent to its inputs by construction. The key relation is Eq. (9), q(z) = (1/2)[1 + 3 w_de(z) Omega_de(z)], which is derived algebraically from the continuity equations with an arbitrary interaction Q; the interaction cancels exactly. The paper then combines this relation with externally reconstructed q0 ~ -0.3 +/- 0.1 and q1 ~ 0.1 +/- 0.03 from Lodha et al. [15] and with stated assumptions on Omega_de,0 ~ 0.7 +/- 0.1 and Omega_de(z=1) within ~10% of the LambdaCDM value. The derived values w0 ~ -0.76 and w1 ~ -1.13 to -1.19 are arithmetic consequences of these inputs, not parameters fitted to the conclusion. No fitted quantity is renamed as a prediction. Self-citations such as [5] provide motivation and the four phenomenological properties, but the crossing inference is not obtained by citing [5]; it follows from Eq. (9) and the external data reconstruction. The paper also explicitly acknowledges its limitations, noting that 'a more thorough calculation would need to assume a specific form of interaction, which we have avoided here' (Section IV) and that growth-of-structure agreement is not established for the tilting model (Section VII). The Omega_de(z ~ 1) assumption is a genuine prior, and if it were relaxed the conclusion would weaken, but that is a robustness or correctness concern, not circularity. The derivation chain is self-contained in the sense required here, so the circularity score is 0.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The paper's quantitative conclusions rest on a handful of external data values and physics assumptions rather than on fitted parameters introduced here. No new particles, forces, fields, or dimensions are postulated; the running Planck mass and Horndeski G4(phi) coupling are existing theoretical structures. The main assumptions are listed above.

free parameters (6)

q0 (today's deceleration parameter, GP reconstruction from [15]) = -0.3 +/- 0.1
Used in Eqs. (9)-(10) to derive the bare w0 and the required dark energy density; central to the weaker-acceleration-today constraint.
q1 (deceleration at z=1, GP reconstruction) = 0.1 +/- 0.03
Used to derive w1 at z=1 and the required Omega_de(z=1) about 0.27 for stronger mid-redshift acceleration.
w_eff_de(z=0) (effective dark energy equation of state today) = -0.8 +/- 0.07
Taken from the Gaussian process reconstruction in [15]; used to compute the required uplift and the dark matter equation-of-state shift.
Omega_de,0 (assumed effective dark energy fraction today) = 0.7 +/- 0.1
Chosen as 'quite reasonable' to limit growth disruption; directly sets w0 via Eq. (9).
Omega_de(z=1) deviation tolerance = 10% above LCDM value
Allowed deviation chosen by hand in Section V to assess mid-redshift requirements; larger deviations would worsen matter-sector damage.
Bare thawing w0 at z=0 = -0.9
Assumed for the illustrative tilting model in Section VI; not fitted to data.

assumptions (6)

standard math Combined dark matter plus dark energy energy-momentum conservation with interaction Q (Eqs. 1-2)
Basis for the effective equation-of-state definitions; follows from diffeomorphism invariance.
domain assumption Gaussian process reconstruction of q(z) and w_eff(z) from [15] is a valid representation of BAO+SN+CMB data
All quantitative inputs q0, q1, and w_eff_de are taken from Fig. 9 of [15] without re-analysis.
domain assumption Observational limits on a nonzero dark matter equation of state (10^-3 to 10^-1 depending on time dependence) apply to the effective w_m induced by interactions
Used to reject uplifting and depressing models; limits are drawn from references [16-23] and assumed applicable.
domain assumption For Horndeski G4-only theories, the running Planck mass is tied to alpha_M, alpha_B=-alpha_M, and the sound speed c_s^2 is proportional to alpha_M at early times
Underpins the tilting analysis in Section VI; relies on references [24-26].
ad hoc to paper Thawing PNGB potential with phi_i about 0 describes the intrinsic dark energy in the tilting example
Illustrative model choice in Section VI, not required for the main no-interaction conclusion.
domain assumption The four data-inspired properties from [5] (w<-1 at z>0.5, superevolution, crossing, w>-1 at z<0.5) are taken at face value
The entire analysis starts from these properties, which the paper notes are below the 5-sigma threshold.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Uplifting, Depressing, and Tilting Dark Energy." pith.science (2026). https://pith.science/paper/ZIR3DMUZ

@misc{pith2026250602122,
  author       = {Pith},
  title        = {Pith review of: Uplifting, Depressing, and Tilting Dark Energy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZIR3DMUZ}},
  note         = {Machine review of arXiv:2506.02122}
}

abstract

Current data in the form of baryon acoustic oscillation, supernova, and cosmic microwave background distances prefer a cosmology that accelerates more strongly than $\Lambda$CDM at $z\approx0.5-1.5$, and more weakly at $z\lesssim0.5$. We examine dark energy physics that can accommodate this, showing that interactions (decays, coupling to matter, nonminimal coupling to gravity) fairly generically tend not to give a satisfactory solution (in terms of fitting both distances and growth) even if they enable the effective dark energy equation of state to cross $w=-1$. To fit the cosmological data it appears the dark energy by itself must cross $w=-1$, a highly unusual physical behavior.

Discussion (0). Sign in to comment.

Forward citations

Cited by 6 Pith papers

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

Rolling Galileons: Evolving Braiding Strength for Viable Dark Energy
astro-ph.CO 2026-07 conditional novelty 7.0 of 10

Rolling Galileon gravity, with field-dependent coupling coefficients, can produce a viable phantom-crossing dark energy with healthy void screening and an acceptable fit to expansion data.
Cosmological Evidence for Dark Axion-Dark Baryon Interactions from Apparent Phantom Crossing
astro-ph.CO 2026-07 conditional novelty 6.0 of 10

Dark axion–dark baryon interactions improve the fit to CMB+DESI+SNe by Δχ²=-14.5 over ΛCDM, via a non-monotonic dark-matter mass that mimics phantom crossing, while leaving the Hubble tension unresolved.
Realizing the phantom-divide crossing with vector and scalar fields
astro-ph.CO 2026-01 conditional novelty 6.0 of 10

A scalar-vector-tensor dark-energy model crosses the phantom divide at low redshift with no ghost or Laplacian instabilities and growth signatures close to LCDM.
Scaling solutions in three-form cosmology
astro-ph.CO 2026-02 conditional novelty 5.0 of 10

A generalized three-form dark-energy Lagrangian admits stable scaling attractors that track the dominant cosmic fluid and, via a double-potential extension, exit to late-time acceleration — physical content dual to kn...
A short review on Quintom dark energy theory
astro-ph.CO 2026-05 unverdicted novelty 2.0 of 10

Quintom dark energy models permit the equation of state to cross w=-1, supporting bouncing cosmologies and CMB-based tests of dark energy nature.
Looking beyond lambda
astro-ph.CO 2025-08 unverdicted novelty 2.0 of 10

A perspective piece argues that LambdaCDM is showing cracks and that cosmologists should prepare for a beyond-LambdaCDM era with more complex dark energy models.

Reference graph

Works this paper leans on

28 extracted references · 5 canonical work pages · cited by 6 Pith papers

[5]

Linder, Interpreting Dark Energy Data Away from Λ, arXiv:2410.10981

E.V. Linder, Interpreting Dark Energy Data Away from Λ, arXiv:2410.10981

arXiv
[15]

Lodha et al., Extended Dark Energy analysis using DESI DR2 BAO measurements, arXiv:2503.14743

K. Lodha et al., Extended Dark Energy analysis using DESI DR2 BAO measurements, arXiv:2503.14743

arXiv
[1]

DESI Collaboration, DESI DR2 Results II: Measure- ments of Baryon Acoustic Oscillations and Cosmological Constraints, arXiv:2503.14738

arXiv
[2]

DESI Collaboration, DESI DR2 Results I: Baryon Acoustic Oscillations from the Lyman Alpha Forest, arXiv:2503.14739

arXiv
[3]

Caldwell, E.V

R.R. Caldwell, E.V. Linder, The Limits of Quintessence, Phys. Rev. Lett. 95 (2005) 141301 [arxiv:astro- ph/0505494]

work page arXiv 2005
[4]

Linder, The Paths of Quintessence, Phys

E.V. Linder, The Paths of Quintessence, Phys. Rev. D 73, 063010 (2006) [arXiv:astro-ph/0601052]

arXiv 2006
[6]

Bellini, I

E. Bellini, I. Sawicki, Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity, JCAP 1407, 050 (2014) [arXiv:1404.3711]

arXiv 2014
[7]

Vikman, Can dark energy evolve to the Phantom?, Phys

A. Vikman, Can dark energy evolve to the Phantom?, Phys. Rev. D 72, 043527 (2005) [arXiv:astro-ph/0407107]

arXiv 2005

Show all 28 references

[8]

Caldwell, M

R.R. Caldwell, M. Doran, Dark-Energy Evolution Across the Cosmological-Constant Boundary, Phys.Rev. D 72, 043527 (2005) [arXiv:astro-ph/0501104]

2005 arXiv
[9]

Sen, Reconstructing K-essence, JCAP 0603, 010 (2006) [arXiv:astro-ph/0512406]

A.A. Sen, Reconstructing K-essence, JCAP 0603, 010 (2006) [arXiv:astro-ph/0512406]

2006 arXiv
[10]

Chakraborty, P.K

A. Chakraborty, P.K. Chanda, S. Das, K. Dutta, DESI results: Hint towards coupled dark matter and dark en- ergy, arXiv:2503.10806
[11]

Khoury, M-X

J. Khoury, M-X. Lin, M. Trodden, Apparent w <−1 and a Lower S8 from Dark Axion and Dark Baryons Interac- tions, arXiv:2503.16415
[12]

W.J. Wolf, C. Garc ´ ıa-Garc ´ ıa, T. Anton, P.G. Fer- reira, Cosmological Evidence for Non-Minimal Coupling, arXiv:2504.07679

arXiv
[13]

Andriot, Phantom Matters, arXiv:2505.10410

D. Andriot, Phantom Matters, arXiv:2505.10410

arXiv
[14]

Y. Cai, X. Ren, T. Qiu, M. Li, X. Zhang, Quintom theory of dark energy after DESI DR2, arXiv:2505.24732

arXiv
[16]

C. M. M¨ uller, Cosmological bounds on the equation of state of dark matter, Physical Review D 71, 047302 (2005) [arXiv:astro-ph/0410621]

2005 arXiv
[17]

Armendariz-Picon and J.T

C. Armendariz-Picon and J.T. Neelakanta, How cold is cold dark matter?, JCAP 1403, 49 (2014) [arXiv:1309.6971]

2014 arXiv
[18]

Thomas, M

D.B. Thomas, M. Kopp, and C. Skordis, Constrain- ing the properties of dark matter with observations of the cosmic microwave background, ApJ 830, 155 (2016) [arXiv:1601.05097]

2016 arXiv
[19]

Ili´ c, M

S. Ili´ c, M. Kopp, C. Skordis, and D.B. Thomas, Dark matter properties through cosmic history, Phys. Rev. D 104, 043520 (2021) [arXiv:2004.09572]

2021 arXiv
[20]

Yadav, S.K

V. Yadav, S.K. Yadav, and A.K. Yadav, Observational constraints on generalized dark matter properties in the presence of neutrinos with the final Planck release, Phys. Dark Universe 42, 101363 (2023) [arXiv:2307.05155]

2023 arXiv
[21]

Meiers, L

M. Meiers, L. Knox, and N. Sch¨ oneberg, Exploration of the pre-recombination universe with a high-dimensional model of an additional dark fluid, Phys. Rev. D 108, 103527 (2023) [arXiv:2307.09522]

2023 arXiv
[22]

Naidoo, Signs of a non-zero equation-of-state for dark matter, arXiv:2308.13617

K. Naidoo, Signs of a non-zero equation-of-state for dark matter, arXiv:2308.13617

arXiv
[23]

Zhumabek, M

T. Zhumabek, M. Denissenya, E.V. Linder, Model Inde- pendent Dark Matter Properties from Cosmic Growth, JCAP 2402, 018 (2024) [arXiv:2311.13795]

2024 arXiv
[24]

Linder, Challenges in Connecting Modified Grav- ity Theory and Observations, Phys

E.V. Linder, Challenges in Connecting Modified Grav- ity Theory and Observations, Phys. Rev. D 95, 023518 (2017) [arXiv:1607.03113]

2017 arXiv
[25]

Linder, G

E.V. Linder, G. Seng¨ or, S. Watson, Is the Effective Field Theory of Dark Energy Effective?, JCAP 1605, 053 (2016) [arXiv:1512.06180]

2016 arXiv
[26]

Linder, Limited Modified Gravity, JCAP 2010, 042 (2020) [arXiv:2003.10453]

E.V. Linder, Limited Modified Gravity, JCAP 2010, 042 (2020) [arXiv:2003.10453]

2020 arXiv
[27]

Frieman, C.T

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

1995 arXiv
[28]

Y-S. Song, W. Hu, I. Sawicki 2007, Phys. Rev. D 75, 044004 [arXiv:astro-ph/0610532]

2007 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [5]

Linder, Interpreting Dark Energy Data Away from Λ, arXiv:2410.10981

E.V. Linder, Interpreting Dark Energy Data Away from Λ, arXiv:2410.10981

arXiv

[2] [15]

Lodha et al., Extended Dark Energy analysis using DESI DR2 BAO measurements, arXiv:2503.14743

K. Lodha et al., Extended Dark Energy analysis using DESI DR2 BAO measurements, arXiv:2503.14743

arXiv

[3] [1]

DESI Collaboration, DESI DR2 Results II: Measure- ments of Baryon Acoustic Oscillations and Cosmological Constraints, arXiv:2503.14738

arXiv

[4] [2]

DESI Collaboration, DESI DR2 Results I: Baryon Acoustic Oscillations from the Lyman Alpha Forest, arXiv:2503.14739

arXiv

[5] [3]

Caldwell, E.V

R.R. Caldwell, E.V. Linder, The Limits of Quintessence, Phys. Rev. Lett. 95 (2005) 141301 [arxiv:astro- ph/0505494]

work page arXiv 2005

[6] [4]

Linder, The Paths of Quintessence, Phys

E.V. Linder, The Paths of Quintessence, Phys. Rev. D 73, 063010 (2006) [arXiv:astro-ph/0601052]

arXiv 2006

[7] [6]

Bellini, I

E. Bellini, I. Sawicki, Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity, JCAP 1407, 050 (2014) [arXiv:1404.3711]

arXiv 2014

[8] [7]

Vikman, Can dark energy evolve to the Phantom?, Phys

A. Vikman, Can dark energy evolve to the Phantom?, Phys. Rev. D 72, 043527 (2005) [arXiv:astro-ph/0407107]

arXiv 2005