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Upper limits on dark energy-dark matter interaction from DESI DR2 in a field-theoretic analysis

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Pith's one-line read DESI DR2 data rule out the strong-coupling regime of a field-theoretic dark matter–dark energy interaction, the interaction that would transmute thawing quintessence into freezing, and bound the surviving weak coupling at log λ around −5.5.

desk verdict Field-theoretic DM-DE interaction model with new DESI DR2 limits; background argument solid, perturbation-level limits need validation of the averaging scheme and a specified DM mass. read the letter →

arxiv 2411.11177 v3 pith:A2H3GNME submitted 2024-11-17 astro-ph.CO

Amin Aboubrahim , Pran Nath This is my paper · ORCID
classification astro-ph.CO
keywords darkenergymatter-darkinteractionquintessenceDESIDR2ultralightscalarfieldmatterthawingandfreezingequationofstateMCMCcosmologicalconstraints
topics Dark EnergyDark Matter
open problems Dark MatterDark Energy
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 asks whether dark energy could be a dynamical quintessence field rather than a cosmological constant, and whether dark matter and dark energy interact. It builds a Lagrangian-based two-field model — an ultralight scalar dark matter field coupled to a quintessence field through a potential $\frac{\lambda}{2}\chi^{2}\varphi^{2}$ — and shows that the widely used fluid equations with hand-added $\pm Q$ source terms are inconsistent with field theory. The central result is that DESI DR2 data cut the model in two: the strong-coupling regime ($\lambda \geq 10^{-2}$), which would transmute thawing quintessence into a freezing one, is ruled out, while the weak-coupling regime survives and is bounded from above, with $\log\lambda \lesssim -5.5$ once perturbations are included. $\Lambda$CDM still sits inside the $1\sigma$ region of the $w_0$–$w_a$ plane, but the best-fit points lie in the fourth quadrant, mildly favouring an evolving dark energy equation of state without crossing the phantom divide.

What carries the argument

The machinery is a two-field Lagrangian: an ultralight scalar dark matter field $\chi$ with potential $V_1 = \frac{1}{2}m_\chi^2\chi^2$, a pseudo-Nambu-Goldstone quintessence field $\varphi$ with $V_2 = \mu^{4}(1+\cos(\varphi/F))$, and the interaction $V_{12} = \frac{\lambda}{2}\chi^{2}\varphi^{2}$. Because $\chi$ oscillates far faster than the Hubble rate, the Klein-Gordon equation is recast into averaged variables ($\tilde{\Omega}_\chi$, $\theta$, $y$) so the oscillations are absorbed into $\theta$ and the time-averaged field behaves as pressureless dark matter. The physical switch is the effective mass the interaction gives the quintessence field, $m_\varphi^2 = \lambda\chi^2 - \mu^{4}/F^{2}$: for strong $\lambda$ this becomes positive and drives late-time oscillations of $\varphi$, and the total potential $V_2+V_{12} \simeq 2\mu^{4} + V_0\varphi^{2}$ matches the $\cosh$-type double-exponential potential of scaling-freezing quintessence, the transmutation that DESI rules out. The quantitative work is done by implementing these background and perturbation equations in a Boltzmann solver and MCMC-sampling the four model parameters ($F$, $\varphi_{\rm ini}$, $\mu^{4}$, $\lambda$) together with the standard cosmological parameters against Planck CMB, DESI DR2 BAO and three supernova samples; the perturbation-sector constraints on $\lambda$ are the ones that set the final upper limits.

What would settle it

A decisive check would be to feed the strong-coupling benchmarks ($\lambda \ge 10^{-2}$) directly into the DESI DR2 likelihood using the model's actual distance and power-spectrum predictions, bypassing the fitted $w_0$–$w_a$ compression; if any strongly coupled benchmark landed within $2\sigma$ of the data, the claim that this regime is ruled out would collapse.

Watch

Extended reading notes

Core claim

The paper's claim is that a field-theoretically consistent interaction between dark matter and dark energy, $V_{12}=\frac{\lambda}{2}\chi^{2}\varphi^{2}$ between an ultralight scalar DM field $\chi$ and a pseudo-Nambu-Goldstone quintessence field $\varphi$ with $V_{2}=\mu^{4}(1+\cos(\varphi/F))$, produces a dark energy equation of state whose behaviour is controlled by the size of $\lambda$. For strong coupling ($\lambda\ge 10^{-2}$, in units of $m_{\rm pl}^{-2}\,{\rm Mpc}^{-2}$) the interaction gives the quintessence field a positive effective mass late in cosmic history, the total potential rolls into a $\cosh$-like double-exponential shape, and the equation of state transmutes from thawing to scaling freezing; this freezing behaviour conflicts with DESI DR2's preference for $w_0>-1$, $w_a<0$, so the strong-coupling region is excluded. In the weak-coupling regime the thawing character is retained, and a full MCMC analysis against Planck 2018 CMB, DESI DR2 BAO and three supernova samples (PantheonPlus+SH0ES, Union3, DESY5) sets upper limits on the interaction strength: $\log\lambda < -5.49$ to $-5.69$ at 95% CL with perturbations included, compared with $-2.78$ to $-3.26$ from background evolution alone. In the $w_0$–$w_a$ plane $\Lambda$CDM lies inside the $1\sigma$ contour while all best-fit points fall in the fourth quadrant, and the information criteria ($\Delta{\rm DIC}<0$, $\Delta{\rm AIC}>10$) show the data still prefer the non-interacting model.

Load-bearing premise

The load-bearing premise is that the fast-oscillating dark matter field, once time-averaged, behaves exactly like pressureless cold dark matter, and that the perturbation calculation — started from zero perturbations and gauge-fixed by adding a tiny cold dark matter component ($\Omega_{\rm CDM} h^2 = 10^{-5}$) — faithfully represents the model; if either assumption fails, the quoted bounds on the interaction strength could be wrong.

Editorial extensions

If this is right

  • The strong-coupling regime ($\lambda \geq 10^{-2}$) is excluded: a dark matter–dark energy interaction strong enough to transmute thawing quintessence into scaling freezing is incompatible with DESI DR2.
  • With perturbations included, the surviving interaction strength is bounded by $\log\lambda < -5.49$ to $-5.69$ at 95% CL depending on the supernova sample, roughly two orders of magnitude tighter than the background-only bounds of $-2.78$ to $-3.26$.
  • $\Lambda$CDM remains inside the $1\sigma$ contour of the $w_0$–$w_a$ plane, yet the best-fit points for all data combinations lie in the fourth quadrant, leaving room for a mildly evolving dark energy equation of state that never crosses the phantom divide.
  • Model comparison by information criteria shows the data prefer the non-interacting model ($\Delta{\rm DIC}<0$; $\Delta{\rm AIC}>10$), so the interaction is constrained rather than required by DESI DR2.
  • The model can only moderately ease the Hubble tension ($H_0$ near 69 km/s/Mpc versus the local value of 73.04), while its $S_8$ values agree with recent weak lensing measurements.

Reading between the lines

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

  • Translated out of the model's units ($m_{\rm pl}^{-2}\,{\rm Mpc}^{-2}$) into a dimensionless particle coupling for a given dark matter mass, $\log\lambda \lesssim -5.5$ would put the interaction far beyond any foreseeable laboratory sensitivity; the paper does not perform this translation, but the bound implies that an observable dark matter–dark energy scattering would require physics beyond this
  • Because the tightest limits come from the perturbation sector, where the synchronous gauge is fixed by adding a tiny cold dark matter component ($\Omega_{\rm CDM} h^2 = 10^{-5}$), the jump from background bounds ($\log\lambda \lesssim -3$) to perturbation bounds ($\log\lambda \lesssim -5.5$) deserves an independent check in a different gauge or with a treatment that avoids that crutch.
  • The feature-importance analysis shows that which parameter drives the fit depends on the supernova calibration, with the coupling $\lambda$ most important for PantheonPlus and the potential scale $F$ for Union3 and DESY5; a consequence left implicit is that the quoted upper limit on $\lambda$ is sensitive to which supernova sample is trusted.
  • Re-running the same machinery with a different quintessence potential would test whether the fourth-quadrant preference for $(w_0, w_a)$ is a generic feature of field-theoretic dark matter–dark energy interactions or a particularity of the cosine potential chosen here.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper studies a field-theoretic interacting quintessence-dark matter model (QCDM) with an ultralight scalar dark matter field chi and a quintessence field phi coupled through V_int = (lambda/2) chi^2 phi^2. It argues that fluid-based interacting dark energy-dark matter models are inconsistent with field theory, derives background and perturbation equations, and identifies strong and weak coupling regimes for lambda. Using DESI DR2 w0-wa contours, the paper claims to rule out the strong-coupling region (lambda >~ 10^-2) on the basis of the transmutation of thawing quintessence into freezing quintessence, and then derives upper limits on lambda in the weak-coupling region. A separate CLASS+Cobaya MCMC analysis with Planck, DESI DR2 BAO, and three supernova datasets yields perturbation-level upper limits log lambda < -5.49 and < -5.69 for two of the dataset combinations, with Delta AIC > 10 favoring LambdaCDM in all cases and best-fit w0-wa points lying in the fourth quadrant.

Significance. If the central results hold, the paper provides a useful field-theoretic counterpoint to the common phenomenological interacting-fluid models and delivers quantitative DESI DR2 constraints on a concrete DM-DE interaction. The work has several genuine strengths: the derivation in Section 3 and Appendix A that energy exchange in the fluid picture is inconsistent with a local field theory is explicit and instructive; the background analysis identifies a sharp, physically motivated distinction between strong and weak coupling; and the MCMC analysis uses standard public likelihoods and honestly reports that LambdaCDM is preferred by Delta AIC > 10. The upper limits on lambda, if trustworthy, would be of direct interest for model building. However, the perturbation-level limits in Table 2 rest on an averaged-field treatment and a gauge-fixing workaround that are not validated, and the strong-coupling exclusion depends on an undocumented scan. These load-bearing gaps currently prevent the paper from delivering a fully supported upper-limit claim.

major comments (4)
  1. [Section 6] The perturbation-level constraints in Table 2 rest on two assumptions that are stated but not validated: (i) that setting chi_1 = chi_1' = 0 and phi_1 = phi_1' = 0 is harmless because the perturbations are 'quickly driven to the attractor solution'; and (ii) that adding a tiny CDM component with Omega_CDM h^2 = 10^-5 fixes the synchronous gauge even though the scalar field has a dynamical equation of state. For a scalar field, zero initial perturbations do not generally eliminate the residual gauge mode in synchronous gauge, and the paper provides no convergence test, no comparison with a different gauge, and no demonstration that the 10^-5 CDM component is negligible for the perturbation likelihood. Without such a check, the limits log lambda < -5.49 and < -5.69 quoted in Table 2 could be biased by the gauge choice or the initialization scheme.
  2. [Section 5.1] The claim that the strong-coupling region is ruled out is the paper's headline result, but it rests on an undocumented scan. The text says 'We thoroughly checked that no parameter combination can be chosen that will fit the w0 and wa values in the strong coupling regime' (Section 5.1), yet no ranges for F, phi_ini, mu^4, and lambda, no number of sampled points, no fitting criterion, and no treatment of m_chi are given, and no code or data release is provided. The exclusion should either be made reproducible or replaced by a documented MCMC or grid scan over the strong-coupling region; as written, the reader cannot verify the central 'rule out' claim.
  3. [Section 4] The averaged-variable scheme in Eqs. (4.10)-(4.12) is central to the background and perturbation analysis, but it is not validated against a direct integration of the Klein-Gordon system (4.4)-(4.5) for any parameter set or redshift. In particular, the interaction source terms in Eqs. (4.10)-(4.11) contain oscillatory combinations such as chi' V_12,chi and V_12, and it is not shown that the coarse-grained variables reproduce the time-averaged exact evolution, especially during the epoch when the phi field itself begins to oscillate around a ~ 0.1 (Section 5.1). If this averaging is inaccurate, the fitted w0 and wa values and hence the lambda limits in Table 2 could be biased. A direct-integrator comparison for representative benchmarks is needed.
  4. [Section 5, Eqs. (5.1)-(5.3)] The dark matter mass m_chi is never specified anywhere in Sections 5-6 or in Table 2, yet the attractor initial conditions in Eqs. (5.1)-(5.3) depend explicitly on m_chi through y_ini = 2 m_chi/H0 a_ini^2 Omega_rad0^{-1/2}. The value of m_chi also controls the oscillation frequency and the validity of the time-averaging approximation. Without specifying m_chi, or demonstrating that all results are independent of it, the physical regime being constrained is not fully defined and the numerical results are not reproducible.
minor comments (5)
  1. [Section 4] The first sentence refers to a 'flat FLR W metric'; this should be the 'flat FLRW metric'.
  2. [Section 5.2, Eq. (5.15)] The chi^2 in Eq. (5.15) uses sigma_i, but the uncertainty sigma_i in the fit to w_phi(a) is not defined; please specify how the error band around the model EoS is estimated.
  3. [Section 6, Eq. (6.1)] The prior ranges for the sampled parameters log mu^4, F, phi_ini, and log lambda are not stated, despite the statement that flat priors are imposed; prior ranges should be given, since they can affect the quoted upper limits on log lambda.
  4. [Table 2 and Section 6 text] The text 'All three data sets indicate a weak DM-DE coupling' is ambiguous because Table 2 shows four dataset combinations; please specify which three are meant and how the CMB+DESI column, which gives a two-sided log lambda interval rather than an upper limit, is treated.
  5. [Figures 6 and 9] The color bars for H0 and log lambda in Figures 6 and 9 are very small and difficult to read in the reproduced manuscript; increasing the font size and labeling the units explicitly would improve clarity.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the DESI DR2 upper bounds on lambda come from an MCMC over external Planck/DESI/SN likelihoods, and the w0-wa comparisons are forward-model outputs, not fitted inputs.

full rationale

The central claim, that DESI DR2 data exclude the strong-coupling regime and place upper limits on the dark matter-dark energy interaction strength, is not circular. The limits in Table 2 (log lambda below -5.49 to -5.69) come from interfacing CLASS with Cobaya and sampling over Planck, DESI DR2 BAO, and supernova likelihoods; lambda is a sampled parameter constrained by external data, not a fitted quantity relabeled as a prediction. The w0 and wa values are derived parameters: they are obtained by fitting the model's own w_phi(a) to the CPL form via Eqs. (5.12)-(5.14) and then compared with, not fitted to, DESI's w0-wa contours. This is a forward-model prediction and does not reduce to the input. The strong-coupling exclusion likewise follows from computing w_phi(a) for lambda >= 10^-2, fitting Eq. (5.7), and showing the resulting (w0, wa) fall outside DESI's 2-sigma region; the comparison is against external data. The only self-citation is motivational ('Motivated by a previous work [56, 57], where the authors have shown that such a field-theoretic approach can alleviate the H0 tension and resolve the S8 tension'), and the technical machinery, including the averaged variables of Eqs. (4.7)-(4.9), the attractor initial conditions (5.1)-(5.3), and the perturbation attractor [77], is drawn from independent external references. No parameter is defined in terms of the target result, and no load-bearing premise is justified solely by a self-citation. The averaging and synchronous-gauge procedure (Omega_CDM h^2 = 10^-5) is a modeling assumption that could affect the limits, but it is not equivalent to the DESI constraints it is used to derive; at most it is a correctness risk. The score of 2 reflects only the minor, non-load-bearing self-citation in the Introduction, not any reduction of the central claim to its inputs.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The central constraint rests on the specific Lagrangian, the oscillating-scalar averaging procedure, the perturbation initial conditions and gauge handling, and the mapping of the model's equation of state to CPL parameters. The paper states most of these, but the dark matter mass and the exact strong-coupling scan are left implicit.

free parameters (7)
  • lambda (dark energy-dark matter interaction strength) = Upper limits: log lambda < -5.49 (DESY5), < -5.69 (Union3); background-only log lambda < -2.78 to -3.26
    Sampled with a flat prior; the headline constraint from DESI DR2.
  • F (quintessence potential scale) = Posterior ranges, e.g. F > 0.561 m_Pl (CMB+DESI) to 0.51+0.20-0.22 (with DESY5)
    Scale in the quintessence potential V2 = mu^4 (1 + cos(phi/F)); sampled in the MCMC.
  • phi_ini (initial quintessence field value) = Upper limits < 0.157 to < 0.560 m_Pl depending on dataset
    Shooting parameter that sets the late-time dark energy evolution.
  • mu^4 (quintessence potential energy scale) = log mu4 approximately -7.23 to -7.18 in m_Pl^2/Mpc^2
    Sampled and adjusted via shooting to match Omega_phi0.
  • m_chi (dark matter scalar mass) = Not specified
    Mass of the scalar dark matter field; enters the initial condition y_ini, Eq. (5.1), but is not sampled or reported.
  • w(a) fit parameters alpha, beta, p, q = Not tabulated
    Parameters of the fitting functions Eqs. (5.7) and (5.12) used to extract w0 and wa; the mapping to DESI contours depends on them.
  • Omega_CDM h^2 (gauge-fixing CDM fraction) = 10^-5
    Artificial CDM component added to fix the synchronous gauge for the scalar-field dark matter, as described in Section 6.
assumptions (6)
  • standard math FLRW background and linear perturbation theory, as implemented in CLASS, describe the universe.
    Used throughout; standard cosmology.
  • domain assumption Rapid oscillations of the chi field time-average to a pressureless CDM fluid, so the averaged variables Eqs. (4.10)-(4.12) capture dark matter evolution.
    Section 4; essential for numerical tractability of the ultralight scalar field.
  • domain assumption The interaction term V12 = lambda/2 chi^2 phi^2 is the only dark matter-dark energy coupling, with no other potential terms of comparable importance.
    Section 2, Eq. (4.3).
  • ad hoc to paper The perturbations chi_1 and phi_1 can be initialized at zero and reach the attractor, and a small CDM component fixes the synchronous gauge despite the non-pressureless scalar.
    Section 6; a modeling choice to handle gauge freedom.
  • ad hoc to paper The fitting functions Eqs. (5.7) and (5.12) faithfully represent the model's equation of state over the range used to extract w0 and wa.
    Section 5; the comparison with DESI contours relies on this mapping.
  • domain assumption DESI DR2 CPL constraints are a valid target even though the model's equation of state is not CPL; matching w0 and wa from a fit captures the relevant observable.
    Sections 5-6; standard practice but not exact.

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Cite this review

Pith. "Pith review of Upper limits on dark energy-dark matter interaction from DESI DR2 in a field-theoretic analysis." pith.science (2026). https://pith.science/paper/A2H3GNME

@misc{pith2026241111177,
  author       = {Pith},
  title        = {Pith review of: Upper limits on dark energy-dark matter interaction from DESI DR2 in a field-theoretic analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/A2H3GNME}},
  note         = {Machine review of arXiv:2411.11177}
}
abstract

One of the important issues both in particle physics and cosmology relates to whether dark energy is a cosmological constant $\Lambda$, or is dynamical in nature such as quintessence. In this work, we discuss a model of quintessence interacting with dark matter and analyze the resulting phenomenology of the dark energy equation of state. We identify two regions where the equation of state behaves differently depending on the size of the dark matter-dark energy interaction strength. We show that the strong coupling region induces a transmutation of quintessence from thawing to freezing. Using the recent data release from the Dark Energy Spectroscopic Instrument (DESI), we rule out this possibility of transmutation and investigate the weak coupling region to derive upper limits on the interaction strength. Our analysis indicates that while $\Lambda$CDM lies within the $1\sigma$ contour in the $w_0$-$w_a$ plane, the best fit points lie in the fourth quadrant and show deviations from the $\Lambda$CDM prediction.

Figures

Figures reproduced from arXiv: 2411.11177 by the authors.

Figure 1
Figure 1. Top panels: plot of the energy density fractions (left) and the energy densities evolution (right) as a function of the scale factor a. Bottom panels: plot of the evolution of the equations of state (EoS) of DM and DE and the total EoS (left) and a time-average over the oscillations in wϕ and wT (right panel). The DM EoS, wχ, is being averaged over in both panels after a short period of oscillations. The color code … view at source ↗
Figure 2
Figure 2. Evolution of the total potential V2(ϕ) + V12(ϕ, χ) (left panel) and the scalar DE field ϕ (right panel) against the scale factor a in the presence of DM-DE interaction. The three benchmarks for (ϕini, µ4 ) are the same as in [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Evolution of wϕ for quintessence for five values of λ as a function of the redshift z. The solid lines are wϕ predicted by QCDM and the dashed lines are fits based on Eq. (5.7) including a 1σ error band around each curve. In each case, quintessence transmutes from thawing (left shoulder) to scaling freezing (right shoulder) induced by λ. We now address the peculiar evolution of wϕ seen in the lower right panel of [… view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: A plot of the EoS of ϕ as a function of the scale factor a exhibiting the thawing behavior (left) when λ = 0 and scaling freezing (right) when λ ̸= 0. The 1σ regions from DESI are shown as blue and green bands. A comparison of the left and the right panels indicates th…
Figure 5
Figure 5. Figure 5: Left panel versus right panel correspond to the no interaction versus non-zero interaction cases. The evolution of the quintessence potential V2(ϕ) (blue), the interaction potential V12 = λϕ2χ 2/2 (red) and the total potential (orange) as a function of the scale factor…
Figure 6
Figure 6. Figure 6: Scatter plots in the w0-wa plane overlaid on top of the posterior contours from DESI DR2. The left panel exhibits the Hubble parameter H0 as the color axis while the right panel shows log λ. The model is able to produce benchmarks that lie in the 1σ and 2σ posteriors o…
Figure 7
Figure 7. Figure 7: The mean absolute Shapley value, |Si |, of the four model input parameters for the three data sets considered by DESI. The parameter with the largest |Si | value has the most impact in bringing the (w0, wa) values to within 2σ of their experimental value. Our model con…
Figure 8
Figure 8. Figure 8: A scatter plot of the model data points showing the Shapley value, Sλ, of the DM-DE coupling λ versus the parameter wa. The color axis represents the values of log λ. The analysis in the left panel is done for the DESI+CMB+PantheonPlus data set while the right panel is…
Figure 9
Figure 9. Figure 9: Scatter plots in the w0-wa plane similar to [PITH_FULL_IMAGE:figures/full_fig_p018_9.png]
Figure 10
Figure 10. Figure 10: Triangle plot showing the 2D joint and 1D marginalized posteriors of log µ 4 , ϕini, F, log λ, H0, σ8 and Ωm in the interacting dark matter-dark energy model for the following data set combinations: CMB+DESI+PPS (red contours), CMB+DESI+DESY5 (blue contours) and CMB+D…
Figure 11
Figure 11. Figure 11: The 2D contours at 68% and 95% CL for the DM-DE coupling strength and H0 (left panel) and S8 (right panel). The gray bands in the left panel correspond to the SH0ES [84] value H0 = 73.04 +±1.04 km/s/Mpc and the ones in the right panel correspond to the KiDS-Legacy [93…
Figure 12
Figure 12. Figure 12: Left panel: Results for the posterior distributions of w0 and wa for the four data set combinations: CMB+DESI (dashed contours), CMB+DESI+PPS (red contours), CMB+DESI+DESY5 (blue contours) and CMB+DESI+Union3 (green contours). The in￾tersection of the dotted vertical …
Figure 13
Figure 13. Figure 13: Results from the second scenario. Plots of the energy density fraction (top left) and the energy density (top right) of all species and the equations of state (EoS) of DM and DE and the total EoS (bottom panels) as a function of the scale factor a. The color code in t…
Figure 14
Figure 14. Figure 14: Triangle plots showing the correlations between different input and output parameters of the model. Notice the strong positive correlation between λ and w0 and between µ 4 and wa. A mild negative correlation exists between λ and wa. 31 [PITH_FULL_IMAGE:figures/full_f…
Figure 15
Figure 15. Figure 15: Same as in [PITH_FULL_IMAGE:figures/full_fig_p032_15.png]
Figure 16
Figure 16. Figure 16: Triangle plot showing the 2D joint and 1D marginalized posteriors of log µ 4 , ϕini, λ, H0, τre, σ8, Ωm, θs, As and ns in the interacting dark matter-dark energy model for the following data set combinations: CMB+DESI (dashed brown contours), CMB+DESI+Pantheon+SH0ES (…

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