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Late-time Background Constraints on Linear and Non-linear Interacting Dark Energy after DESI DR2
Cosmology and Nongalactic Astrophysics · Submitted 6 Jan 2026
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim These results highlight the promising, but problematic, nature of dark sector interactions, as well as the need to extend the analysis using early-time physics and datasets.
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In this study, we present observational constraints on a class of phenomenological interacting dark energy (IDE) models that admit analytical solutions for the Hubble parameter $H(z)$. We consider a set of five linear and three non-linear IDE scenarios, encompassing both interactions proportional to the dark matter and/or dark energy densities, as well as non-linear combinations of the two. For all eight IDE models, we find a better fit than $\Lambda$CDM from a $\Delta\chi^2$ analysis for both combinations of datasets considered. When using the Akaike Information Criterion ($\Delta$AIC), we find a similarly improved fit in all cases, except for one dataset combination in $Q=3H\delta\rho_{\rm de}$. Our analysis also shows a preference for sign-switching interactions, with energy transfer from dark energy to dark matter at low redshift, reversing direction at higher redshift. These results should be interpreted with caution, as the latter direction of energy transfer is accompanied by negative dark energy densities in the past, which may be unphysical. Models that do not allow sign-changing behaviour instead show a preference for energy flow from dark matter to dark energy, and hence negative dark energy densities. The only exceptions are $Q=3H\delta\rho_{\rm de}$ and $Q=3H\delta\left(\tfrac{\rho_{\rm de}^2}{\rho_{\rm dm}+\rho_{\rm de}}\right)$, which exhibit energy flow in the opposite direction. Furthermore, for all interactions considered, we find a phantom-divide crossing in the effective dark energy equation of state $w^{\rm eff}_{\rm de}$, with the dark energy density decreasing ($w^{\rm eff}_{\rm de}>-1$) at present and at low redshift, while increasing ($w^{\rm eff}_{\rm de}<-1$) in the past at high redshift. These results highlight the promising, but problematic, nature of dark sector interactions, as well as the need to extend the analysis using early-time physics and datasets.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this study, we present observational constraints on a class of phenomenological interacting dark energy (IDE) models that admit analytical solutions for the Hubble parameter $H(z)$. | contribution 1.00 | 0.91 | 0.04 | asserted 0.98 |
| s1 | We consider a set of five linear and three non-linear IDE scenarios, encompassing both interactions proportional to the dark matter and/or dark energy densities, as well as non-linear combinations of the two. | method 0.60 | 0.74 | 0.03 | asserted 0.97 |
| s2 | For all eight IDE models, we find a better fit than $\Lambda$CDM from a $\Delta\chi^2$ analysis for both combinations of datasets considered. | result 1.00 | 0.97 | 0.41 | asserted 1.00 |
| s3 | When using the Akaike Information Criterion ($\Delta$AIC), we find a similarly improved fit in all cases, except for one dataset combination in $Q=3H\delta\rho_{\rm de}$. | result 1.00 | 0.97 | 0.11 | asserted 1.00 |
| s4 | Our analysis also shows a preference for sign-switching interactions, with energy transfer from dark energy to dark matter at low redshift, reversing direction at higher redshift. | result 1.00 | 0.95 | 0.31 | asserted 1.00 |
| s5 | These results should be interpreted with caution, as the latter direction of energy transfer is accompanied by negative dark energy densities in the past, which may be unphysical. | limitation 0.93 | 0.61 | 0.10 | hedged possibility 0.94 |
| s6 | Models that do not allow sign-changing behaviour instead show a preference for energy flow from dark matter to dark energy, and hence negative dark energy densities. | result 0.99 | 0.90 | 0.08 | asserted 1.00 |
| s7 | The only exceptions are $Q=3H\delta\rho_{\rm de}$ and $Q=3H\delta\left(\tfrac{\rho_{\rm de}^2}{\rho_{\rm dm}+\rho_{\rm de}}\right)$, which exhibit energy flow in the opposite direction. | result 1.00 | 0.91 | 0.06 | asserted 1.00 |
| s8 | Furthermore, for all interactions considered, we find a phantom-divide crossing in the effective dark energy equation of state $w^{\rm eff}_{\rm de}$, with the dark energy density decreasing ($w^{\rm eff}_{\rm de}>-1$) at present and at low redshift, while increasing ($w^{\rm eff}_{\rm de}<-1$) in the past at high redshift. | result 1.00 | 0.97 | 0.16 | asserted 1.00 |
| s9 | These results highlight the promising, but problematic, nature of dark sector interactions, as well as the need to extend the analysis using early-time physics and datasets. | future work 0.53 | 0.31 | 0.69 | asserted 0.80 |
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The paper
Original abstract
In this study, we present observational constraints on a class of phenomenological interacting dark energy (IDE) models that admit analytical solutions for the Hubble parameter $H(z)$. We consider a set of five linear and three non-linear IDE scenarios, encompassing both interactions proportional to the dark matter and/or dark energy densities, as well as non-linear combinations of the two. For all eight IDE models, we find a better fit than $\Lambda$CDM from a $\Delta\chi^2$ analysis for both combinations of datasets considered. When using the Akaike Information Criterion ($\Delta$AIC), we find a similarly improved fit in all cases, except for one dataset combination in $Q=3H\delta\rho_{\rm de}$. Our analysis also shows a preference for sign-switching interactions, with energy transfer from dark energy to dark matter at low redshift, reversing direction at higher redshift. These results should be interpreted with caution, as the latter direction of energy transfer is accompanied by negative dark energy densities in the past, which may be unphysical. Models that do not allow sign-changing behaviour instead show a preference for energy flow from dark matter to dark energy, and hence negative dark energy densities. The only exceptions are $Q=3H\delta\rho_{\rm de}$ and $Q=3H\delta\left(\tfrac{\rho_{\rm de}^2}{\rho_{\rm dm}+\rho_{\rm de}}\right)$, which exhibit energy flow in the opposite direction. Furthermore, for all interactions considered, we find a phantom-divide crossing in the effective dark energy equation of state $w^{\rm eff}_{\rm de}$, with the dark energy density decreasing ($w^{\rm eff}_{\rm de}>-1$) at present and at low redshift, while increasing ($w^{\rm eff}_{\rm de}<-1$) in the past at high redshift. These results highlight the promising, but problematic, nature of dark sector interactions, as well as the need to extend the analysis using early-time physics and datasets.
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References
How the literature uses it
16 arXiv papers cite this in 18 sentences
Papers citing it · 12 sentences without a confident label
Compares with it 1 paper
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A similar trend was recently observed in Ref. [ref] , even when incorporating cosmic chronometer measurements.
Generalizing the CPL Parametrization through Dark Sector Interaction · Constant coupling models · 0.89
Cites it as background 5 papers
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The possibility of an interaction in the dark sector has been extensively investigated using both parametric approaches [ref] and non-parametric approaches [ref] .
Beyond dynamical dark energy: the role of dark sector interactions after DESI DR2 · Introduction · 1.00
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An incomplete list of these works is given in [ref] .
The optimal redshift for dark energy II: application to cosmological data and the evidence for the phantom crossing of the CPL equation of state · Introduction · 0.93
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For discussions spanning both directions, see Refs. [ref] .]
Unifying Early and Late Dark Energy: Dynamical Requirements and Obstructions · Introduction · 0.98
What it cites · 174 sentences without a confident label
Builds on 3 papers
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This paper should therefore be understood as a continuation of Refs. [ref] .
2509.04494 · Introduction · 0.99
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This paper should therefore be understood as a continuation of Refs. [ref] .
2509.04495 · Introduction · 0.99
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This paper should therefore be understood as a continuation of Refs. [ref] .
2509.04496 · Introduction · 0.99
Uses the method or tool of 3 papers
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We use the public Markov Chain Monte Carlo code [ref] , together with modified versions of [ref] tailored to each interacting scenario.
Conservative Constraints on Early Cosmology: an illustration of the Monte Python cosmological parameter inference code · Observational constraints · 1.00
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We use the public Markov Chain Monte Carlo code [ref] , together with modified versions of [ref] tailored to each interacting scenario.
The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes · Observational constraints · 1.00
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We use the public Markov Chain Monte Carlo code [ref] , together with modified versions of [ref] tailored to each interacting scenario.
MontePython 3: boosted MCMC sampler and other features · Observational constraints · 1.00
Uses data or values from 7 papers
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We consider the following datasets: * Pantheon+ Type Ia supernova data [ref] , calibrated with SH0ES Cepheid data. * DESI DR2 Baryon Acoustic Oscillation data [ref] . * Cosmic Clock measurements [ref] . * Big Bang Nucleosynthesis as a prior on $Ω_b h^2 = 0.02218 ±0.00055$ [ref] [The same prior is used in the DESI DR2 analysis [ref] to break the well-known degeneracy in $H_0 r_d$.].
DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints · Observational constraints · 0.99
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We consider the following datasets: * Pantheon+ Type Ia supernova data [ref] , calibrated with SH0ES Cepheid data. * DESI DR2 Baryon Acoustic Oscillation data [ref] . * Cosmic Clock measurements [ref] . * Big Bang Nucleosynthesis as a prior on $Ω_b h^2 = 0.02218 ±0.00055$ [ref] [The same prior is used in the DESI DR2 analysis [ref] to break the well-known degeneracy in $H_0 r_d$.].
The Pantheon+ Analysis: Cosmological Constraints · Observational constraints · 0.99
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We consider the following datasets: * Pantheon+ Type Ia supernova data [ref] , calibrated with SH0ES Cepheid data. * DESI DR2 Baryon Acoustic Oscillation data [ref] . * Cosmic Clock measurements [ref] . * Big Bang Nucleosynthesis as a prior on $Ω_b h^2 = 0.02218 ±0.00055$ [ref] [The same prior is used in the DESI DR2 analysis [ref] to break the well-known degeneracy in $H_0 r_d$.].
PRyMordial: The First Three Minutes, Within and Beyond the Standard Model · Observational constraints · 0.99
Compares with 1 paper
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As an example, recent constraints on the same linear interactions studied here—but with the direction of energy flow and the sign of $(1+w)$ chosen to ensure stability—can be found in [ref] .
Constraints on interacting dark energy models from Planck 2015 and redshift-space distortion data · Theoretical constraints on the models · 0.85
Cites as support 11 papers
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In general, we find that when energy flows from dark energy to dark matter, a divergent phantom-crossing behaviour is observed for $w̃(z)$ [ref] .
Dark coupling · Phantom-crossing, effective equations of state $w_dm^eff$, $w_de^eff$ and the reconstructed equation of state $w̃$ · 0.96
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In general, we find that when energy flows from dark energy to dark matter, a divergent phantom-crossing behaviour is observed for $w̃(z)$ [ref] .
2509.04494 · Phantom-crossing, effective equations of state $w_dm^eff$, $w_de^eff$ and the reconstructed equation of state $w̃$ · 0.96
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In addition, the matter power spectrum is suppressed with respect to late-time probes, which alleviates the $S_8$ tension [ref] .
Dark energy-dark matter interactions as a solution to the $S_8$ tension · Interacting dark energy models · 0.98
Cites as background 227 papers
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Large galaxy surveys such as DESI [ref] or DES [ref] , extraordinarily precise measurements of the Cosmic Microwave Background from Planck [ref] , and Supernovae light curve observations [ref] , among many others, have elevated cosmology to a discipline built upon exquisite and precise observations.
The Pantheon+ Analysis: Cosmological Constraints · Introduction · 0.93
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Large galaxy surveys such as DESI [ref] or DES [ref] , extraordinarily precise measurements of the Cosmic Microwave Background from Planck [ref] , and Supernovae light curve observations [ref] , among many others, have elevated cosmology to a discipline built upon exquisite and precise observations.
DESI DR2 Results I: Baryon Acoustic Oscillations from the Lyman Alpha Forest · Introduction · 0.93
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Large galaxy surveys such as DESI [ref] or DES [ref] , extraordinarily precise measurements of the Cosmic Microwave Background from Planck [ref] , and Supernovae light curve observations [ref] , among many others, have elevated cosmology to a discipline built upon exquisite and precise observations.
The Dark Energy Survey Supernova Program: A Reanalysis Of Cosmology Results And Evidence For Evolving Dark Energy With An Updated Type Ia Supernova Calibration · Introduction · 0.93
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