Constraints on interacting dark energy with a constant equation of state in light of DESI DR2: The role of the interaction term

arXiv:2610.30784 · astro-ph.CO, gr-qc, hep-ph · Submitted 2026-10-22 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: I'm Vera.

Jocelyn: And I'm Jocelyn, here with Subrahmanyan.

Vera: We're looking at the paper: "Constraints on interacting dark energy with a constant equation of state in light of DESI DR2".

Jocelyn: Here's the gist of the paper. The study investigates how dark energy and dark matter interact within interacting dark energy (IDE) models characterized by a constant equation of state parameter w, using cosmological data from CMB, DESI DR2 BAO measurements, and Type Ia supernova data to constrain the interaction term Q.

Vera: Model Framework The background evolution in a spatially flat Friedmann–Robertson–Walker universe is governed by the Friedmann equation (1) which involves the energy densities of dark energy, cold dark matter (CDM), baryons, and radiation The continuity equations for the dark sector are modified as follows: ρ˙de + 3H(1 + w)ρde = Q, (2) and ρ˙c + 3Hρc = −Q, (3) where Q characterizes the rate of energy transfer between dark energy and CDM To describe the effect of the dark-sector interaction in terms of an effective EoS, the continuity equations can be recast into an equivalent noninteracting form as ρ˙de + 3H(1 + w eff de)ρde = 0, (4) and ρ˙c + 3H(1 + w eff c)ρc = 0, (5) where the effective EoS parameters are given by w eff de = w − Q / 3Hρde and w eff c = Q / 3Hρc Interaction Term Parameterization The interaction term Q is phenomenologically parameterized, assuming that the energy transfer rate is proportional to the energy density of either dark energy or cold dark matter To ensure dimensional consistency, a natural choice for the interaction term is the Hubble parameter H The four representative forms considered are IwCDM1 with Q = βHρde, IwCDM2 with Q = βHρc, IwCDM3 with Q = βH0ρde, and IwCDM4 with Q = βH0ρc The dimensionless coupling parameter β determines the strength and direction of the energy exchange: for β > 0, energy is transferred from cold dark matter to dark energy; for β < 0, the transfer is reversed; and for β = 0, no energy transfer occurs Observational Constraints and Findings The analysis utilized CMB data from Planck, ACT, and SPT, DESI DR2 BAO measurements, and type Ia supernova data from PantheonPlus, DES-Dovekie, and DESY5 The results show that the IDE models with Q ∝ ρde generally exhibit a stronger preference for nonzero dark-sector interactions For the CMB+DESI+DES-Dovekie data, the IDE model with Q = βH0ρde yields β = −2.52+0.80 − 0.54 and w = −1.510+0.170 − 0.120, corresponding to deviations from β = 0 and w = −1 at the 3.2σ and 3.0σ levels, respectively Interestingly, the effective EoS of the IDE model with Q = βH0ρde exhibits a redshift evolution resembling that of the w0waCDM model, crossing the phantom divide Bayesian evidence further indicates that this IDE model is favored over ΛCDM and the other three IDE models Model Comparison and Effectiveness The study compares four representative forms of the interaction term Q using the CMB, DESI, and SN data to determine which IDE model with a constant dark energy EoS parameter w receives the strongest observational support The results show that IwCDM3 generally shows more pronounced departures from the ΛCDM limit than the IwCDM1 model among models with an interaction rate proportional to the dark energy density For the CMB+DESI+DES-Dovekie data, IwCDM3 gives β = −2.52+0.80 − 0.54 and w = −1.510+0.170 − 0.120, corresponding to deviations from β = 0 and w = −1 at approximately the 3.2σ and 3.0σ levels, respectively The significance of these departures depends on the SN compilation, with DESY5 yielding the strongest preference whereas PantheonPlus yields the weakest Overall, IwCDM3 shows both the strongest preference for a nonzero dark-sector interaction and the strongest observational support among the four models considered This is because its effective EoS evolves from the phantom regime at high redshift, crosses the phantom divide w eff de = −1, and enters the quintessence-like region toward low redshift, closely resembling the behavior generated by the w0waCDM model The Bayesian evidence further indicates that models with Q ∝ ρde are more favored by current observations, particularly IwCDM3 Future precision late-time observations from the Large Synoptic Survey Telescope, Euclid, and subsequent DESI data releases will help determine whether the preference for dark-sector interactions persists and to distinguish between different interaction forms.

Jocelyn: Page 1 --- The gist: The study investigates how dark energy and dark matter interact within interacting dark energy (IDE) models characterized by a constant equation of state parameter w, using cosmological data from CMB, DESI DR2 BAO measurements, and Type Ia supernova data to constrain the interaction term Q.

Vera: How it works The background evolution in a spatially flat Friedmann–Robertson–Walker universe is governed by the Friedmann equation (1) which involves the energy densities of dark energy, cold dark matter (CDM), baryons, and radiation The continuity equations for the dark sector are modified as follows: ρ˙de + 3H(1 + w)ρde = Q, (2) and ρ˙c + 3Hρc = −Q, (3) where Q characterizes the rate of energy transfer between dark energy and CDM To describe the effect of the dark-sector interaction in terms of an effective EoS, the continuity equations can be recast into an equivalent noninteracting form as ρ˙de + 3H(1 + w eff de)ρde = 0, (4) and ρ˙c + 3H(1 + w eff c)ρc = 0, (5) where the effective EoS parameters are given by w eff de = w − Q / 3Hρde and w eff c = Q / 3Hρc Observational Constraints and Findings The analysis utilized CMB data from Planck, ACT, and SPT, DESI DR2 BAO measurements, and type Ia supernova data from PantheonPlus, DES-Dovekie, and DESY5 The results show that the IDE models with Q ∝ ρde generally exhibit a stronger preference for nonzero dark-sector interactions For the CMB+DESI+DES-Dovekie data, the IDE model with Q = βH0ρde yields β = −2.52+0.80 − 0.54 and w = −1.510+0.170 − 0.120, corresponding to deviations from β = 0 and w = −1 at the 3.2σ and 3.0σ levels, respectively <ref:2610.

Title and authors: Vera: So we're looking at this paper now called "Constraints on interacting dark energy with a constant equation of state in light of DESI DR2: The role of the interaction term". It looks like they are really digging into how dark energy and dark matter can actually be talking to each other in these models where the equation of state w is just a constant number.

Jocelyn: Yeah, and it's focusing on how observations from DESI DR2, along with CMB and supernova data, constrain that interaction term Q. It seems like they're trying to figure out if this interaction is even necessary or if we can explain the results without it.

Subrahmanyan: From a theoretical side, this is interesting because it tests how coupling between the two sectors affects the evolution of density perturbations, especially on large scales where dark energy starts playing a bigger role than usual >.

Vera: Exactly. The paper summarizes that they're testing interacting dark energy models with a constant w parameter and using data from CMB, DESI DR2 BAO measurements, and type Ia supernova data to pin down the interaction term Q >.

Jocelyn: And what they found in their summary is that the IDE models with Q proportional to rho de generally show a stronger preference for having a nonzero dark-sector interaction compared to models where it's proportional to cold dark matter >.

Subrahmanyan: That’s significant because if the preference for interaction really depends on how you define that coupling term Q, then we need better observational data or better theoretical tools to tell which form of Q is actually happening in nature >.

Vera: Well, and they point out some specific results from their analysis using CMB plus DESI plus DES-Dovekie data showing that the IDE model with Q equals beta H0 rho de gives them a beta value around negative two point five two plus zero point eight zero minus zero point five four and a w value of negative one point five one zero plus zero point seventeen minus zero point one two.

Jocelyn: That means they're seeing deviations from the standard ΛCDM model at the three decimal sigma level for both beta and w >.

Title and authors: Subrahmanyan: Those deviations are what we expect if there’s some interaction happening, but we have to be careful about whether those specific numbers are robust or just artifacts of a particular model setup >.

Vera: They also found that the effective equation of state in that Q equals beta H0 rho de model evolves in a way that looks like it's coming from a w0waCDM model, crossing the phantom divide at some point and then moving towards quintessence-like behavior at lower redshifts >.

Jocelyn: So they're suggesting that this interaction term can mimic some of the behaviors we see in evolving dark energy models without us having to assume the intrinsic dark energy EoS is changing over time >.

Subrahmanyan: That's a neat point because it simplifies things theoretically, but it doesn’t tell us if the actual mechanism causing that evolution is what's happening >.

Vera: And they also mentioned that Bayesian evidence actually favors this specific IDE model over the standard ΛCDM and the other three interaction models they tested >.

Jocelyn: So, when you look at the statistical support from their analysis, this particular interaction form seems to be getting a lot of attention in the community >.

Subrahmanyan: That strong evidence is interesting because it pushes us to think about what kind of physics could lead to that specific coupling term Q proportional to rho de >.

Vera: Moving on from the paper's improvements, they suggested refining how we look at these models by showing that "IDE models with Q proportional to rho de generally exhibit a stronger preference for nonzero dark-sector interactions" compared to those proportional to cold dark matter >.

Jocelyn: That's a practical improvement because it helps us narrow down which interaction forms we should actually be focusing our observational efforts on rather than testing everything equally >.

Subrahmanyan: I agree, it gives us a clearer target for future data analysis because we can prioritize the models that are statistically most likely to be correct based on the current constraints >.

Title and authors: Vera: And they also improved their handling of cosmological perturbations by adopting the extended parameterized post-Friedmann framework, which lets them self-consistently calculate dark matter evolution coupled to dark energy changing w >.

Jocelyn: That’s key because without that self-consistent calculation, you just get a bunch of disconnected pieces from different analyses >.

Subrahmanyan: The paper also noted that for models like IwCDM1 and IwCDM3, they systematically favor a higher matter abundance accompanied by a strongly suppressed clustering amplitude across all dataset combinations >.

Vera: So they're not just changing the expansion history; they’re impacting how structure forms in the universe too, which is important for connecting cosmology to what we actually see in galaxy surveys >.

Jocelyn: That link between dark sector coupling and structure formation is something I’d like to follow up on when we look at those next time-domain observations >.

Subrahmanyan: Indeed, that's where the real confirmation or refutation of these interaction models will likely come from, by looking for those suppressed clustering amplitudes in future surveys >.

Vera: So to wrap up this discussion on "Constraints on interacting dark energy with a constant equation of state in light of DESI DR2: The role of the interaction term", we see that IwCDM3 is favored because its effective EoS crosses the phantom divide and resembles a w0waCDM model >.

Jocelyn: It really shows that these interactions can produce an apparent phantom-divide crossing even without changing the intrinsic dark energy equation of state over time >.

Subrahmanyan: From my view, this paper solidifies the idea that coupling is not just an extra parameter to tune a fit, but a physical mechanism we need to try and identify through future structure formation observations >.

Vera: We'll keep an eye on how the next set of DESI data releases confirm these constraints or push us in a different direction >.

Jocelyn: I think it’s going to be fascinating to see which interaction form wins out when we look at more precise late-time measurements >.

Subrahmanyan: We need those precise observations to figure out if the preference for Q proportional to rho de really sticks or if it's just a statistical fluke from the current data set >.

The paper's summary: Vera: So to recap this paper, they’re taking these specific cosmological measurements from CMB and DESI DR2, along with those supernova data points, and they are trying to pin down the interaction term Q in interacting dark energy models where the equation of state w is just a constant number.

Jocelyn: Right. Basically, they're testing how much dark energy actually talks to cold dark matter and seeing if that interaction term Q can be measured or ruled out by what we see in the universe today.

Subrahmanyan: From my side, it’s about whether this coupling parameter Q is a physical thing we need to account for, or just a mathematical trick to fit the data better than standard dark energy.

Vera: Well, their main finding is that the models where the interaction term Q is proportional to the dark energy density—those are IwCDM models with Q proportional to rho de—they show a stronger preference for having some kind of nonzero interaction compared to other forms.

Jocelyn: That’s interesting because it suggests that if there *is* an interaction happening, it’s more likely to be connected to how much dark energy is present right now.

Subrahmanyan: But they also found that the specific IwCDM3 model, where Q is proportional to H0 rho de, gets the strongest statistical support out of all four forms they tested.

Vera: And that’s because its effective equation of state evolves in a way that looks like it’s mimicking what we see in a w0waCDM model—it crosses that phantom divide and then moves toward something more quintessence-like at lower redshifts.

Jocelyn: So, they’re showing us how this interaction term can create the *look* of an evolving dark energy equation of state even if the actual intrinsic dark energy EoS is just a constant w parameter.

Subrahmanyan: That’s a big deal theoretically because it means we might be seeing something that looks like dynamic dark energy when maybe it’s just the interaction term Q doing all the heavy lifting on the expansion history.

Vera: The paper also pointed out how this affects structure formation too; for IwCDM1 and IwCDM3, they systematically favor a higher matter abundance along with a strongly suppressed clustering amplitude across all those different data combinations they looked at.

Jocelyn: So it’s not just about the expansion of space; it’s about how dark energy coupling changes the way galaxies and clusters actually clump together in the cosmic web.

Subrahmanyan: That connection to structure formation is what I care about most because if this interaction model is right, we should see those suppressed clustering amplitudes when we look at future galaxy surveys.

Vera: The authors say that while they found strong support for IwCDM3, the significance of those deviations from standard ΛCDM depends heavily on which supernova compilation you use; DESY5 gave them the strongest preference, but PantheonPlus gave them the weakest.

Jocelyn: That makes sense because we’re dealing with different data sets having different strengths and weaknesses when trying to constrain these parameters.

Subrahmanyan: So for someone just listening, this paper shows that a specific interaction term Q proportional to rho de is statistically favored by current data, but it flags that future precision late-time observations from things like Euclid or the next DESI releases will be needed to settle whether this preference actually holds true.

The paper's improvements: Tom: So, we're looking at how this paper suggests we should look at these interacting dark energy models in the future, specifically how to make them better tools for us to use with our data.

Vera: They suggest that a key improvement is figuring out which interaction forms are actually worth testing.

Jocelyn: Right, they point out that we shouldn't just test every single interaction term equally; they say we should focus on the ones where the interaction term Q is proportional to the dark energy density, because those show a stronger preference for a nonzero coupling.

Subrahmanyan: That makes sense because if we have to test five different ways dark energy and dark matter interact, it gets messy; focusing on the most likely physical mechanism streamlines our research.

Vera: They also mentioned adopting the extended parameterized post-Friedmann framework to handle the dark matter evolution more consistently, which means they can calculate how cold dark matter changes density coupled to a changing w parameter in a self-consistent way.

Jocelyn: That’s good because it stops you from having disconnected pieces of information from different analyses; you get one cohesive picture of the whole system evolving together.

Subrahmanyan: And that self-consistency is crucial when we try to connect cosmology to structure formation, because if the dark matter evolution doesn't match what we see in simulations, then our whole picture is flawed.

Vera: Plus, they noted that for models like IwCDM1 and IwCDM3, there’s a systematic effect where they favor a higher abundance of matter along with a much suppressed clustering amplitude across all the different datasets they combined.

Jocelyn: So it means that if these interaction models are true, we should expect to see those suppressed clustering amplitudes when we look at future surveys for galaxy clusters or groups.

Subrahmanyan: Exactly; that’s the observational test I mentioned earlier, Vera. If those cluster counts don't show a suppression in the way these models predict, then we have a major problem with that specific interaction form.

Vera: The authors are essentially saying that by refining how we model this coupling and how we calculate the resulting structure growth, we can get much cleaner constraints on what’s actually happening.

Jocelyn: It moves us past just finding a number for beta or w, and toward understanding the actual physical process causing that interaction.

Subrahmanyan: And I think that is where the next big step is; we need to look for those specific signatures in the large-scale structure data from Euclid or future DESI releases to confirm these model preferences.

Conclusion: Vera: So to wrap things up on "Constraints on interacting dark energy with a constant equation of state in light of DESI DR2: The role of the interaction term," this paper shows that the IwCDM3 model is statistically favored because its effective equation of state crosses that phantom divide and mimics a w0waCDM behavior.

Jocelyn: It really means these interactions can produce the look of an evolving dark energy equation without actually changing the intrinsic dark energy EoS over time.

Subrahmanyan: That’s a big point because it suggests that coupling is not just some extra tuning parameter we add to a fit, but potentially a real physical mechanism we need to try and identify through future structure formation observations.

Vera: They found that while IwCDM3 is the best fit among the four forms tested, the actual statistical significance of those deviations from standard ΛCDM depends on which specific supernova data compilation you use.

Jocelyn: It's a fair caveat because we can see different results depending on whether we’re looking at PantheonPlus or DESY5 data sets.

Subrahmanyan: From my side, it highlights that the nature of this interaction is still highly dependent on the observational setup; that means our next set of large-scale structure surveys will be absolutely critical to confirm or kill these models.

Vera: So, looking at this paper, we see a strong preference for Q proportional to rho de among these interaction forms, especially IwCDM3.

Jocelyn: It’s encouraging because it gives us a clearer target for what kind of interaction we should be looking for in the next round of time-domain and lensing data.

Subrahmanyan: I think the real implication is that we need to build models that account for this coupling, because ignoring it could lead us to fundamentally misunderstand dark energy dynamics.

Vera: And they’re leaving us with a clear path forward: future precision late-time observations from things like Euclid and subsequent DESI data releases will be key to figuring out if this preference for dark-sector interactions actually persists or if we find something different.

Jocelyn: Exactly, because we need those tighter constraints to really settle which interaction form wins out in the real universe.

Subrahmanyan: Next time, we’ll be talking about how these structure formation predictions for IwCDM1 and IwCDM3 suggest a higher matter abundance and suppressed clustering amplitude across all combinations of data.

Zhao-Yu Li, Tian-Nuo Li, Guo-Hong Du, Sheng-Han Zhou, Yun-He Li, Jing-Fei Zhang, Xin Zhang

Liaoning Key Laboratory of Cosmology and Astrophysics, Northeastern University · School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS · MOE Key Laboratory of Data Analytics and Optimization for Smart Industry, Northeastern University · National Frontiers Science Center for Industrial Intelligence and Systems Optimization, Northeastern University

astro-ph.CO, gr-qc, hep-ph

Submitted: 2026-10-22

Updated: 2026-10-22

Comments: 11 pages, 4 figures, 2 tables

License: http://creativecommons.org/licenses/by-nc-nd/4.0/

The gist: The gist: The study investigates how dark energy and dark matter interact within interacting dark energy (IDE) models characterized by a constant equation of state parameter w, using cosmological

Key concepts

Interacting Dark Energy (IDE) Models: These models describe a universe where dark energy and cold dark matter are not independent; they exchange energy with each other via a term Q. This interaction is modeled by modifying the standard continuity equations for both components, allowing researchers to test if dark sector energy flows between them.
Equation of State Parameter (w): This parameter describes the pressure-to-density ratio for dark energy. A constant value of w simplifies the model, but deviations from -1 suggest dynamic behavior. The study uses this to characterize the fundamental nature of dark energy within the IDE framework.
Interaction Term (Q): Q quantifies the rate at which energy is transferred between dark matter and dark energy. It is parameterized by a coupling constant $\beta$. A non-zero Q implies that the components are dynamically linked, leading to different cosmological predictions than in standard $\Lambda$CDM models.

Summary

The gist: The study investigates how dark energy and dark matter interact within interacting dark energy (IDE) models characterized by a constant equation of state parameter w, using cosmological data from CMB, DESI DR2 BAO measurements, and Type Ia supernova data to constrain the interaction term Q.

Model Framework

The background evolution in a spatially flat Friedmann–Robertson–Walker universe is governed by the Friedmann equation (1) which involves the energy densities of dark energy, cold dark matter (CDM), baryons, and radiation The continuity equations for the dark sector are modified as follows: ρ˙de + 3H(1 + w)ρde = Q, (2) and ρ˙c + 3Hρc = −Q, (3) where Q characterizes the rate of energy transfer between dark energy and CDM To describe the effect of the dark-sector interaction in terms of an effective EoS, the continuity equations can be recast into an equivalent noninteracting form as ρ˙de + 3H(1 + w eff de)ρde = 0, (4) and ρ˙c + 3H(1 + w eff c)ρc = 0, (5) where the effective EoS parameters are given by w eff de = w − Q / 3Hρde and w eff c = Q / 3Hρc

Interaction Term Parameterization

The interaction term Q is phenomenologically parameterized, assuming that the energy transfer rate is proportional to the energy density of either dark energy or cold dark matter To ensure dimensional consistency, a natural choice for the interaction term is the Hubble parameter H The four representative forms considered are IwCDM1 with Q = βHρde, IwCDM2 with Q = βHρc, IwCDM3 with Q = βH0ρde, and IwCDM4 with Q = βH0ρc The dimensionless coupling parameter β determines the strength and direction of the energy exchange: for β > 0, energy is transferred from cold dark matter to dark energy; for β < 0, the transfer is reversed; and for β = 0, no energy transfer occurs

Observational Constraints and Findings

The analysis utilized CMB data from Planck, ACT, and SPT, DESI DR2 BAO measurements, and type Ia supernova data from PantheonPlus, DES-Dovekie, and DESY5 The results show that the IDE models with Q ∝ ρde generally exhibit a stronger preference for nonzero dark-sector interactions For the CMB+DESI+DES-Dovekie data, the IDE model with Q = βH0ρde yields β = −2.52+0.80 − 0.54 and w = −1.510+0.170 − 0.120, corresponding to deviations from β = 0 and w = −1 at the 3.2σ and 3.0σ levels, respectively Interestingly, the effective EoS of the IDE model with Q = βH0ρde exhibits a redshift evolution resembling that of the w0waCDM model, crossing the phantom divide Bayesian evidence further indicates that this IDE model is favored over ΛCDM and the other three IDE models

Model Comparison and Effectiveness

The study compares four representative forms of the interaction term Q using the CMB, DESI, and SN data to determine which IDE model with a constant dark energy EoS parameter w receives the strongest observational support The results show that IwCDM3 generally shows more pronounced departures from the ΛCDM limit than the IwCDM1 model among models with an interaction rate proportional to the dark energy density For the CMB+DESI+DES-Dovekie data, IwCDM3 gives β = −2.52+0.80 − 0.54 and w = −1.510+0.170 − 0.120, corresponding to deviations from β = 0 and w = −1 at approximately the 3.2σ and 3.0σ levels, respectively The significance of these departures depends on the SN compilation, with DESY5 yielding the strongest preference whereas PantheonPlus yields the weakest

Conclusion

Overall, IwCDM3 shows both the strongest preference for a nonzero dark-sector interaction and the strongest observational support among the four models considered This is because its effective EoS evolves from the phantom regime at high redshift, crosses the phantom divide w eff de = −1, and enters the quintessence-like region toward low redshift, closely resembling the behavior generated by the w0waCDM model The Bayesian evidence further indicates that models with Q ∝ ρde are more favored by current observations, particularly IwCDM3 Future precision late-time observations from the Large Synoptic Survey Telescope, Euclid, and subsequent DESI data releases will help determine whether the preference for dark-sector interactions persists and to distinguish between different interaction forms.

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How it works

Observational Constraints and Findings

Improvements for AI systems

Improved dark energy parameter fitting by identifying interaction forms: The improved system can distinguish between interaction forms by showing that IDE models with Q proportional to rho de generally exhibit a stronger preference for nonzero dark-sector interactions compared to those proportional to cold dark matter.
Enhanced cosmological constraint handling: The AI can perform model selection using the Bayes factors of the different models in Fig. 4, allowing it to determine that IwCDM3 receiving the strongest statistical support among the four models considered.
Effective dark energy evolution modeling: The system can accurately reconstruct background dynamics by using the effective EoS of IwCDM3 exhibits a pronounced redshift evolution, crossing the phantom divide and closely resembling the behavior generated by the w0waCDM model.
Structure formation prediction: The improved AI can predict structure growth modifications by noting that for IwCDM1 and IwCDM3 models, they systematically favor a higher matter abundance accompanied by a strongly suppressed clustering amplitude across all dataset combinations.

Abstract

Recent DESI baryon acoustic oscillation (BAO) analyses suggest a preference for an evolving dark energy equation of state (EoS) that crosses the phantom divide w=-1. Interactions between dark energy and dark matter can also produce an apparent phantom-divide crossing in the effective dark energy EoS. In this work, we investigate interacting dark energy (IDE) models with a constant EoS parameter w, using cosmic microwave background (CMB) observations from Planck, ACT, and SPT, DESI DR2 BAO measurements, and type Ia supernova data from PantheonPlus, DES-Dovekie, and DESY5. We consider four typical forms of the interaction term Q. Our results show that the IDE models with Q proportional toρ de generally exhibit a stronger preference for nonzero dark-sector interactions. In particular, for the CMB+DESI+DES-Dovekie data, the IDE model with Q=βH 0ρ de yields β=-2.52+0.80-0.54 and w=-1.510+0.170-0.120, corresponding to deviations from β=0 and w=-1 at the 3.2σ and 3.0σ levels, respectively. Interestingly, the effective EoS of the IDE model with Q=βH 0ρ de exhibits a redshift evolution resembling that of the w 0w a CDM model, crossing the phantom divide. Bayesian evidence further indicates that this IDE model is favored over Λ CDM and the other three IDE models. Our analysis helps identify which interaction forms better account for current cosmological observations.