Testing the Coexistence of Dark Energy and Dark Matter with Late-time Observational Data

This paper proposes an interacting dark sector model with an analytical Hubble function that, when constrained by diverse late-time observational data including new DESI measurements, outperforms standard $\Lambda$CDM and $w$CDM models in fitting the data while offering a viable explanation for cosmic acceleration and a statistically lower $H_0$ value.

The Gist

The Big Picture: A Cosmic Mystery

Imagine the universe is a giant, expanding balloon. For a long time, scientists thought this balloon was just slowly inflating because of the momentum from the Big Bang. But about 20 years ago, we discovered something weird: the balloon isn't just inflating; it's speeding up.

To explain this, scientists invented two invisible "ghosts":

1. Dark Matter: The invisible glue holding galaxies together.
2. Dark Energy: The mysterious force pushing the balloon apart faster and faster.

The standard story (called $\Lambda$CDM) says these two ghosts are strangers. They live in the same house (the universe) but never talk to each other. Dark Energy just pushes, and Dark Matter just pulls.

The New Idea: The "Roommate" Theory

This paper asks a different question: What if Dark Matter and Dark Energy are actually roommates who talk to each other?

The authors propose a model called "Coexistence." In this scenario, the two ghosts aren't just ignoring each other; they are exchanging energy. Maybe Dark Matter is slowly turning into Dark Energy, or they are trading energy back and forth like roommates sharing a pizza.

The paper uses a mathematical tool called the Lotka-Volterra system. You might know this from biology class—it's the math used to describe how predators and prey (like wolves and rabbits) interact.

• If there are too many rabbits, the wolves eat more and grow.
• If there are too many wolves, they eat all the rabbits and starve.
• Eventually, they find a balance where they can coexist.

The authors are saying: Maybe Dark Matter and Dark Energy are like wolves and rabbits, constantly adjusting to keep the universe stable.

The Experiment: Checking the Receipts

To see if this "Roommate Theory" is true, the authors went to the store and checked the receipts. They gathered the latest, most expensive data available from the universe:

• Cosmic Chronometers: Measuring the age of old galaxies to see how fast the universe is expanding right now.
• DESI (The New Data): A massive survey mapping millions of galaxies (like a cosmic GPS).
• Supernovae: Exploding stars that act as "standard candles" to measure distance.
• Gamma-Ray Bursts: The brightest explosions in the universe, acting as beacons from very far away (and very long ago).

They ran their "Roommate" model against these receipts and compared it to the old "Stranger" models ($\Lambda$CDM and $w$CDM).

The Results: Who Wins?

Here is what they found:

1. The Roommate Model Fits Better: When they looked at the data, the "Coexistence" model (where the ghosts talk) actually fit the numbers slightly better than the standard "Stranger" models. It explained the data with a bit more precision.
2. The "Too Complicated" Problem: In science, if you have a model with more moving parts (more variables), it's easier to make it fit the data. The "Roommate" model has extra knobs to turn (interaction constants).
   • The authors used a statistical rule called AIC (Akaike Information Criterion). Think of this as a "complexity tax." If a model is too complicated, it gets penalized.
   • The Verdict: While the Roommate model fit the data better, the "tax" for being more complicated meant it wasn't statistically proven to be the winner over the standard models. They are essentially tied.
3. The Hubble Constant ($H_0$) Surprise: One interesting finding is that the Roommate model predicts a slightly lower value for the current expansion rate of the universe. This is important because there is a famous argument in physics called the Hubble Tension (where different ways of measuring the speed of the universe give different answers). This model might help lower that tension, but the authors admit they need more data to be sure.
4. High Redshifts (The Distant Past): When they looked at data from very far away (very old universe), the Roommate model started to look exactly like the standard "Stranger" model. It seems that in the early universe, the ghosts weren't talking much, but they might be talking more now.

The Conclusion

The paper concludes that the idea of Dark Matter and Dark Energy interacting (coexisting) is physically possible and viable. It's a valid way to describe the universe.

However, the current data isn't strong enough to say, "Okay, the Roommate model is definitely the truth." It's just as good as the standard model, but slightly more complex.

The Takeaway:
Think of the universe as a dance. The standard model says Dark Matter and Dark Energy are dancing in the same room but never touching. This paper suggests they might be holding hands and spinning together. The music (the data) sounds a little better with them holding hands, but we need more songs (more data) to be 100% sure that's how they dance.

The authors plan to look at even more data (specifically from the Cosmic Microwave Background) in the future to see if the "hand-holding" theory wins the dance-off.

Technical Summary

1. Problem Statement

The standard cosmological model, $\Lambda$CDM, faces significant challenges, including theoretical pathologies (e.g., the cosmological constant problem) and persistent observational tensions (notably the $H_0$ and $S_8$ tensions). Recent data from the Dark Energy Spectroscopic Instrument (DESI), particularly the DR1 and DR2 releases, have suggested that dark energy may be dynamical rather than a static cosmological constant, potentially crossing the "phantom divide" ($w < -1$).

While interacting dark sector models (where energy is exchanged between dark matter and dark energy) offer a phenomenological solution to these issues, specific models describing the coexistence of these two components within a single cosmic fluid remain under-constrained by the latest high-precision data. The authors aim to test the viability of a specific interacting model that allows for the coexistence of dark energy and dark matter against the most recent late-time observational datasets.

2. Methodology

Theoretical Framework

The authors investigate a phenomenological interacting dark sector model where the energy transfer between dark matter ($\rho_m$) and dark energy ($\rho_d$) is governed by a Lotka-Volterra system (a predator-prey dynamic often used in ecology).

• Interaction Term: The energy exchange rate $Q(t)$ is defined as:
  $$Q(t) = Q_0(t)\rho_m\rho_d + Q_1(t)\rho_d$$
  where $Q_0(t) = \alpha/H$ and $Q_1(t) = \beta H$, with $\alpha$ and $\beta$ being coupling constants.
• Analytical Solution: Unlike many interacting models that require numerical integration, this specific formulation admits a closed-form analytical solution for the Hubble function $H(a)$:
  $$H(a) = H_0 \left( 1 - \hat{\Omega}_{m0} + \hat{\Omega}_{m0} a^{p_1} \right)^{p_2} a^{-3(1+p_3)}$$
  where $p_1, p_2, p_3$ are functions of the coupling constants ($\alpha, \beta$) and the dark energy equation of state ($w_d$).
• Limits: The model reduces to $\Lambda$CDM when $\alpha=\beta=0$ and $w_d=-1$, and to $w$CDM when $\alpha=\beta=0$.

Observational Data

The study utilizes a comprehensive set of late-time cosmological data to constrain the model parameters:

1. Cosmic Chronometers (OHD): 34 direct measurements of the Hubble parameter $H(z)$, including 31 standard points and 3 new data points derived from DESI analysis.
2. Baryon Acoustic Oscillations (BAO): Data from the DESI DR2 release.
3. Supernovae Type Ia (SNIa): Three distinct catalogues:
   • PantheonPlus (PP)
   • Union3.0 (U3)
   • DES-Dovekie (DESD)
4. Gamma-Ray Bursts (GRBs): 193 events calibrated via the Amati correlation, extending the redshift range up to $z \approx 8.1$.

Statistical Analysis

• Parameter Estimation: The authors used the COBAYA framework with MCMC sampling to derive posterior distributions for the free parameters: $H_0$, $\hat{\Omega}_{m0}$, $r_{drag}$, $w_d$, $\alpha$, and $\beta$.
• Model Comparison: Due to the differing number of free parameters (6 for Coexistence, 4 for $w$CDM, 3 for $\Lambda$CDM), the Akaike Information Criterion (AIC) was employed to determine the preferred model, penalizing models with excessive degrees of freedom.

3. Key Results

Parameter Constraints

The analysis yielded the following key findings regarding the model parameters across various dataset combinations:

• Hubble Constant ($H_0$): The coexistence model consistently yields a statistically smaller value for $H_0$ compared to the reference models (e.g., $H_0 \approx 67.0 - 68.1$ km/s/Mpc for coexistence vs. $\approx 68.5 - 69.9$ for $\Lambda$CDM in specific datasets).
• Coupling Constants ($\alpha, \beta$):
  • For datasets without GRBs, the parameter $\beta$ is consistent with zero within the $1\sigma$ confidence interval, suggesting the model often reverts to a "compartmentalization" scenario (where the fluids are effectively decoupled in a specific limit).
  • When GRB data is included, the constraints tighten, and the values $\alpha = \beta = 0$ often fall outside the $1\sigma$ region, indicating a preference for non-zero interaction at high redshifts.
• Equation of State ($w_d$): The model favors a dynamical dark energy equation of state ($w_d \neq -1$), typically ranging between $-0.65$ and $-0.90$.

Model Performance

• Goodness of Fit: The coexistence model consistently provides a lower minimum chi-squared ($\chi^2_{min}$) value than both $\Lambda$CDM and $w$CDM across all dataset combinations.
• AIC Analysis:
  • While the coexistence model fits the raw data better, the AIC (which penalizes complexity) shows that the model is statistically equivalent to the $w$CDM model in most cases ($|\Delta AIC| < 2$).
  • In specific cases (e.g., U3 + OHD + BAO), the data shows a weak preference for the coexistence model over $\Lambda$CDM.
• High-Redshift Behavior: The inclusion of GRB data reveals that at large redshifts ($z > 2$), the coexistence model behaves similarly to the $w$CDM model. This suggests that the specific interaction mechanism becomes less distinguishable from standard dynamical dark energy in the early universe.

4. Significance and Conclusions

• Viability of Coexistence: The study confirms that a cosmological scenario where dark energy and dark matter coexist via a Lotka-Volterra interaction is physically viable and consistent with current late-time observational data.
• Competitive Alternative: The coexistence model serves as a robust alternative to standard $\Lambda$CDM, offering a better raw fit to the data and a potential mechanism to address the dynamical nature of dark energy suggested by DESI.
• Hubble Tension: The model's tendency to predict a lower $H_0$ value is significant, as it aligns more closely with "early universe" measurements (like CMB) than the higher values often derived from local distance ladders, though the paper notes that a full resolution of the $H_0$ tension requires CMB data integration (planned for future work).
• Future Directions: The authors conclude that while the phenomenological model works well, the next step is to identify the fundamental theoretical mechanism (e.g., scalar fields or modified gravity) that could naturally produce this specific dynamical evolution. Additionally, incorporating CMB data is essential to fully test the model's implications for cosmological tensions.

In summary, the paper demonstrates that interacting dark sector models capable of describing coexistence are not only mathematically tractable but also statistically competitive with standard cosmological models when tested against the latest DESI and supernova data.