Diffusive dark fluids with Planck-2018 and DESI BAO DR2 Measurements

This paper constrains a diffusive dark fluid cosmological model using Planck 2018 CMB and DESI DR2 BAO data, finding that the model yields Hubble constant values consistent with Planck measurements and demonstrates distinct effects on cosmic evolution and structure formation compared to the standard $\Lambda$CDM model.

The Gist

Imagine the universe as a giant, expanding balloon. For decades, scientists have had a "standard recipe" for how this balloon inflates, called the ΛCDM model. This recipe assumes the balloon is filled with three main ingredients:

1. Normal matter (the stuff we are made of, like stars and you).
2. Dark matter (an invisible glue that holds galaxies together).
3. Dark energy (a mysterious force pushing the balloon to expand faster and faster).

However, there's a problem with this recipe. When scientists measure how fast the balloon is expanding right now (using local telescopes), they get one number. When they look back at the "baby picture" of the universe (using the Cosmic Microwave Background from the Planck satellite), they get a slightly different number. This disagreement is known as the Hubble Tension, and it's like two chefs arguing over the exact temperature of the oven.

The New Idea: The "Leaky" Universe

In this paper, authors Shambel Sahlu and Amare Abebe propose a new recipe. Instead of Dark Matter and Dark Energy being separate, static ingredients, they suggest they are leaking into each other.

Think of the universe as a house with two rooms:

• Room A: Dark Matter (the heavy furniture).
• Room B: Dark Energy (the air pressure).

In the old recipe, the door between these rooms was locked. In this new Diffusive Dark Fluid model, the door is slightly open. Energy is slowly "diffusing" (leaking) from one room to the other, like steam moving from a hot kitchen to a cooler living room. This constant exchange changes how the universe expands and how structures (like galaxies) form.

What Did They Do?

The authors didn't just guess; they tested this new recipe against the two most powerful "taste testers" in modern astronomy:

1. Planck 2018: The "baby picture" of the universe (looking back 13.8 billion years).
2. DESI DR2: A massive new survey mapping millions of galaxies to see how the universe looks today.

They used a super-computer simulation (like a cosmic flight simulator) to see if their "leaky" universe model could fit the data better than the standard recipe.

The Results: A Better Fit?

Here is what they found, translated into everyday terms:

• The Hubble Tension: The standard recipe (ΛCDM) and the new "leaky" recipe both struggle to match the local measurements of the universe's expansion speed. However, the new "leaky" model is statistically closer to the "baby picture" (Planck data) than the old model is. It's like the new recipe is slightly less burnt than the old one, even if neither is perfect yet.
• Galaxy Clumping: The authors also looked at how galaxies clump together. In their model, because energy is leaking between the dark components, it changes how fast galaxies form.
  • Small scales: The "leaky" model makes galaxies clump together more aggressively.
  • Medium scales: It actually suppresses (slows down) the clumping.
  • Large scales: It boosts the clumping again.

The Analogy of the Crowd

Imagine a crowd of people (Dark Matter) trying to form groups (galaxies) while a wind (Dark Energy) blows them apart.

• In the old model: The wind just blows, and the people try to hold on.
• In this new model: The people and the wind are secretly trading energy. Sometimes the people get a burst of energy to hold hands tighter; other times the wind gets stronger and blows them apart. This trade-off creates a different pattern of groups than we expected.

The Bottom Line

This paper suggests that the universe might not be a static system where Dark Matter and Dark Energy just sit there. Instead, they might be in a constant, subtle dance, exchanging energy like a leaky bucket.

While this new model doesn't completely solve the mystery of why the universe is expanding at different speeds depending on how you measure it, it offers a promising new direction. It shows that if we allow these invisible components to interact, our mathematical models of the universe become more flexible and might eventually explain the "tension" that has been bothering cosmologists for years.

The authors conclude that with more data in the future, this "diffusive" idea could be the key to unlocking the true nature of our expanding universe.

Technical Summary

1. Problem Statement

The paper addresses two major challenges in modern cosmology:

• The Hubble Tension ($H_0$): A significant discrepancy exists between the value of the Hubble constant derived from early-universe measurements (Planck 2018 CMB data, $H_0 \approx 67.4$ km/s/Mpc) and late-universe measurements (SH0ES/SNIa, $H_0 \approx 73.0$ km/s/Mpc).
• Structure Formation: The standard $\Lambda$CDM model faces challenges in explaining the growth of cosmic structures and the nature of the interaction between Dark Matter (DM) and Dark Energy (DE).

The authors investigate whether a Diffusive Dark Fluid model, where energy is exchanged between DM and DE via a diffusion mechanism (rather than direct non-gravitational coupling), can alleviate these tensions and modify the evolution of cosmic structures.

2. Methodology

The study employs a rigorous theoretical and statistical framework:

• Theoretical Framework:

  • Diffusive Interaction: The model assumes a non-conservative energy-momentum tensor where energy flows between dark components via a diffusion current ($N^\nu = \gamma u^\nu$).
  • Background Evolution: The authors derive modified Friedmann equations and continuity equations for DM and DE. Unlike standard interacting models, this diffusion term introduces scale-dependent effects.
  • Perturbation Theory: The study extends to linear perturbations in the conformal-Newtonian gauge. Crucially, it accounts for the scale-dependent density contrast ($\delta_i$) and the matter power spectrum ($P_m$), distinguishing it from models that assume purely homogeneous dark energy.
  • Assumptions: Dark energy is treated as a cosmological constant ($w_{de} = -1$) with no intrinsic perturbations ($\delta_{de} \approx 0$), while momentum transfer is neglected to focus on energy transfer effects.

• Statistical Analysis:

  • Tools: The authors utilized the modified CLASS (Cosmic Linear Anisotropy Solving System) code coupled with COBAYA (Cosmology Bayesian Analysis) for Monte Carlo Markov Chain (MCMC) simulations.
  • Datasets:
    1. Planck 2018: High-$\ell$ TT, TE, EE likelihoods; low-$\ell$ TT, EE; and CMB lensing.
    2. DESI DR2 (2024): Baryon Acoustic Oscillation (BAO) distance and correlation measurements (isotropic $D_V$ and anisotropic $D_M, D_H$).
    3. Joint Analysis: Combined Planck 2018 + DESI DR2 BAO.
  • Parameters Constrained: $H_0$, $\Omega_m$, $\sigma_8$, $n_s$, $\ln(10^{10}A_s)$, and the diffusion interaction parameter $Q_{dm}$.

3. Key Contributions

• Integration of Latest Data: This is one of the first works to constrain the diffusive dark fluid model using the DESI DR2 (2024) BAO data in combination with Planck 2018, providing tighter constraints than previous studies using only Planck.
• Scale-Dependent Analysis: The paper explicitly computes and visualizes the scale-dependent density contrast and the matter power spectrum, demonstrating how diffusion affects structure formation differently across various wavenumbers ($k$).
• Refined $H_0$ Constraints: The study provides precise statistical comparisons of the $H_0$ tension under the diffusive model versus the standard $\Lambda$CDM model against both Planck and SH0ES data.

4. Key Results

A. Cosmological Parameters and $H_0$ Tension

• Planck 2018 Consistency: The diffusive model yields an $H_0$ value of $67.3876^{+1.0765}{-1.0709}$** km/s/Mpc (Planck only) and **$68.3804^{+0.5639}{-0.5852}$ km/s/Mpc (Planck + DESI).
  • The deviation from the Planck 2018 central value ($67.4$) is negligible (**0.01$\sigma$** and **1.29$\sigma$**, respectively).
  • This indicates the diffusive model is statistically consistent with early-universe CMB data.
• SH0ES Tension: When compared to the SH0ES measurement ($H_0 = 73.04 \pm 1.04$), the diffusive model shows a tension of 3.78$\sigma$ (Planck only) and 3.92$\sigma$ (Planck + DESI).
  • Conclusion: While the model fits Planck data well, it does not resolve the Hubble tension with SH0ES data; the tension remains significant ($\geq 3.5\sigma$).
• Interaction Parameter ($Q_{dm}$): The diffusion parameter is constrained to be very close to zero ($Q_{dm} \approx 0.0005$), suggesting that while the model is viable, the current data does not strongly favor a large diffusion rate over the standard $\Lambda$CDM limit.

B. Structure Formation and Power Spectrum

The study analyzes the matter power spectrum $P_m(k, z)$ and its deviation $\Delta P_m$ relative to $\Lambda$CDM:

• Small Scales ($k \gtrsim 10^{-1} h$ Mpc$^{-1}$): The diffusive model enhances matter fluctuations compared to $\Lambda$CDM, showing BAO-like wiggles with higher amplitude.
• **Intermediate Scales ($10^{-2} \lesssim k \lesssim 10^{-1} h$Mpc$^{-1}$):** The model exhibits **monotonic suppression** of matter fluctuations relative to$\Lambda$CDM.
• Large Scales ($k \lesssim 10^{-2} h$ Mpc$^{-1}$): The deviation is smooth and positive, indicating an enhancement of fluctuations.
• Redshift Evolution: The amplitude of the power spectrum at $z=1$ is consistently higher than at $z=0$ across all scales for the diffusive model.

5. Significance and Conclusion

• Viability of Diffusive Models: The diffusive dark fluid model remains a statistically viable alternative to $\Lambda$CDM, particularly regarding consistency with CMB data (Planck 2018).
• Limitations on Hubble Tension: The study concludes that while the diffusion mechanism modifies cosmic evolution, it does not currently solve the Hubble tension when confronted with the SH0ES dataset. The tension remains at the $\sim 4\sigma$ level.
• Structural Impact: The model predicts distinct, scale-dependent signatures in the matter power spectrum. These signatures (enhancement at small/large scales, suppression at intermediate scales) offer potential observational tests for future large-scale structure surveys.
• Future Work: The authors suggest that a comprehensive analysis including SNIa compilations and more extensive datasets is required to fully determine if this model can alleviate cosmological tensions.

In summary, the paper successfully constrains a diffusive dark fluid model using the latest DESI and Planck data, confirming its compatibility with early-universe observations while highlighting its inability to fully resolve the $H_0$ crisis with current late-universe data, and providing detailed predictions for structure formation.