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Semi-cosmographic constraints on decaying dark matter and dynamical dark energy: DESI DR2 BAO and 21\, cm intensity-mapping forecasts

This paper presents a semi-cosmographic framework combining a Padé-rational parametrization of luminosity distance with a two-body decaying dark matter model to constrain dark energy and dark matter evolution using DESI DR2 BAO data and SKA1-Mid 21-cm intensity-mapping forecasts, without assuming a specific dark energy model.

Original authors: Mohit Yadav, Pankaj Chavan, Tapomoy Guha Sarkar

Published 2026-03-25

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CC0 1.0

Original authors: Mohit Yadav, Pankaj Chavan, Tapomoy Guha Sarkar

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Solving the Universe's Mystery

Imagine the Universe is a giant, expanding balloon. For decades, scientists have been trying to figure out exactly how fast this balloon is inflating and what is pushing it to expand faster.

We know the balloon is made of two mysterious ingredients we can't see:

Dark Matter: The "glue" that holds galaxies together (about 25% of the Universe).
Dark Energy: The mysterious force pushing the balloon to expand faster (about 70% of the Universe).

The standard theory (called $\Lambda$ CDM) says Dark Matter is perfectly stable (it never changes) and Dark Energy is a constant, unchanging force (like a fixed pressure inside the balloon). But recent measurements show some cracks in this theory. The Universe seems to be behaving slightly differently than expected.

This paper asks: What if Dark Matter isn't perfectly stable? What if it's slowly decaying (falling apart) over time? And, to be extra careful, what if we don't assume anything about Dark Energy at all?

The Detective's Toolkit: "Semi-Cosmography"

Usually, to study the Universe, scientists pick a specific theory (a "model") and try to prove it. This paper takes a different approach called Semi-Cosmography.

Think of it like this:

Standard Cosmography: Trying to describe the shape of a car just by looking at its speedometer and steering wheel, without knowing if it's a Ferrari or a Ford.
The Paper's "Semi" Approach: They use a flexible mathematical tool (called a Padé approximation) to describe the Universe's expansion history without assuming a specific engine type (Dark Energy). However, they do assume a specific story for the "glue" (Dark Matter): that it is a parent particle slowly decaying into two children—one invisible and one heavy.

It's like saying: "I don't know what kind of car this is, but I'm going to assume the fuel tank is leaking. Let's see if the car's speed matches that story."

The Two Clues: BAO and 21-cm Radio

To test their theory, the authors used two different types of cosmic "rulers" to measure the Universe.

1. The Geometric Ruler (DESI BAO)

Imagine the early Universe had a giant sound wave ripple frozen in time. Today, galaxies are slightly more likely to be separated by this specific distance. This is called Baryon Acoustic Oscillations (BAO).

The Analogy: It's like measuring the distance between trees in a forest to see how much the forest has stretched.
The Result: Using data from the DESI telescope, they measured these distances very precisely. However, this is like looking at a car's speed from a distance; it tells you how fast the car is going, but it doesn't tell you why the engine is humming or if the fuel tank is leaking. The "leaking" (decaying dark matter) effect was hidden by the flexibility of their math.

2. The Growth Ruler (21-cm Intensity Mapping)

This is the paper's "secret weapon." They looked at a forecast for future data from a giant radio telescope (SKA1-Mid). This telescope listens to the "hum" of neutral hydrogen gas (the 21-cm signal) across the sky.

The Analogy: While BAO measures the distance between galaxies, this method measures how the galaxies are clumping together.
The Magic: If Dark Matter is decaying, it turns into radiation and "warm" particles. This makes it harder for galaxies to clump together, like trying to build a sandcastle when the wind is blowing.
The Result: By adding this "clumping" data to the "distance" data, the scientists could finally see the leak. The 21-cm data broke the tie. It showed that the Universe's structure is slightly less clumpy than the standard "stable" theory predicts, which fits perfectly with the idea of decaying Dark Matter.

What Did They Find?

The "Leak" is Real (Maybe): When they combined the distance data (DESI) with the clumping data (21-cm forecast), they found strong evidence that Dark Matter might indeed be decaying.
The Decay Rate: They calculated that the "parent" Dark Matter particles have a lifetime of about 46 billion years (much longer than the current age of the Universe, but long enough to be noticeable).
The "Children": When the parent decays, it splits into two. One part is massless (like light), and the other is a heavy "daughter" particle. The data suggests this heavy daughter behaves almost exactly like normal, cold Dark Matter, just with a tiny bit of extra "kick."
Dark Energy: Because they didn't assume a specific model for Dark Energy, they reconstructed what it looks like based on the data. The result? It still looks very much like the standard "Cosmological Constant" (a steady, unchanging force), but the new data makes the standard model look slightly less perfect than before.

The Takeaway

This paper is a masterclass in not making assumptions. By using a flexible math tool for the expansion of the Universe and combining two different types of cosmic measurements (distance and structure), they were able to isolate a specific behavior of Dark Matter.

In short: They found that if you assume Dark Matter is slowly falling apart, the Universe's history makes a lot more sense, especially when you look at how galaxies are clustering together. It's a step toward understanding that the "dark sector" of the Universe might be more dynamic and complex than we previously thought.

1. Problem Statement

The standard $\Lambda$ CDM cosmological model, while successful, faces theoretical challenges regarding the fundamental nature of Dark Matter (DM) and Dark Energy (DE), as well as persistent observational tensions (e.g., the Hubble $H_0$ and $S_8$ tensions).

Dark Matter: The assumption that DM is perfectly stable and cold (CDM) is an unproven hypothesis. Decaying Dark Matter (DDM) scenarios, where a parent particle decays into a massless (dark radiation) and a massive daughter, offer a potential solution to small-scale structure issues and cosmological tensions.
Dark Energy: Most studies assume a specific parametric model for DE (e.g., $\Lambda$ or CPL). This introduces model bias.
Methodological Limitation: Purely data-driven "cosmography" (expanding observables in redshift) often suffers from limited convergence radii at high redshifts ( $z \ge 1$ ). Conversely, fully dynamical models rely on specific theoretical assumptions.
Goal: The authors aim to constrain a two-body Decaying Dark Matter (DDM) scenario and reconstruct the Dark Energy Equation of State (EoS) without assuming a specific DE model, using a "semi-cosmographic" framework. They utilize current DESI DR2 Baryon Acoustic Oscillation (BAO) data and forecast future 21-cm intensity mapping data to break degeneracies between expansion history and structure growth.

2. Methodology

A. Semi-Cosmographic Framework

The authors employ a hybrid approach:

Cosmographic Expansion (Model-Independent DE): Instead of assuming a DE potential or parameterization (like $w_0 w_a$ ), they model the Luminosity Distance $D_L(z)$ using a Padé rational approximant in terms of the variable $\xi = \sqrt{1+z}$ .
$D_L^P(z) = \frac{c}{H_0} \left[ \frac{2(\xi^4 - a_1\xi^3 - (1-a_1)\xi^2)}{b_1\xi^2 + c_1\xi + (2-a_1-b_1-c_1)} \right]$
This form ensures better convergence at high redshifts compared to Taylor expansions. From this, the Hubble parameter $H_P(z)$ is derived kinematically.
Dynamical Dark Matter (Phenomenological DM): The DM sector is modeled as a non-relativistic parent particle ( $\rho_0$ $ρ_{0}$ ) decaying into a massless daughter ( $\rho_1$ $ρ_{1}$ , dark radiation) and a massive daughter ( $\rho_2$ $ρ_{2}$ ).
- Parameters: Decay rate $\Gamma = 1/\tau$ and energy partition parameter $\epsilon$ (determining the mass ratio and recoil velocity).
- Evolution: The background densities evolve via coupled continuity equations. The massive daughter acquires a time-dependent effective Equation of State $w_2(a)$ due to the "kick" velocity from decay, behaving as warm DM initially and cooling over time.
Reconstruction of DE EoS: By embedding the kinematic $H_P(z)$ into the Friedmann equations with the specific DDM densities, the authors derive an effective semi-cosmographic Dark Energy EoS, $w_\phi^P(z)$ . This allows them to infer the DE behavior purely from the data and the assumed DDM physics, without pre-selecting a DE model.

B. Observational Probes

DESI DR2 BAO: Uses BAO measurements from the Dark Energy Spectroscopic Instrument (DESI) Data Release 2. This provides geometric constraints on the expansion history ( $D_M, D_H, D_V$ ) across redshifts $z \in [0.295, 2.33]$ .
21-cm Intensity Mapping (Forecast): To break degeneracies, the authors include a forecast for the 21-cm power spectrum at $z \simeq 1.75$ $z ≃ 1.75$ using a SKA1-Mid-like interferometer.
- Unlike BAO (which probes geometry), 21-cm intensity mapping probes the growth of structure and matter clustering.
- They construct a mock anisotropic power spectrum $P_{HI}(k, \mu, z)$ including Alcock-Paczyński rescaling, redshift-space distortions, and thermal noise.
- Caveat: The analysis assumes a Cold Dark Matter (CDM)-based bias for HI, acknowledging this is an approximation for a DDM universe.

C. Statistical Analysis

MCMC: Markov Chain Monte Carlo analysis is used to constrain the joint parameter space:
- Cosmographic: $h, a_1, b_1, c_1$
- DDM: $\epsilon, \tau, \Omega_{dm}$
Data Combinations:
1. DESI BAO alone.
2. DESI BAO + Mock 21-cm power spectrum.

3. Key Contributions

Novel Framework: Development of a semi-cosmographic method that combines a model-independent Padé expansion for the background geometry with a specific phenomenological DDM model. This avoids the "model bias" of assuming a specific DE form while still incorporating physical DM dynamics.
Degeneracy Breaking: Demonstration that geometric probes (BAO) alone cannot tightly constrain DDM parameters because the flexible Padé expansion can absorb the effects of decay on the expansion history. However, adding clustering information (21-cm) breaks this degeneracy, as decay suppresses structure growth in a way that cannot be mimicked by simple background expansion changes.
Reconstruction of EoS: Successful reconstruction of the Dark Energy EoS ( $w_\phi(z)$ ) and the massive daughter's EoS ( $w_2(z)$ ) directly from the data constraints, rather than assuming a functional form.

4. Results

A. Parameter Constraints

DESI BAO Only:
- Background parameters ( $h, \Omega_{dm}$ ) and Padé coefficients are constrained at the few-percent level.
- DDM parameters ( $\epsilon, \tau$ ) remain weakly constrained. The posterior distributions are broad, indicating that BAO data alone cannot distinguish between a stable CDM universe with a specific DE history and a decaying DM universe with a different DE history.
DESI + 21-cm (Joint Analysis):
- The addition of the 21-cm power spectrum significantly tightens the constraints on DDM parameters.
- Best-fit values: $\log_{10} \epsilon \approx -1.97$ ( $\epsilon \approx 1.1\%$ ) and $\log_{10}(\tau/\text{yr}) \approx 10.66$ ( $\tau \approx 46$ Gyr).
- The allowed region in the $(\epsilon, \tau)$ plane shrinks substantially, proving that clustering data is essential for constraining decay physics.

B. Equation of State Reconstructions

Dark Energy ( $w_\phi$ ):
- DESI Only: The reconstructed $w_\phi(z)$ is consistent with a cosmological constant ( $w = -1$ ) but with large uncertainties.
- Joint Analysis: The uncertainty band tightens. The reconstruction shows a mild trend toward $w_\phi > -1$ (phantom-like or evolving DE) at $z \gtrsim 1.5$ , though $w=-1$ is not strictly excluded. The inclusion of growth data reduces the uncertainty propagation from the DDM sector to the DE sector.
Massive Daughter ( $w_2$ ):
- In the joint analysis, the massive daughter is constrained to behave effectively as cold dark matter ( $w_2 \approx 0$ ) at late times ( $z < 2.3$ ). The tight constraints on $\epsilon$ and $\tau$ force the daughter's recoil velocity to be small, meaning it cools rapidly.

C. Comparison with Literature

The joint constraints are compatible with previous studies (e.g., Abellán et al., Fuß & Garny) but favor a slightly shorter lifetime ( $\tau$ ) compared to some Planck-only analyses, highlighting the power of the 21-cm clustering data.

5. Significance and Conclusion

Methodological Validation: The paper validates the semi-cosmographic approach as a robust tool for testing extensions to the standard model without assuming a specific Dark Energy theory.
Importance of Clustering: The study conclusively shows that geometric probes alone are insufficient to constrain decaying dark matter. The suppression of structure growth (clustering) is the unique signature of DDM that must be measured to break degeneracies with the expansion history.
Future Prospects: While the 21-cm results are forecasts based on idealized assumptions (ignoring foregrounds and systematics), they demonstrate the immense potential of future radio telescopes (like SKA) to resolve the nature of Dark Matter and Dark Energy.
Physical Insight: The results suggest that if Dark Matter decays, it likely does so into a small fraction of dark radiation and a massive daughter that behaves very similarly to Cold Dark Matter in the late universe, consistent with current large-scale structure observations.

In summary, this work provides a rigorous, model-agnostic framework to test the stability of Dark Matter, demonstrating that combining high-precision geometric data (DESI) with future clustering data (21-cm) is the key to unlocking the physics of the dark sector.