The motivation stems from a familiar frustration. The Lambda-CDM model — the concordance cosmology in which about 25 percent of the Universe’s energy budget is cold dark matter and roughly 70 percent is a cosmological constant — fits an impressive range of observations, from the cosmic microwave background to galaxy clustering. Yet it offers no fundamental explanation for either dark sector, and persistent tensions in the data, including disagreements over the Hubble constant and the clustering amplitude S8, hint that the framework may be incomplete. Decaying dark matter has emerged as a compelling alternative because a parent particle that slowly transforms into lighter daughters could simultaneously relieve the small-scale structure problems of cold dark matter and ease the Hubble and S8 tensions. There is, the authors argue, no compelling reason why dark matter should be perfectly stable in the first place.

The team’s framework is deliberately called semi-cosmographic, a middle path between fully model-dependent fits and completely agnostic data reconstructions. Pure cosmography expands observable quantities such as the luminosity distance as series in redshift, with the expansion coefficients constrained directly by data. But simple Taylor expansions break down above redshift one, precisely where much modern data lies. The researchers instead adopt a Padé rational approximant — a ratio of two polynomials in the variable xi, defined as the square root of one plus redshift — to describe the luminosity distance, which improves convergence at high redshift and reproduces sensible asymptotic behavior in both the low- and high-redshift limits. The three Padé parameters are treated as free quantities to be pinned down by observation rather than tied to any preselected dark energy model.

Into this flexible expansion history the authors embed a physically motivated two-body decaying dark matter sector. In their scenario, a non-relativistic parent dark matter particle decays with a constant rate Gamma, equal to the inverse of its lifetime tau, into two daughters: a massless relativistic particle, interpretable as dark radiation, and a massive daughter particle. A single dimensionless parameter epsilon controls how the parent’s rest energy is shared between the two channels. When epsilon is small, the massive daughter receives only a tiny recoil kick and behaves essentially like cold matter; when epsilon approaches one half, the daughter is born nearly relativistic. Crucially, because each decay injects daughter particles with a fixed physical momentum that then redshifts as the Universe expands, the massive daughter population is a superposition of particles produced at different epochs — early-produced daughters cool into effectively cold matter while late-produced ones remain warm. The result is a time-dependent effective equation of state for the massive daughter, which the team computes self-consistently by integrating the coupled continuity equations that govern how the parent, massless daughter and massive daughter densities evolve.

The heart of the analysis is the reconstruction of an effective residual dark energy. Once the Padé expansion history is specified and the decaying dark matter, baryon and radiation densities are known, whatever remains under the standard Friedmann equation for a spatially flat Universe must be attributed to a residual dark-energy component. Its effective equation of state, w_phi of z, is therefore not an independent model prediction but a conditional reconstruction — a diagnostic of what kind of dark energy behavior is required if the decaying dark matter picture holds. The authors are careful to stress this interpretive caveat: different parameterizations of the background expansion or different matter-sector assumptions could yield quantitatively different residual reconstructions even when the fits to data are comparably good.

For the observational constraints, the team turned to the DESI DR2 baryon acoustic oscillation data set, comprising thirteen measurements of transverse, radial, volume-averaged and anisotropic distance combinations across redshifts from about 0.295 to 2.33, along with their full covariance matrix. These geometric observables probe the smooth expansion history with exquisite precision, and the analysis recovered few-percent-level constraints on the Padé parameters and the background density parameters. However, the decay parameters — the kick strength epsilon and the lifetime tau — remained only weakly constrained by BAO data alone. The reason is subtle but important: the Padé ansatz is flexible enough that changes in the decay sector can be absorbed into adjustments of the expansion history, so many combinations of the two parameter sets reproduce nearly the same distance-redshift relation. Geometry alone cannot break that degeneracy.

This is where the 21 centimeter line enters the story. Rather than detecting individual galaxies, intensity mapping measures the collective radio emission from neutral hydrogen across large swaths of sky, tracing the large-scale distribution of matter in the post-reionization Universe between redshifts one and three. Unlike baryon acoustic oscillations, the 21 centimeter power spectrum is sensitive not only to the background expansion but also to the growth rate and scale dependence of matter clustering — exactly the quantities that decaying dark matter modifies. Decay reduces the late-time matter density and free-streaming of the kicked daughters suppresses clustering below a characteristic scale, effects that cannot be mimicked by simply reshaping the smooth background. The researchers constructed an optimistic mock power-spectrum data set at redshift 1.75 for an SKA1-MID-like interferometer with 197 dishes of fifteen-meter diameter, a system temperature of 60 Kelvin, and 4000 hours of observing time, using a simulation-based emulator calibrated on N-body simulations of two-body decaying dark matter to model the nonlinear suppression of the matter power spectrum.

The forecast results are striking. When the mock 21 centimeter likelihood is combined with the DESI DR2 BAO data, the decay parameters collapse from a broad, poorly constrained region to tight posteriors: a kick parameter of roughly 1.1 percent and a lifetime of approximately 29 gigayears at 68 percent credibility — values that place the dark matter comfortably in a regime where it behaves almost, but not exactly, like the standard cold variety. The reconstructed equation of state of the massive daughter is driven to values of order ten to the minus five over the redshift range zero to 2.3, meaning the daughter behaves effectively as cold matter for late-time structure formation. Meanwhile, the residual dark-energy equation of state, which was broadly consistent with a cosmological constant in the BAO-only analysis, becomes noticeably tighter in the joint forecast, with the band overlapping the value minus one considerably less — a weak tension that the authors interpret cautiously rather than as evidence against the cosmological constant, especially since the uncertainty grows with redshift.

The team also verified that their approach is internally consistent. Because the sound horizon used to calibrate the BAO measurements was fixed to its Planck CMB value, one might worry that decaying dark matter with a relativistic daughter could alter pre-recombination physics and invalidate that calibration. The researchers checked every posterior sample against a no-decay reference, quantifying shifts in the pre-recombination expansion rate, the matter-radiation equality redshift and the sound horizon itself. The verdict: almost no decay occurs before the drag epoch, and the maximum sound-horizon shift falls below the CMB uncertainty, confirming that the fixed calibration is self-consistent within the allowed parameter regions. Comparisons with earlier literature, including the work of Abellán and collaborators and of Fuß and Garny, show broad agreement in the low-epsilon, long-lifetime regime, though the inclusion of clustering information nudges the preferred lifetime somewhat shorter.

The authors are candid about the limitations of their forecast. The neutral hydrogen bias used in the mock analysis is calibrated on standard cold dark matter simulations and may not fully capture how decaying dark matter reshapes the halo population; foreground contamination from Galactic synchrotron emission — many orders of magnitude brighter than the cosmological signal — and the chromatic foreground wedge of the interferometer could degrade the constraints by factors of two to three, and the analysis deliberately excludes such systematics as an optimistic proof of concept. Even so, the central lesson stands with unusual clarity: geometric probes like BAO, however precise, cannot by themselves disentangle a changing expansion history from genuine particle decay. Growth-sensitive information — whether from 21 centimeter intensity mapping, weak gravitational lensing or the Lyman-alpha forest — is essential to isolate the physics of an unstable dark sector. As the Square Kilometre Array moves toward operational maturity, the crossroads of cosmography, decaying dark matter and radio cosmology may offer one of the sharpest tests yet of whether the Universe’s most abundant matter is truly as permanent as we have assumed.

Subject of Research: Semi-cosmographic reconstruction of residual dark energy in a two-body decaying dark matter cosmology using DESI DR2 BAO data and 21 cm intensity-mapping forecasts

Article Title: Padé semi-cosmographic reconstruction of residual dark energy in decaying dark matter cosmology: DESI DR2 BAO constraints and mock 21 cm forecasts

Article References: Yadav, M., Chavan, P., & Sarkar, T. G. (2026). Padé semi-cosmographic reconstruction of residual dark energy in decaying dark matter cosmology: DESI DR2 BAO constraints and mock 21 cm forecasts. The European Physical Journal C, 86(9), Article 1093. https://doi.org/10.1140/epjc/s10052-026-16335-2

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16335-2

Keywords: dark matter, dark energy, decaying dark matter, Padé approximant, cosmography, DESI DR2, baryon acoustic oscillations, 21 cm intensity mapping, SKA, equation of state, cosmological constant, large-scale structure