This paper presents a data-driven method to tell whether the Universe’s accelerated expansion is due to a changing dark energy or to energy being exchanged between dark energy and dark matter. The authors build a nonparametric reconstruction that uses both how the Universe expands and how structure grows. That combined approach can break a long-standing ambiguity: the same expansion history can be explained either by a time-varying dark energy equation of state or by a dark-sector interaction, or by a mix of both.

The team promoted the effective comoving matter density to a free function and put the corresponding interaction directly into the linear equation that controls matter perturbations. They reconstructed the expansion rate H(z) and the growth observable fσ8(z) with Gaussian processes (a flexible, data-driven way to infer functions). Hyperparameters were marginalized in a Bayesian analysis using the MCMC code emcee. The data sets included the Pantheon+ Type Ia supernova sample (1701 lightcurves, using 1590 objects with z>0.01), 31 Hubble-rate points from cosmic chronometers, baryon acoustic oscillation (BAO) measurements including DESI DR2, and 20 redshift-space-distortion (RSD) measurements of fσ8(z) over 0.02<z<1.944. They also used standard priors for the sound horizon and for σ8 from Planck 2018.

At a high level, expansion data fix the background geometry H(z) while RSD data probe the growth of matter clustering. Combining these two kinds of information lets the authors isolate whether deviations from the Lambda cold dark matter (ΛCDM) baseline come from a changing dark energy equation of state wde(z) (where the equation of state is the pressure divided by the energy density of dark energy) or from an interaction history Q(z) that moves energy between dark energy and dark matter. The paper considers two simple physical “closures” for the interaction: one where the energy transfer is proportional to the local dark matter density, and one where it is proportional to a smooth dark energy density. Each closure affects the growth equation in different ways and leads to distinct observational signatures.