Pad'e semi-cosmographic reconstruction of residual dark energy in decaying dark matter cosmology: DESI DR2 BAO constraints and mock 21 cm forecasts

Pure cosmographic reconstructions provide a model-agnostic approach towards constraining cosmic evolution.We develop a hybrid phenomenological semi-cosmographic framework that adopts a Padé-rational fraction parametrization of the luminosity distance, and incorporates a phenomenologically motivated two-body decaying dark matter (DDM) sector. In this framework, the effective residual dark-energy equation of state is obtained by subtracting the contributions of DDM, baryons, and radiation from the Padé approximation to the expansion history under the assumptions of flat FLRW cosmology and the standard Friedmann equations. Cosmological observables computed from these semi-cosmographic quantities are fitted to the data to reconstruct cosmological evolution. We present two separate analyses. First, we perform a data fit to the current DESI DR2 BAO measurements. Second, we report a forecast based on an optimistic mock 21,cm intensity-mapping power spectrum at z 1.75 for a SKA1-MID-like instrument, used jointly with the DESI DR2 BAO data. The forecast serves as proof of concept to demonstrate a possible improvement in model constraints when measurements of the 21,cm power spectrum complement the BAO background observables. Posterior constraints on the Padé and DDM parameters are obtained using Markov Chain Monte Carlo (MCMC) analysis, and we present the corresponding equations of state of the massive daughter and the effective reconstructed dark energy.