Dark energy reconstructions combining baryonic acoustic oscillation data with galaxy clusters and intermediate-redshift catalogs

Context. Cosmological parameters and dark energy (DE) behavior are generally constrained assuming a priori models. Aims. We work out a model-independent reconstruction to bind the key cosmological quantities and the DE evolution. Methods. Through the model-independent B & eacute;zier interpolation method, we reconstructed the Hubble rate from the observational Hubble data and derived analytic expressions for the distances of galaxy clusters, type Ia supernovae, and uncorrelated baryonic acoustic oscillation (BAO) data. In view of the discrepancy between Sloan Digital Sky Survey (SDSS) and Dark Energy Spectroscopic Instrument (DESI) BAO data, they were kept separate in two distinct analyses. Correlated BAO data were employed to break the baryonic-dark matter degeneracy. All these interpolations enable us to single out and reconstruct the DE behavior with the redshift z in a totally model-independent way. Results. In both analyses, with SDSS-BAO or DESI-BAO datasets, the constraints agree at a 1-sigma confidence level (CL) with the flat Lambda CDM model. The Hubble constant tension appears solved in favor of the Planck satellite value. The reconstructed DE behavior exhibits deviations at small z (> 1-sigma CL), but agrees (< 1-sigma CL) with the cosmological constant paradigm at larger z. Conclusions. Our method hints at a slowly evolving DE, consistent with a cosmological constant at early times.