Dark energy reconstructions combining BAO data with galaxy clusters and intermediate redshift catalogs

Cosmological parameters and dark energy (DE) behavior are generally constrained assuming \textit{a priori} models. We work out a model-independent reconstruction to bound the key cosmological quantities and the DE evolution. Through the model-independent \textit{B\'ezier interpolation} method, we reconstruct the Hubble rate from the observational Hubble data and derive 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 are kept separate in two distinct analyses. Correlated BAO data are 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. In both analyses, with SDSS-BAO or DESI-BAO data sets, the constraints agree at $1$--$\sigma$ 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 $z$. Our method hints for a slowly evolving DE, consistent with a cosmological constant at early times.