Abstract
We propose a model-independent \textit{Bézier parametric interpolation} to alleviate the degeneracy between baryonic and dark matter abundances by means of intermediate-redshift data. To do so, we first interpolate the observational Hubble data to extract cosmic bounds over the (reduced) Hubble constant, $h_0$, and interpolate the angular diameter distances, $D(z)$, of the galaxy clusters, inferred from the Sunyaev-Zeldovich effect, constraining the spatial curvature, $Ω_k$. Through the so-determined Hubble points and $D(z)$, we interpolate uncorrelated data of baryonic acoustic oscillations bounding the baryon ($ω_b = h^2_0Ω_b$) and total matter ($ω_m = h^2_0Ω_m$) densities, reinforcing the constraints on $h_0$ and $Ω_k$ with the same technique. Instead of pursuing the usual treatment to fix $ω_b$ via the value obtained from the cosmic microwave background to remove the matter sector degeneracy, we here interpolate the acoustic parameter from correlated baryonic acoustic oscillations. The results of our Monte Carlo--Markov chain simulations turn out to agree at $1$--$σ$ confidence level with the flat $Λ$CDM model. While our findings are roughly suitable at $1$--$σ$ with its non-flat extension too, the Hubble constant appears in tension up to the $2$--$σ$ confidence level. Accordingly, we also reanalyze the Hubble tension with our treatment and find our expectations slightly match local constraints.