Cosmological constraints from CODEX galaxy clusters spectroscopically confirmed by SDSS-IV/SPIDERS DR16

This paper presents a cosmological analysis based on the properties of X-ray selected clusters of galaxies from the CODEX survey which have been spectroscopically followed up within the SPIDERS programme as part of the sixteenth data release (DR16) of SDSS-IV. The cosmological sub-sample contains a total of 691 clusters over an area of 5350 deg² with newly measured optical properties provided by a reanalysis of the CODEX source catalogue using redMaPPer and the DESI Legacy Imaging Surveys (DR8). Optical richness is used as a proxy for the cluster mass, and the combination of X-ray, optical, and spectroscopic information ensures that only confirmed virialized systems are considered. Clusters are binned in observed redshift, $\tilde{z} \in \left[0.1, 0.6 \right)$ and optical richness, $\tilde{\lambda } \in \left[25, 148 \right)$ and the number of clusters in each bin is modelled as a function of cosmological and richness-mass scaling relation parameters. A high-purity sub-sample of 691 clusters is used in the analysis and best-fitting cosmological parameters are found to be $\Omega _{m_{0}}=0.34^{+0.09}_{-0.05}$ and $\sigma _8=0.73^{+0.03}_{-0.03}$. The redshift evolution of the self-calibrated richness-mass relation is poorly constrained due to the systematic uncertainties associated with the X-ray component of the selection function (which assumes a fixed X-ray luminosity-mass relation with h = 0.7 and $\Omega _{m_{0}}=0.30$). Repeating the analysis with the assumption of no redshift evolution is found to improve the consistency between both cosmological and scaling relation parameters with respect to recent galaxy cluster analyses in the literature.