CODEX clusters. The Survey, the Catalog, and Cosmology of the X-ray
  Luminosity Function
  Large area catalogs of galaxy clusters constructed from ROSAT All Sky Survey
provide the base for our knowledge on the population of clusters thanks to the
long-term multiwavelength efforts on their follow-up. Advent of large area
photometric surveys superseding in depth previous all-sky data allows us to
revisit the construction of X-ray cluster catalogs, extending the study to
lower cluster masses and to higher redshifts and to provide the modelling of
the selection function. We perform a wavelet detection of X-ray sources and
make extensive simulations of the detection of clusters in the RASS data. We
assign an optical richness to each of the 24,788 detected X-ray sources in the
10,382 square degrees of SDSS BOSS area, using redMaPPer version 5.2. We name
this survey COnstrain Dark Energy with X-ray (CODEX) clusters. We show that
there is no obvious separation of sources on galaxy clusters and AGN, based on
distribution of systems on their richness. This is a combination of increasing
number of galaxy groups and their selection as identification of an X-ray
sources either by chance or due to groups hosting an AGN. To clean the sample,
we use a cut on the optical richness at the level corresponding to the 10\%
completeness of the survey and include it into the modelling of cluster
selection function. We present the X-ray catalog extending to a redshift of 0.6
down to X-ray fluxes of $10^{-13}$ ergs s$^{-1}$ cm$^{-2}$. We provide the
modelling of the sample selection and discuss the redshift evolution of the
high end of the X-ray luminosity function (XLF). Our results on $z<0.3$ XLF are
in agreement with previous studies, while we provide new constraints on the
$0.3<z<0.6$ XLF. We find a lack of strong redshift evolution of the XLF,
provide exact modeling of the effect of low number statistics and AGN
contamination and present the resulting constraints on the flat $\Lambda$CDM.
