Recent advancements in X-ray cluster Cosmology in preparation for
eROSITA


X-ray emission from the hot gas contained in galaxy clusters has long
been established as a reliable method to selected large and clean
samples of galaxy clusters. Utilising such samples to constrain the
density and amplitude of fluctuation of matter in the Universe, as well as
the evolution of Dark Energy, however, requires to overcome several
observational challenges as well as to control several systematic effects.
First, I review the established modelling framework to extract
cosmological information from cluster catalogues and present the
expected performance of eROSITA as a cosmological experiment. After
that, I will present recent and ongoing efforts to control the dominant
systematic effects plaguing cluster cosmology, ranging from mass
calibration over optical confirmation and redshift estimation to the
characterisation of the X-ray selection function. Finally, I will present
novel techniques that allow one to empirically validate cluster
cosmological results.