Galaxy clusters are a powerful cosmological probe, being able to track the evolution of large scale structure in the latest Universe.
The theoretical modelling for the cosmological analysis of galaxy clusters is based on three main ingredients : the scaling relation between cluster observable and cluster mass (the mass-observable relation), the mass and redshift distribution of clusters (described by the halo mass function) and the description of the cluster detection and selection process (modelled through the selection function). In this talk I will show how different assumptions for these ingredients can impact the accuracy and precision of cosmological constraints inferred from galaxy clusters.
I will discuss a new analysis of clusters detected in mm wavelengths by the Planck satellite, highlighting the need of an improved description and calibration for the mass-observable relation. I will also show an independent point of view on the mass calibration problem, through a novel analysis based on the combination of Planck and South Pole Telescope cluster catalogs.
I will conclude my talk focusing on how to improve our analysis in view of future surveys, such as the Euclid satellite. In particular, I will show how the calibration of the halo mass function can strongly impact the results on cosmological parameters.