Derivation of the Hubble parameter using galaxy clusters

In this work we describe a possible way to use X-ray and microwave observations of nearby galaxy clusters to derive the value of the Hubble constant, that parametrises the expansion rate of the Universe. We provide a brief introduction to the Sunyaev-Zel'dovich effect that allows to detect galaxy clusters at microwave frequencies, and the method to combine it with X-ray observables. We emphasize what kind of considerations should be done when applying the method on real data and study the effect of the geometry of the clusters on the final result.