The Cosmological potential of distant clusters with Athena/WFI

Deep extragalactic surveys in X-rays are shown to be powerful tools to detect galaxy clusters and study their properties and evolution. The Athena Wide Field Imager will probe the galaxy cluster population down to the group scale out to z=2. The 1<z<2 range is the era of  cluster assembly but very poorly sampled to date. This is of great interest not only to study cluster-AGN  interactions, but also to  address open questions on precision cosmology. We consider two survey designs sharing the same total Texp = 9Ms, one of 50 deg² at 80ks, and a second, wider of 200 deg² at 20ks. In both cases, our derivation of the selection function  shows that several hundreds of clusters will be detected in the 1<z<2 range. Using a forward modelling of the X-ray cluster observable parameters, we provide cosmological forecasts for both survey configurations.