The cosmological analysis of X-ray cluster surveys. V. The potential of cluster counts in the 1 < z < 2 range

Context. Cosmological studies have now entered Stage IV according to the Dark Energy Task Force (DETF) prescription. New missions (Euclid, Rubin Observatory, SRG/eROSITA) will cover very large fractions of the sky with unprecedented depth. These are expected to provide the required ultimate accuracy in the dark energy (DE) equation of state (EoS), which is required for the elucidation of the origin of the acceleration of cosmic expansion. However, none of these projects have the power to systematically unveil the galaxy cluster population in the 1 < z < 2 range. There therefore remains the need for an Athena-like mission to run independent cosmological investigations and scrutinise the consistency between the results from the 0 < z < 1 and 1 < z < 2 epochs.
Aims: We study the constraints on the DE EoS and on primordial non-gaussanities for typical X-ray cluster surveys executed by a generic Athena-like Wide Field Imager. We focus on the impact of cluster number counts in the 1 < z < 2 range.
Methods: We consider two survey designs: 50 deg² at 80 ks (survey A) and 200 deg² at 20 ks (survey B). We analytically derive cluster number counts and predict the cosmological potential of the corresponding samples, A and B, by means of a Fisher analysis. We adopt an approach that forward models the observed properties of the cluster population in the redshift-count rate-hardness ratio parameter space.
Results: The achieved depth allows us to unveil the halo mass function down to the group scale out to z = 2. We predict the detection of thousands of clusters down to a few 10¹³h⁻¹ M_⊙, in particular 940 and 1400 clusters for surveys A and B, respectively, at z > 1. Such samples will allow a detailed modelling of the evolution of cluster physics along with a standalone cosmological analysis. Our results suggest that survey B has the optimal design as it provides greater statistics. Remarkably, high-redshift clusters represent 15% or less of the full samples but contribute at a much higher level to the cosmological accuracy: by alleviating various degeneracies, these objects allow a significant reduction of the uncertainty on the cosmological parameters: Δw_a is reduced by a factor of ∼2.3 and Δ f_NL^loc by a factor of ∼3.
Conclusions: Inventorying the deep high-z X-ray cluster population can play a crucial role in ensuring overall cosmological consistency. This will be the major aim of future new-generation Athena-like missions.