The potential of X-ray cluster surveys to constrain primordial non-Gaussianity

We present forecasts for constraints on deviations from Gaussian distribution of primordial density perturbations from future high-sensitivity X-ray surveys of galaxy clusters. Our analysis is based on computing the Fisher matrix for number counts and large-scale power spectrum of clusters. The surveys that we consider have high sensitivity and wide area to detect about 2.5 x 105 extended sources, and to provide reliable measurements of robust mass proxies for about 2 x 104 clusters. Based on the so-called self-calibration approach, and including Planck priors in our analysis, we constrain at once nine cosmological parameters and four nuisance parameters, which define the relation between cluster mass and X-ray flux. Because of the scale dependence of large-scale bias induced by local-shape non-Gaussianity, we find that the power spectrum provides strong constraints on the non-Gaussianity f(NL) parameter, which complement the stringent constraints on the power spectrum normalization, Sigma(8), from the number counts. To quantify the joint constraints on the two parameters, Sigma(8) and f(NL), that specify the timing of structure formation for a fixed background expansion, we define the figure of merit FoM(SFT) = (det[Cov(sigma(8), f(NL))])(-1/2). We find that our surveys constrain deviations from Gaussianity with a precision of delta f(NL) similar or equal to 10 at 1 Sigma confidence level, with FoM(SFT) similar or equal to 39. We point out that constraints on f(NL) are weakly sensitive to the uncertainties in the knowledge of the nuisance parameters. As an application of non-Gaussian constraints from available data, we analyse the impact of positive skewness on the occurrence of XMMU-J2235, a massive distant cluster recently discovered at z similar or equal to 1.4. We confirm that in a WMAP-7 Gaussian Lambda CDM cosmology, within the survey volume, similar or equal to 5 x 10-3 objects like this are expected to be found. To increase the probability of finding such a cluster by a factor of at least 10, one needs to evade either the available constraints on f(NL) or on the power-spectrum normalization Sigma(8).