Primordial non-Gaussianity and extreme-value statistics of galaxy clusters

What is the size of the most massive object one expects to find in a survey of a given volume? In this paper, we present a solution to this problem using extreme-value statistics, taking into account primordial non-Gaussianity and its effects on the abundance and the clustering of rare objects. We calculate the probability density function (PDF) of extreme-mass clusters in a survey volume, and show how primordial non-Gaussianity shifts the peak of this PDF. We also study the sensitivity of the extreme-value PDFs to changes in the mass functions, survey volume, redshift coverage, and the normalization of the matter power spectrum, sigma(8). For local non-Gaussianity parametrized by f(NL), our correction for the extreme-value PDF due to the bias is important when f(NL) greater than or similar to 100, and becomes more significant for wider and deeper surveys. Applying our formalism to the massive high-redshift cluster XMMUJ0044.0-2-33, we find that its existence is consistent with f(NL) = 0, although the conclusion is sensitive to the assumed values of the survey area and sigma(8). We also discuss the convergence of the extreme-value distribution to one of the three possible asymptotic forms, and argue that the convergence is insensitive to the presence of non-Gaussianity.