22-26 August 2011, Porto, Portugal
Extreme Value Theory and Primordial Non-Gaussianity. What is the size of the most massive object one expects to find in a survey of a given volume and redshift? In this talk, I present a solution to this problem using Extreme Value Theory (EVT). Though EVT has long been used in finance and engineering, there have only been a handful of cosmological applications, and none in the context of primordial non-Gaussianity. I show how EVT naturally gives the probability density function (pdf) of maximum-mass clusters in a survey volume, and how primordial non-Gaussianity shifts the peak of this pdf. The non-Gaussian effects on the pdf of extreme-mass objects are shown to be greatly enhanced at high redshifts. The dependence of our results on the mass functions and critical overdensity will also be discussed. In addition, I show that the probability distribution of the most massive clusters are well described by the so-called Fréchet family of distribution, regardless of the presence of non-Gaussianity. Finally, I discuss an extension of our technique to calculate the size of the largest void one expects to find in a given volume and redshift. |
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