The highlight of my day was a great NYU CCPP Brown-Bag talk by Mikhail Ivanov (NYU) about the one-point pdf of dark-matter density in the Universe, using a modified spherical-collapse model, based on things in this paper. It turns out that you can do a very good job of predicting counts-in-cells or equivalent one-point functions for the dark-matter density by considering the relationship between the linear theory and a non-linearity related to the calculable non-linearity you can work out in spherical collapse. More specifically, his approach is to expand the perturbations in the neighborhood of a point into a monopole term and a sum of radial functions times spherical harmonics. The monopole term acts like spherical collapse and the higher harmonics lead to a multiplicative correction. The whole framework depends on some mathematical properties of gravitational collapse that Ivanov can't prove but seem to be true in simulations. The theory is non-perturbative in the sense that it goes well into non-linear scales, and does well. That's some impressive theory, and it was a beautiful talk.
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