Speaker
Description
We study the simplest non-perturbative statistics -- the one-point probability distribution function (PDF) for the averaged matter density inside spherical cells. The leading part to the PDF is defined by spherical collapse dynamics, whereas the next-to-leading part comes from the integration over fluctuations around the saddle-point solution. The latter calculation receives sizable contributions from short modes and must be renormalized. We propose a new approach to renormalization by modeling the effective stress-energy tensor for short perturbations. The model contains three free parameters. Two of them are related to the counterterms in the one-loop matter power spectrum and bispectrum, one more parameterizes their redshift dependence. This relation can be used to impose priors in fitting the model to the PDF data. We confront the model with the results of high-resolution N-body simulations and find excellent agreement for cell radii $r_∗ ≥ 10\, {\rm Mpc/h}$ at all redshifts down to $z = 0$.
Additionally, we explore the sensitivity of the one-point PDF to the cosmological parameters. Our results suggest that our PDF model is sensitive to the value of $\sigma_8$ at the sub-per cent level. Another promising direction is to model the counterterm parameters in the Effective Field Theory of Large Scale Structure. Our PDF model provides comparable or better constraints on the counterterm coefficients than the correlation functions.
The talk is based on the published paper -- https://iopscience.iop.org/article/10.1088/1475-7516/2023/08/079.
