Evolution of skewness and kurtosis of cosmic density fields

TL;DR

This paper investigates how skewness and kurtosis of cosmic density fields evolve over time and scale in LCDM simulations, revealing complex behaviors not captured by existing theories.

Contribution

It provides detailed numerical analysis and fitting formulas for the evolution of skewness and kurtosis in cosmic web simulations, highlighting their unique dependence on redshift and smoothing scale.

Findings

Skewness and kurtosis show complex scale and redshift dependence.

At early epochs, skewness and kurtosis approach constant levels.

Current theories do not adequately describe the evolution of these moments.

Abstract

Methods. We perform numerical simulations of the evolution of the cosmic web for the conventional LCDM model. The simulations cover a wide range of box sizes L = 256 - 4000 Mpc/h, mass and force resolutions and epochs from very early moments z = 30 to the present moment z = 0. We calculate density fields with various smoothing lengths to find the dependence of the density field on smoothing scale. We calculate PDF and its moments - variance, skewness and kurtosis. Results. We focus on the third (skewness S) and fourth (kurtosis K) moments of the distribution functions: their dependence on the smoothing scale, the amplitude of fluctuations and the redshift. During the evolution the reduced skewness $S_3= S/\sigma$ and reduced kurtosis $S_4=K/\sigma^2$ present a complex behaviour: at a fixed redshift curves of $S_3(\sigma)$ and $S_4(\sigma)$ steeply increase with $\sigma$ at $\sigma\le 1$ and then flatten out and become constant at $\sigma\ge2$. If we fix the smoothing scale $R_t$, then after reaching the maximum at $\sigma\approx 2$, the curves at large $\sigma$ start to gradually decline. We provide accurate fits for the evolution of $S_{3,4}(\sigma,z)$. Skewness and kurtosis approach at early epochs constant levels, depending on smoothing length: $S_3(\sigma) \approx 3$ and $S_4(\sigma) \approx 15$. Conclusions. Most of statistics of dark matter clustering (e.g., halo mass function or concentration-mass relation) are nearly universal: they mostly depend on the $\sigma$ with the relatively modest correction to explicit dependence on the redshift. We find just the opposite for skewness and kurtosis: the dependence of moments on evolutionary epoch $z$ and smoothing length $R_t$ is very different, together they determine the evolution of $S_{3,4}(\sigma)$ uniquely. The evolution of $S_3$ and $S_4$ cannot be described by current theoretical approximations.