# Statistical Analysis of Large-Scale Structure of Universe

## TL;DR

This paper discusses statistical methods for analyzing the large-scale structure of the universe, focusing on the growth of density fluctuations and deriving a power-law relation for the matter power spectrum.

## Contribution

It introduces a Fourier harmonic approach to study the growth of density fluctuations in one- and three-dimensional cases, providing new insights into the matter power spectrum.

## Key findings

- Derived a power-law relation for the matter power spectrum.
- Highlighted the importance of statistical parameters for cosmological models.
- Discussed potential future observations with ATHENA and SKA.

## Abstract

While galaxy cluster catalogs were compiled many decades ago, other structural elements of cosmic web are detected at definite level only in the newest works. For example, extragalactic filaments were described by velocity field and SDSS galaxy distribution during the last years. Large-scale structure of the Universe could be also mapped in the future using ATHENA observations in X-rays and SKA in radio band. Until detailed observations are not available for the most volume of Universe, some integral statistical parameters can be used for its description. Such methods as galaxy correlation function, power spectrum, statistical moments and peak statistics are commonly used with this aim. The parameters of power spectrum and other statistics are important for constraining the models of dark matter, dark energy, inflation and brane cosmology. In the present work we describe the growth of large-scale density fluctuations in one- and three-dimensional case with Fourier harmonics of hydrodynamical parameters. In result we get power-law relation for the matter power spectrum.