Large-scale Structures revealed by Wavelet Decomposition

TL;DR

This paper reviews how wavelet decomposition techniques can analyze large-scale cosmic structures, revealing new features and aiding model differentiation in observational and simulated data.

Contribution

It introduces comprehensive wavelet-based statistical methods for analyzing large-scale structures, demonstrating their effectiveness in identifying features and distinguishing models.

Findings

Wavelet methods effectively reconstruct power spectra.

Statistical measures reveal features not detected before.

Wavelet analysis helps differentiate structure formation models.

Abstract

We present a detailed review of large-scale structure (LSS) study using the discrete wavelet transform (DWT). After describing how one constructs a wavelet decomposition we show how this bases can be used as a complete statistical discription of LSS. Among the topics studied are the the DWT estimation of the probability distribution function; the reconstruction of the power spectrum; the regularization of complex geometry in observational samples; cluster identification; extraction and identification of coherent structures; scale-decomposition of non-Gaussianity, such as spectra of skewnes and kurtosis and scale-scale correlations. These methods are applied to both observational and simulated samples of the QSO Lyman-alpha forests. It is clearly demonstrated that the statistical measures developed using the DWT are needed to distinguish between competing models of structure formation. The DWT also reveals physical features in these distributions not detected before. We conclude with a look towards the future of the use of the DWT in LSS.