Wavelet Analysis of One-Dimensional Cosmological Density Fluctuations

Wavelet analysis is proposed as a new tool for studying the large·scale structure formation of the universe. To reveal its usefulness, the wavelet decomposition of a one-dimensional model of cos· mological density fluctuations is performed. In contrast with Fourier analysis, the wavelet analysis has the advantage of the ability to retain information concerning location of local density peaks in addition to that of their scales. The wavelet decomposition of evolving density fluctuations with various initial conditions is examined. We argue that the wavelet analysis is an alternative useful tool for data analysis as well as nonlinear analysis and may be usefully employed in the Sloan Digital Sky Survey and COBE analyses