Applications Of The Continuous Wavelet Analysis To The Large-Scale Structure Of The Universe

Continuous wavelet analysis has been increasingly employed in various fields of science and engineering due to its remarkable ability to maintain optimal resolution in both space and scale.In this thesis,we explore the application of statistical tools based on the continuous wavelet transform to the study of the large-scale structure of the Universe.First,we propose a novel scheme for constructing real even continuous wavelets,in which the wavelet functions are obtained by taking the first-order derivative of the real even smoothing functions with respect to the scale parameter.Due to this scheme,the inverse continuous wavelet transform is only a single integral with respect to the scale parameter.We then generalize this empirically obtained single integral inverse transform to hold for general real even wavelets.To compute the continuous wavelet transform efficiently,we compare four fast algorithms and find the FFT-based algorithm yields the best performance.Next,we extend the one-dimensional continuous wavelet transform to higher dimensions,including the isotropic wavelet transform and the anisotropic wavelet transform.Based on the isotropic wavelet transform,we propose two new statistics: the environment-dependent wavelet power spectrum(env-WPS)and the environment-dependent wavelet cross-correlation function(env-WCC),and apply them to the cosmological simulation data sets.In this work,we use the density fields of TNG100-1 at redshifts of z = 3-0,Illustris-1,m100n1024,and m100n512 at z = 0.By comparing the TNG100-1 density field at z = 0 and the Gaussian density field with the same Fourier power spectrum,we find that their respective env-WPS exhibit significantly different properties,which thus suggests that env-WPS is fully capable of detecting the non-Gaussian nature of the density field and is a superior statistical tool to the Fourier power spectrum.Further,we analyze the correlation between the spatial distributions of the dark matter and baryons by using the env-WCC,and analyze the baryonic effect on the matter clustering by comparing the env-WPS of hydrodynamic simulations with those of their matched dark matter only simulations.We find that the impacts of baryonic physical processes on the matter spatial distribution are strongly dependent on the local density environment and scale,showing different environmental dependencies on different scales.By comparing the fullphysics,no AGN,and nofeedback simulations with different subgrid models under the m100n512 series,we find that the active galactic nuclei feedback is the most important cause of the change in the matter spatial distribution at z=0.