Analysis of Non-Linear Mode Coupling of Cosmological Density Fluctuations by the Pseudo-Spectral Method

Abstract

The pseudo-spectral method is proposed for following the evolution of density and velocity fluctuations at the weakly non-linear stage in the expanding universe with a good accuracy. In this method, the evolution of density and velocity fluctuations is integrated in the Fourier Space with using FFT. This method is very useful to investigate accurately the non-linear dynamics in the weakly non-linear regime. Because the pseudo-spectral method works directly in the Fourier space, it should be especially useful for examining behavior in the Fourier domain, for an example, the effects of the non-linear coupling of different wave modes on the evolution of the power spectrum. I show the results of this analysis both in one and three dimensional systems.