初始谱指数为-1的非线性重谱(Bispectrum)

重谱即傅立叶空间的三点相关函数，是研究由引力不稳定性产生的大尺度结构的最低非高斯阶统计性质．在傅立叶空间中，发现二维和三维空间的统计性质是等价的，相对三维快速傅立叶，二维快速傅立叶变换可以节省很多计算机资源．结合二维和三维的快速傅立叶变换，利用高精度的初始谱指数为-1的N体数值模拟，测量了从弱线性区域到强非线性区域的重谱．在测量过程中，考虑并严格校正了作用于功率谱和重谱上的数值效应，如离散效应（particle discreteness）、软化因子（force softening）、模拟盒子的大小、混淆效应（alias effect）．发现约化重谱即使在强非线性区域仍然依赖于三角形的形状和尺度，并随着波数的增加而增加，这和前人的假设完全不同．在测量结果的基础上，拟合了重谱的一个适用于初始谱指数为-1的宇宙学模型的经验公式．

The non-linear Bispectrum from the scale-free N-body simulation with the spectral index -1

Bispectrum, the three-point correlation function in Fourier space, is the lower-est order statistic that probes the shape of the large-scale structures generated by the gravitational clustering. The 2-dimensional density field in Fourier space has the same statistical properties as the 3-dimensional field, and the 2-dimensional fast Fourier transform (FFT) needs less computer memory than the 3-dimensional case, then the 2-dimensional FFT can overcome the limitation of the computation. With the 2-dimensional and 3-dimensional FFT, we measured the bispectrum from the weakly non-linear regime to strong non-linear regime using the high resolution N-body simulation with spectral index -1. In this work, all possible effects on the bispectrum measurement of the numerical artifacts, such as finite box size, force softening, particle discreteness, and the effect caused by the mass assignment using the FFT are considered and correted strictly. The measured results show that the reduced bispectrum depends on the shape and size of k-triangle even in the strongly non-linear regime, and increases with wavenumber. These results are in contrast with the hypothesis 'of pioneer. A new fitting formula for the reduced bispectrum is obtained from the measured results.