The non-linear bispectrum with initial spectral index −1 *

Bispectrum, or three-point correlation function in Fourier space, is the lowest order non-Gaussian statistic to study the large-scale structure produced by gravitational instability. In Fourier space, the 2-dimensional density field has the same statistical properties as the 3-dimensional field, and compared with the 3-dimensional fast Fourier transform (FFT), the 2-dimensional FFT can save a lot of computer resources. In a combination of 2- and 3-dimensional FFTs and using a high-resolution N-body numerical simulation with the initial spectral index -1, we have measured the bispectrum from the weakly linear regime to the strongly nonlinear regime. All possible effects of numerical artefacts on the power spectrum and bispectrum, such as particle discreteness, force softening, finite box size and alias effect, are considered and strictly corrected. In contrast with what previous researchers assumed, it is revealed that the reduced bispectrum depends on the triangle shape and scale even in the strongly nonlinear regime, and increases with the wave number. And based on the measured results, a new fitting formula for the bispectum suitable for cosmological models with an initial spectral index −1 is obtained.