We have accurately measured the bispectrum for four scale-free models of structure formation with the spectral index n = 1 , 0 , -1 , and -2 .
The measurement is based on a new method that can effectively eliminate the alias and numerical artifacts , and reliably extend the analysis into the strongly non-linear regime .
The work makes use of a set of state-of-the art N-body simulations that have significantly increased the resolution range compared with the previous studies on the subject .
With these measured results , we demonstrate that the measured bispectrum depends on the shape and size of k -triangle even in the strongly nonlinear regime .
It increases with wavenumber and decreases with the spectral index .
These results are in contrast with the hypothesis that the reduced bispectrum is a constant in the strongly non-linear regime .
We also show that the fitting formula of Scoccimarro & Frieman ( 1999 ) does not describe our simulation results well ( with a typical error about 40 percent ) .
In the end , we present a new fitting formula for the reduced bispectrum that is valid for -2 \leq n \leq 0 with a typical error of 10 percent only .