NONLINEAR EVOLUTION OF THE BISPECTRUM OF COSMOLOGICAL PERTURBATIONS

The bispectrum B(k(1), k(2), k(3)), the three-point function of densit y fluctuations in Fourier space, is the lowest order statistic that ca rries information about the spatial coherence of large-scale structure s. For Gaussian initial conditions, when the density fluctuation ampli tude is small (delta << 1), tree-level (leading order) perturbation th eory predicts a characteristic dependence of the bispectrum on the sha pe of the triangle formed by the three wave vectors. This configuratio n dependence provides a signature of gravitational instability, and de partures from it in galaxy catalogs can be interpreted as due to bias, that is, nongravitational effects. On the other hand, N-body simulati ons indicate that the reduced three-point function becomes relatively shape-independent in the strongly nonlinear regime (delta >> 1). In or der to understand this nonlinear transition and assess the domain of r eliability of shape dependence as a probe of bias, we calculate the on e-loop (next-to-leading order) corrections to the bispectrum in pertur bation theory. We compare these results with measurements in numerical simulations with scale-free and cold dark matter initial power spectr a. We find that the one-loop corrections account very well for the dep artures from the tree-level results measured in numerical simulations on weakly nonlinear scales (delta less than or similar to 1). In this regime, the reduced bispectrum qualitatively retains its tree-level sh ape, but the amplitude can change significantly. At smaller scales (de lta greater than or similar to 1), the reduced bispectrum in the simul ations starts to flatten, an effect that can be partially understood f rom the one-loop results. In the strong clustering regime, where pertu rbation theory breaks down entirely, the simulation results confirm th at the reduced bispectrum has almost no dependence on triangle shape, in rough agreement with the hierarchical Ansatz.