Nonlinear matter bispectrum in general relativity

We show that the relativistic effects are negligibly small in the nonlinear density and velocity bispectra. Although the nonlinearities of the Einstein equation introduce additional nonlinear terms to the Newtonian fluid equations, the corrections to the bispectrum only show up on superhorizon scales. We show this with the next-to-leading order nonlinear bispectrum for a pressureless fluid in a flat Friedmann-Robertson-Walker background by calculating the density and velocity fields up to fourth order. We work in the comoving gauge, where the dynamics is identical to the Newtonian up to second order. We also discuss the leading order matter bispectrum in various gauges, and show yet another relativistic effect near horizon scales that the matter bispectrum strongly depends on the gauge choice.