Title: Non-linear matter bispectrum in general relativity Show Chinese title

Title: 广义相对论中的非线性物质双谱

Abstract: We show that the relativistic effects are negligibly small in the non-linear density and velocity bispectra. Although the non-linearities of Einstein equation introduce additional non-linear terms to the Newtonian fluid equations, the corrections to the bispectrum only show up on super-horizon scales. We show this with the next-to-leading order non-linear 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. Show Chinese abstract

Abstract: 我们证明了在非线性密度和速度双谱中，相对论效应可以忽略不计。尽管爱因斯坦方程的非线性引入了牛顿流体力学方程中的附加非线性项，但这些修正仅在超视界尺度上显现出来。通过计算平坦Friedmann-Robertson-Walker背景中无压流体的密度和速度场直到四阶，我们用接近次领头阶的非线性双谱展示了这一点。我们在共动规范下工作，在此规范中动力学与牛顿理论在二阶以内相同。我们还讨论了各种规范下的主导阶物质双谱，并展示了另一种视界尺度附近的相对论效应，即物质双谱强烈依赖于规范选择。