We develop an analytical forward model based on perturbation theory to predict the redshift-space galaxy overdensity at the field level given a realization of the initial conditions. We find that the residual noise between the model and simulated galaxy density has a power spectrum that is white on large scales, with size comparable to the shot noise. In the mildly nonlinear regime, we see a k²μ² correction to the noise power spectrum, corresponding to larger noise along the line of sight and on smaller scales. The parametric form of this correction has been predicted on theoretical grounds before, and our simulations provide important confirmation of its presence. We have also modeled the galaxy velocity at the field-level and compared it against simulated galaxy velocities, finding that about 10% of the galaxies are responsible for half of the rms velocity residual for our simulated galaxy sample.

我们开发了一个基于微扰理论的分析前向模型，以在实现初始条件的情况下预测场级的红移空间星系密度。我们发现模型和模拟星系密度之间的残余噪声在大尺度上具有白色的功率谱，其大小与散粒噪声相当。在轻度非线性状态下，我们看到 ak ² μ ²对噪声功率谱的校正，对应于沿视线和较小尺度的较大噪声。这种修正的参数形式之前已经在理论基础上进行了预测，我们的模拟提供了对其存在的重要确认。我们还在场级模拟了星系速度，并将其与模拟星系速度进行了比较，发现大约 10% 的星系对我们模拟星系样本的均方根速度残差的一半负责。