We study the cosmic variance limit on constraining primordial non-Gaussianity for a variety of theory-motivated shapes. We consider general arguments for 2D and 3D surveys, with a particular emphasis on the CMB. A scale-invariant N-point correlator can be measured with a signal-to-noise that naively scales with the square root of the number of observed modes. This intuition generally fails for two reasons. First, the signal-to-noise scaling is reduced due to the blurring of the last scattering surface at short distances. This blurring is caused by the combination of projection and damping, but the loss of signal is not due to exponential decay, as both signal and noise are equally damped. Second, the behavior of the N-point correlator in the squeezed and collapsed (for N > 3) limits can enhance the scaling of the signal-to-noise with the resolution, even with a reduced range of momenta probing these limits. We provide analytic estimates for all N-point correlators. We show that blurring affects equilateral-like shapes much more than squeezed ones. We discuss under what conditions the optimistic scalings in the collapsed limit can be exploited. Lastly, we confirm our analytical estimates with numerical calculations of the signal-to-noise for local, orthogonal and equilateral bispectra, and local trispectra. We also show that adding polarization to intensity data enhances the scaling for equilateral-like spectra.

我们研究了约束原始非高斯性的宇宙方差限制，用于各种理论驱动的形状。我们考虑 2D 和 3D 调查的一般论据，特别强调 CMB。可以使用信噪比测量尺度不变的N点相关器，该信噪比随观察模式数量的平方根而天真地缩放。这种直觉通常由于两个原因而失败。首先，由于最后一个散射表面在短距离上的模糊，信噪比降低了。这种模糊是由投影和阻尼的组合引起的，但信号的损失不是由于指数衰减，因为信号和噪声都受到同等的阻尼。二、N点相关器在squeeded和collapsed中的行为（对于N> 3) 限制可以通过分辨率增强信噪比的缩放，即使探测这些限制的动量范围减小。我们为所有N点相关器提供分析估计。我们表明，模糊比挤压形状更能影响等边形状。我们讨论在什么条件下可以利用折叠极限中的乐观缩放。最后，我们通过局部、正交和等边双谱以及局部三谱的信噪比数值计算来确认我们的分析估计。我们还表明，将偏振添加到强度数据可以增强等边光谱的缩放。