Detecting primordial non-Gaussianity on mildly non-linear scales requires precise modelling of late-time structure formation. Accurately predicting the impact of non-linear gravitational collapse, non-linear tracer bias and baryonic physics on the variance and higher order moments of the cosmic density field is challenging, as they strongly depend on the tails of the probability distribution function (PDF) of density fluctuations. A way around this problem is to directly analyse the bulk of the PDF instead. For this purpose we devise a new method to predict the impact of general non-Gaussian initial conditions on the late-time density PDF. With this formalism we show that - even when marginalizing over potential ignorance of the amplitude and slope of the non-linear power spectrum - an analysis of the PDF at mildly non-linear densities can measure the amplitude of different primordial bispectrum shapes to an accuracy of $\Delta f_{\mathrm{NL}}^{\mathrm{loc}} = \pm 3.1\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{equi}} = \pm 10.0\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{ortho}} = \pm 17.0\ $. This assumes a joint analysis of the PDF on smoothing scales of $15$Mpc/$h$ and $30$Mpc/$h$ in a survey volume of $V=100(\mathrm{Gpc}/h)^3$ at $z=1$, analysing only densities of $\delta(15\mathrm{Mpc}/h) \in [-0.4, 0.5]$ ($\approx 87\%$ of probability) and $\delta(30\mathrm{Mpc}/h) \in [-0.3, 0.4]$ ($\approx 95\%$ of probability). Note that a formalism closely related to ours was already successfully applied to observational data \citep{Gruen2018, Friedrich2018}, demonstrating that the methodology developed here can indeed be carried over to real data analysis.

中文翻译：

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没有尾部的原始非高斯性——如何用密度 PDF 的体积测量 fNL

在轻度非线性尺度上检测原始非高斯性需要对后期结构形成进行精确建模。准确预测非线性引力坍缩、非线性示踪偏差和重子物理学对宇宙密度场的方差和高阶矩的影响具有挑战性，因为它们强烈依赖于概率分布函数 (PDF) 的尾部密度波动。解决此问题的一种方法是直接分析大部分 PDF。为此，我们设计了一种新方法来预测一般非高斯初始条件对后期密度 PDF 的影响。通过这种形式，我们表明 - 即使在忽略非线性功率谱的幅度和斜率的潜在无知时 - 在温和非线性密度下对 PDF 的分析可以测量不同原始双谱形状的幅度，精度为$\Delta f_{\mathrm{NL}}^{\mathrm{loc}} = \pm 3.1\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{equi}} = \pm 10.0\ , \ \Delta f_{\mathrm{NL}}^{\mathrm{ortho}} = \pm 17.0\ $. 这假设在 $V=100(\mathrm{Gpc}/h)^3$ 的调查量中，在 $15$Mpc/$h$ 和 $30$Mpc/$h$ 的平滑尺度上对 PDF 进行联合分析z=1$，仅分析 $\delta(15\mathrm{Mpc}/h) \in [-0.4, 0.5]$（$\approx 87\%$ 的概率）和 $\delta(30\mathrm) 的密度{Mpc}/h) \in [-0.3, 0.4]$（$\approx 95\%$ 的概率）。