标题： 非高斯性估计量的概率分布，由CMB四阶相关函数构造 显示英文标题

标题： The probability distribution for non-Gaussianity estimators constructed from the CMB trispectrum

摘要： 近年来，人们广泛关注利用宇宙微波背景（CMB）四谱来探索早期宇宙的物理现象。 在此，我们评估标准估计量 tau_nle 的概率分布函数（PDF），以测量 CMB 四谱的幅度 tau_nl，分别针对零假设（即高斯图，tau_nl = 0）和具有非零四谱（|tau_nl|>0）的地图。 我们发现这两种情况下的 PDF 都高度非高斯。 我们还评估了四谱幅度的测量方差 <tau_nle^2>，作为其基础值 tau_nl 的函数。 我们发现该方差对 tau_nl 有很强的依赖性。 我们还发现，鉴于 PDF 的高度非高斯性质，方差并不能有效表征该分布。 因此，详细了解这些 PDF 对于正确解释任何给定四谱测量的意义至关重要。 例如，如果一个具有最大多极数 lmax = 1500（如普朗克卫星）的 CMB 实验测得 tau_nle = 0，则在 95% 置信水平下，我们的计算表明我们可以得出 tau_nl < 1005；假设使用高斯 PDF 但具有正确的 tau_nl 依赖方差，我们会错误地得出 tau_nl < 4225；进一步忽略方差中的 tau_nl 依赖性，我们会错误地得出 tau_nl < 361。 显示英文摘要

摘要： Considerable recent attention has focussed on the prospects to use the cosmic microwave background (CMB) trispectrum to probe the physics of the early universe. Here we evaluate the probability distribution function (PDF) for the standard estimator tau_nle for the amplitude tau_nl of the CMB trispectrum both for the null-hypothesis (i.e., for Gaussian maps with tau_nl = 0) and for maps with a non-vanishing trispectrum (|tau_nl|>0). We find these PDFs to be highly non-Gaussian in both cases. We also evaluate the variance with which the trispectrum amplitude can be measured, <tau_nle^2>, as a function of its underlying value, tau_nl. We find a strong dependence of this variance on tau_nl. We also find that the variance does not, given the highly non-Gaussian nature of the PDF, effectively characterize the distribution. Detailed knowledge of these PDFs will therefore be imperative in order to properly interpret the implications of any given trispectrum measurement. For example, if a CMB experiment with a maximum multipole of lmax = 1500 (such as the Planck satellite) measures tau_nle = 0 then at the 95% confidence our calculations show that we can conclude tau_nl < 1005; assuming a Gaussian PDF but with the correct tau_nl-dependent variance we would incorrectly conclude tau_nl < 4225; further neglecting the tau_nl-dependence in the variance we would incorrectly conclude tau_nl < 361.