Algorithms for bispectra: Forecasting, optimal analysis, and simulation
Algorithms for bispectra: Forecasting, optimal analysis, and simulation
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双谱算法：预测、优化分析和模拟
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发表时间：
2006
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通讯作者：
M. Zaldarriaga
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作者：
Kendrick M. Smith;M. Zaldarriaga
我们提出了一种角双谱的因式分解方法，它允许快速的预测、分析和模拟算法，而且具有足够的通用性，可以涵盖许多有趣的宇宙微波背景(CMB)双谱。我们描述了一套适用于任何双谱的通用算法，这些双谱可以用因式分解的形式表示。首先，我们给出了Fisher矩阵预测的算法和优化因式分解表示的相关问题，并以Planck的Fisher预测为例。结果表明，CMB可以对局部和等边形状的原始双谱的幅度以及由次级各向异性产生的原始双谱的幅度给出独立的约束。我们还表明，积分的Sachs-Wolfe(ISW)透镜双谱应该被普朗克检测到，如果没有适当地解释，可能会偏离对局部类型的非高斯的估计。其次，我们实现了一种在存在截断和非均匀噪声的情况下完全最优的双谱估计器，扩展了仅限于几种特定形式的双谱的快速估计器的通用性，并将现有实现的运行时间改进了几个数量级。第三，我们给出了一种模拟具有给定功率谱和可因式分解双谱的随机弱非高斯映射的算法。
We propose a factorizability ansatz for angular bispectra which permits fast algorithms for forecasting, analysis and simulation, yet is general enough to encompass many interesting cosmic microwave background (CMB) bispectra. We describe a suite of general algorithms which apply to any bispectrum which can be represented in factorizable form. First, we present algorithms for Fisher matrix forecasts and the related problem of optimizing the factorizable representation, giving a Fisher forecast for Planck as an example. We show that the CMB can give independent constraints on the amplitude of primordial bispectra of both local and equilateral shape as well as those created by secondary anisotropies. We also show that the integrated Sachs–Wolfe (ISW)-lensing bispectrum should be detected by Planck and could bias estimates of the local type of non-Gaussianity if not properly accounted for. Second, we implement a bispectrum estimator which is fully optimal in the presence of sky cuts and inhomogeneous noise, extends the generality of fast estimators which have been limited to a few specific forms of the bispectrum and improves the running time of existing implementations by several orders of magnitude. Third, we give an algorithm for simulating random, weakly non-Gaussian maps with prescribed power spectrum and factorizable bispectrum.