To probe cosmological fields beyond the Gaussian level, three-point statistics can be used, all of which are related to the bispectrum. Hence, measurements of CMB anisotropies, galaxy clustering, and weak gravitational lensing alike have to rely upon an accurate theoretical background concerning the bispectrum and its noise properties. If only small portions of the sky are considered, it is often desirable to perform the analysis in the flat-sky limit. We aim at a formal, detailed derivation of the bispectrum covariance in the flat-sky approximation, focusing on a pure two-dimensional Fourier-plane approach. We define an unbiased estimator of the bispectrum, which takes the average over the overlap of annuli in Fourier space, and compute its full covariance. The outcome of our formalism is compared to the flat-sky spherical harmonic approximation in terms of the covariance, the behavior under parity transformations, and the information content. We introduce a geometrical interpretation of the averaging process in the estimator, thus providing an intuitive understanding. Contrary to foregoing work, we find a difference by a factor of two between the covariances of the Fourier-plane and the spherical harmonic approach. We argue that this discrepancy can be explained by the differing behavior with respect to parity. However, in an exemplary analysis it is demonstrated that the Fisher information of both formalisms agrees to high accuracy. Via the geometrical interpretation we are able to link the normalization in the bispectrum estimator to the area enclosed by the triangle configuration at consideration as well as to the Wigner symbol, which leads to convenient approximation formulae for the covariances of both approaches.
We measure the halo bispectrum covariance in a large set of N-body simulations and compare it with theoretical expectations. We find a large correlation among (even mildly) squeezed halo bispectrum configurations. A similarly large correlation can be found between squeezed triangles and the long-wavelength halo power spectrum. This shows that the diagonal Gaussian contribution fails to describe, even approximately, the full covariance in these cases. We compare our numerical estimate with a model that includes, in addition to the Gaussian one, only the non-Gaussian terms that are large for squ…
In this paper, we predict the covariance matrices of both the power spectrum and the bispectrum, including full non-Gaussian contributions, redshift space distortions, linear bias effects and shot-noise corrections, using perturbation theory (PT). To quantify the redshift-space distortion effect, we focus mainly on the monopole and quadrupole components of both the power and bispectra. We, for the first time, compute the 5- and 6-point spectra to predict the cross-covariance between the power and bispectra, and the auto-covariance of the bispectrum in redshift space. We test the validity of ou…
We investigate three-point statistics in weak lensing convergence, through the integrated bispectrum. This statistic involves measuring power spectra in patches, and is thus easy to measure, and avoids the complexity of estimating the very large number of possible bispectrum configurations. The integrated bispectrum principally probes the squeezed limit of the bispectrum. To be useful as a set of summary statistics, accurate theoretical predictions of the signal are required, and, assuming Gaussian sampling distributions, the covariance matrix. In this paper, we investigate through simulations…
We forecast the benefits induced by adding the bispectrum anisotropic signal to the standard, two- and three-point, clustering statistics analysis. In particular, we forecast cosmological parameter constraints including the bispectrum higher multipoles terms together with the galaxy power spectrum (monopole plus quadrupole) and isotropic bispectrum (monopole) data vectors. To do so, an analytical covariance matrix model is presented. This template is carefully calibrated on well-known terms of a numerical covariance matrix estimated from a set of simulated galaxy catalogues. After testing the …
We compute the tree-level bispectrum of 21cm intensity mapping after reionisation. We work in the directly observable angular and redshift space, focusing on equal-redshift correlations and thin redshift bins, for which the lensing contribution is negligible. We demonstrate the importance of the contributions from redshift-space distortions which typically dominate the result. Taking into account the effects of telescope beams and foreground cleaning, we estimate the signal to noise and show that the bispectrum is detectable by both SKA in single-dish mode and HIRAX in interferometer mode, esp…
Efficient computation of the galaxy angular bispectrum in redshift space
Laboratoire d’Annecy de Physique Théorique, CNRS（阿讷西理论物理实验室，法国国家科学研究中心）；Institute of Astronomy（天文研究所）；Kavli Institute for Cosmology Cambridge（卡弗里宇宙学剑桥研究所）；Ruđer Bošković Institute（鲁德·博什科维奇研究所）；DAMTP, Centre for Mathematical Sciences（应用数学与理论物理系，数学科学中心）
Computing the Small-Scale Galaxy Power Spectrum and Bispectrum in Configuration-Space
我们提出了一类新的估计计算小规模的功率谱和双谱的配置空间通过加权对和三重计数，没有明确使用傅立叶变换。粒子计数截断在$R_0\sim 100h^{-1}\,\mathrm{Mpc}$通过一个连续的窗口函数，这对测量的功率谱多极在小尺度上的影响可以忽略不计。这给出了一个功率谱算法的复杂性$\mathcal{O}(NnR_0^3)$（或$\mathcal{O}(Nn^2R_0^6)$的双谱），测量$N$星系数密度$n$。我们的估计量针对测量几何形状进行了校正，既没有自计数贡献，也没有离散化伪影，使其成为高$k$分析的理想选择。与传统的基于傅立叶变换的方法不同，我们的算法在小尺度上变得更有效（因为可以使用更小的$R_0$），因此我们可以通过将该方法与标准技术相结合来有效地估计跨$k$空间的光谱。我们证明了公用功率谱算法的实用性，将其应用到BOSS DR 12模拟计算高$k$功率谱及其协方差。此外，我们推导出一个理论上的重新缩放高斯协方差矩阵，它结合了调查的几何形状，并发现是在很好的协议，从模拟。计算配置和傅立叶空间统计以同样的方式，使我们能够考虑联合分析，这可以把更强的宇宙学参数的界限，为此，我们还讨论了两点关联函数和小尺度功率谱之间的互协方差。
We present a joint likelihood analysis of the halo power spectrum and bispectrum in real space. We take advantage of a large set of numerical simulations and of an even larger set of halo mock catalogs to provide a robust estimate of the covariance properties. We derive constraints on bias and cosmological parameters assuming a theoretical model from perturbation theory at one-loop for the power spectrum and tree-level for the bispectrum. By means of the Deviance Information Criterion, we select a reference bias model dependent on seven parameters that can describe the data up to $k_{\rm max,P…
Higher-order clustering statistics, like the galaxy bispectrum, can add complementary cosmological information to what is accessible with two-point statistics, like the power spectrum. While the standard way of measuring the bispectrum involves estimating a bispectrum value in a large number of Fourier triangle bins, the compressed modal bispectrum approximates the bispectrum as a linear combination of basis functions and estimates the expansion coefficients on the chosen basis. In this work, we compare the two estimators by using parallel pipelines to analyze the real-space halo bispectrum me…
We present the analysis of the halo bispectrum in redshift-space in terms of its multipoles, monopole, quadrupole and hexadecapole, measured from a large set of simulations. We fit such measurements with a tree-level model in perturbation theory that depends on linear and nonlinear bias parameters as well as on the growth rate $f$ of density fluctuations. The likelihood analysis takes advantage of a very large set of mock catalogs, enabling a robust estimation of the covariance properties for all multipoles. We compare the numerical estimate of the covariance matrix to its Gaussian prediction …
If at First You Don't Succeed, Trispectrum: I. Estimating the Matter Power Spectrum Covariance with Higher-Order Statistics
Columbia University（哥伦比亚大学）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；California Institute of Technology（加州理工学院）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）
Extracting the bispectrum information from the large scale structure observations is challenging due to the complex models and the computational costs to measure the signal and its covariance. Recently, the skew spectrum was proposed to access parts of the bispectrum information with a more effective way and has been confirmed it can provide complementary information to that enclosed in the power spectrum measurements. In this work, we generalize the theory to apply the multitracer technique and explore its ability to constrain the local type primordial non-Gaussianity. Using the spectra and t…
