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 our calculations by comparing them with the covariance matrices measured from the MultiDark-Patchy mock catalogues that are designed to reproduce the galaxy clustering measured from the Baryon Oscillation Spectroscopic Survey Data Release 12. We argue that the simple, leading-order perturbation theory works because the shot-noise corrections for the Patchy mocks are more dominant than other higher-order terms we ignore. In the meantime, we confirm some discrepancies in the comparison, especially of the cross-covariance. We discuss potential sources of such discrepancies. We also show that our PT model reproduces well the cumulative signal-to-noise of the power spectrum and the bispectrum as a function of maximum wavenumber, implying that our PT model captures successfully essential contributions to the covariance matrices.
Modes with wavelengths larger than the survey window can have significant impact on the covariance within the survey window. The supersample covariance has been recognized as an important source of covariance for the power spectrum on small scales, and it can potentially be important for the bispectrum covariance as well. In this paper, using the response function formalism, we model the supersample covariance contributions to the bispectrum covariance and the cross covariance between the power spectrum and the bispectrum. The supersample covariances due to the long wavelength density and tida…
We present a calculation of the angle-averaged squeezed matter bispectrum covariance ${\rm Cov}\left(B_{m}(k_1, k_1', s_1), B_{m}(k_2, k_2', s_2)\right)$, $s_i \ll k_i,k_i'$ ($i=1,2$), that uses matter power spectrum responses to describe the coupling of large- to short-scale modes in the nonlinear regime. The covariance is given by a certain configuration of the 6-point function, which we show is dominated by response-type mode-coupling terms in the squeezed bispectrum limit. The terms that are not captured by responses are small, effectively rendering our calculation complete and predictive …
The covariance matrix of the matter and halo power spectrum and bispectrum are studied. Using a large suite of simulations, we find that the non-Gaussianity in the covariance is significant already at mildly nonlinear scales. We compute the leading disconnected non-Gaussian correction to the matter bispectrum covariance using perturbation theory, and find that the corrections result in good agreement in the mildly nonlinear regime. The shot noise contribution to the halo power spectrum and bispectrum covariance is computed using the Poisson model, and the model yields decent agreement with sim…
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…
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 compare the measurements of the bispectrum and the estimate of its covariance obtained from a set of different methods for the efficient generation of approximate dark matter halo catalogs to the same quantities obtained from full N-body simulations. To this purpose we employ a large set of three-hundred realisations of the same cosmology for each method, run with matching initial conditions in order to reduce the contribution of cosmic variance to the comparison. In addition, we compare how the error on cosmological parameters such as linear and nonlinear bias parameters depends on the app…
Galaxy bispectrum is a promising probe of inflationary physics in the early universe as a measure of primordial non-Gaussianity (PNG), whereas its signal-to-noise ratio is significantly affected by the mode coupling due to non-linear gravitational growth. In this paper, we examine the standard reconstruction method of linear cosmic mass density fields from non-linear galaxy density fields to de-correlate the covariance in redshift-space galaxy bispectra. In particular, we evaluate the covariance of the bispectrum for massive-galaxy-sized dark matter halos with reconstruction by using 4000 inde…
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…
The next generation of ground-based CMB experiments aim to measure temperature and polarization fluctuations up to $\ell_{\rm max} \approx 5000$ over half of the sky. Combined with Planck data on large scales, this will provide improved constraints on primordial non-Gaussianity. However, the impressive resolution of these experiments will come at a price. Besides signal confusion from galactic foregrounds, extra-galactic foregrounds and late-time gravitational effects, gravitational lensing will introduce large non-Gaussianity that can become the leading contribution to the bispectrum covarian…
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…
The galaxy bispectrum, measuring excess clustering of galaxy triplets, offers a probe of dark energy via baryon acoustic oscillations (BAOs). However up to now it has been severely underused due to the combinatorically explosive number of triangles. Here we exploit interference in the bispectrum to identify triangles that amplify BAOs. This approach reduces the computational cost of estimating covariance matrices, offers an improvement in BAO constraints equivalent to lengthening BOSS by 30%, and simplifies adding bispectrum BAO information to future large-scale redshift survey analyses.
In the pursuit of primordial non-Gaussianities, we hope to access smaller scales across larger comoving volumes. At low redshift, the search for primordial non-Gaussianities is hindered by gravitational collapse, to which we often associate a scale $k_{\rm NL}$. Beyond these scales, it will be hard to reconstruct the modes sensitive to the primordial distribution. When forecasting future constraints on the amplitude of primordial non-Gaussianity, $f_{\rm NL}$, off-diagonal components are usually neglected in the covariance because these are small compared to the diagonal. We show that the indu…
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）
We present a novel method to compress galaxy clustering three-point statistics and apply it to redshift space galaxy bispectrum monopole measurements from BOSS DR12 CMASS data considering a $k$-space range of $0.03-0.12\,h/\mathrm{Mpc}$. The method consists in binning together bispectra evaluated at sets of wave-numbers forming closed triangles with similar geometrical properties: the area, the cosine of the largest angle and the ratio between the cosines of the remaining two angles. This enables us to increase the number of bispectrum measurements for example by a factor of $23$ over the stan…
The Marked Power Spectrum as a Practical Bispectrum Measure for Galaxy Redshift Surveys
University of California, Berkeley（加州大学伯克利分校）；Berkeley Center for Cosmological Physics, UC Berkeley（加州大学伯克利分校宇宙学物理中心）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Searching for primordial features with radio surveys: synergy between the power spectrum and bispectrum
Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara（费拉拉大学地球与物理科学系）；INFN, Sezione di Ferrara（意大利国家核物理研究所费拉拉分部）；Department of Physics & Astronomy, University of the Western Cape（西开普大学物理与天文学系）；Van Swinderen Institute, University of Groningen（格罗宁根大学范斯温德伦研究所）；INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna（博洛尼亚天文物理与空间科学观测站（意大利国家天体物理研究所））；National Institute for Theoretical and Computational Sciences（理论与计算科学国家研究所）
We study the information content of the angle-averaged (monopole) redshift space galaxy bispectrum. The main novelty of our approach is the use of a systematic tree-level perturbation theory model that includes galaxy bias, IR resummation, and also accounts for nonlinear redshift space distortions, binning, and projection effects. We analyze data from the PT challenge simulations, whose cumulative volume of 566 $h^{-3}$Gpc$^3$ allows for a precise comparison to theoretical predictions. Fitting the power spectrum and bispectrum of our simulated data, and varying all necessary cosmological and n…
We perform for the first time a joint analysis of the monopole and quadrupoles for power spectrum, bispectrum and integrated trispectrum (i-trispectrum) from the redshift space matter field in N-body simulations. With a full Markov Chain Monte Carlo exploration of the posterior distribution, we quantify the constraints on cosmological parameters for an object density of $n_\mathrm{p}=5\times10^{-4} (h\,\mathrm{Mpc}^{-1})^{3}$, redshift $z=0.5$, and a covariance corresponding to a survey volume of $V_\mathrm{survey} =25\,(h^{-1}\mathrm{Gpc})^3$, a set up which is representative of forthcoming g…
Non-Gaussian (NG) statistics of the thermal Sunyaev-Zeldovich (tSZ) effect carry significant information which is not contained in the power spectrum. Here, we perform a joint Fisher analysis of the tSZ power spectrum and bispectrum to verify how much the full bispectrum can contribute to improve parameter constraints. We go beyond similar studies of this kind in several respects: first of all, we include the complete power spectrum and bispectrum (auto- and cross-) covariance in the analysis, computing all NG contributions; furthermore we consider a multi-component foreground scenario and mod…
Cosmological information from forthcoming galaxy surveys, such as LSST and Euclid, will soon exceed that available from the CMB. Higher order correlation functions, like the bispectrum, will be indispensable for realising this potential. The interpretation of this data faces many challenges because gravitational collapse of matter is a complex non-linear process, typically modelled by computationally expensive N-body simulations. Proposed alternatives using fast dark matter codes (e.g. 2LPT or particle-mesh) are primarily evaluated on their ability to reproduce clustering statistics linked to …
We develop the tools necessary to assess the statistical significance of resonant features in the CMB correlation functions, combining power spectrum and bispectrum measurements. This significance is typically addressed by running a large number of simulations to derive the probability density function (PDF) of the feature-amplitude in the Gaussian case. Although these simulations are tractable for the power spectrum, for the bispectrum they require significant computational resources. We show that, by assuming that the PDF is given by a multi-variate Gaussian where the covariance is determine…
Covariance matrix estimation is a persistent challenge for cosmology. We focus on a class of model covariance matrices that can be generated with high accuracy and precision, using a tiny fraction of the computational resources that would be required to achieve comparably precise covariance matrices using mock catalogues. In previous work, the free parameters in these models were determined using sample covariance matrices computed using a large number of mocks, but we demonstrate that those parameters can be estimated consistently and with good precision by applying jackknife methods to a sin…
We present forecasts on the primordial non-Gaussianity parameter $f_\text{NL}$ of feature models for the future Cosmic Microwave Background Stage-4 (CMB-S4) experiments. The Fisher matrix of the bispectrum estimator was computed using noise covariances expected for preliminary CMB-S4 specifications including ones for the Simons Observatory. We introduce a novel method that improves the computation by orthonormalising the covariance matrix. The most sensitive CMB-S4 experiment with 1' beam and 1$μK$-arcmin noise would yield a factor of 1.7-2.2 times more stringent constraints compared to Planck…
Redshift-space 21-cm bispectrum multipoles as an SKA-era gravity test in the post-reionization Universe
Indian Statistical Institute（印度统计研究所）；McGill University（麦吉尔大学）；Ciela—Montreal Institute for Astrophysical Data Analysis and Machine Learning（Ciela-蒙特利尔天体物理数据分析与机器学习研究所）
We address key points for an efficient implementation of likelihood codes for modern weak lensing large-scale structure surveys. Specifically, we focus on the joint weak lensing convergence power spectrum-bispectrum probe and we tackle the numerical challenges required by a realistic analysis. Under the assumption of (multivariate) Gaussian likelihoods, we have developed a high performance code that allows highly parallelised prediction of the binned tomographic observables and of their joint non-Gaussian covariance matrix accounting for terms up to the 6-point correlation function and super-s…
We present a new class of estimators for computing small-scale power spectra and bispectra in configuration-space via weighted pair- and triple-counts, with no explicit use of Fourier transforms. Particle counts are truncated at $R_0\sim 100h^{-1}\,\mathrm{Mpc}$ via a continuous window function, which has negligible effect on the measured power spectrum multipoles at small scales. This gives a power spectrum algorithm with complexity $\mathcal{O}(NnR_0^3)$ (or $\mathcal{O}(Nn^2R_0^6)$ for the bispectrum), measuring $N$ galaxies with number density $n$. Our estimators are corrected for the surv…
We present a method that allows us for the first time to estimate the signal-to-noise ratio (SNR) of the harmonic-space galaxy bispectrum induced by gravity, a complementary probe to already well established Fourier-space clustering analyses. We show how to do it considering only $\sim1000$ triangle configurations in multipole space, corresponding to a computational speedup of a factor $\mathcal{O}(10^2)-\mathcal{O}(10^3)$, depending on the redshift bin, when including mildly non-linear scales. Assuming observational specifications consistent with forthcoming spectroscopic and photometric gala…
Abstract Covariance matrix estimation is a challenging problem in cosmology. Recent work has shown that model covariance matrices can be precise, and that at relatively large scales they can also be accurate. We introduce a data-driven method that can identify features from a mock covariance matrix that are missing from a corresponding model, then incorporate them into the model without significantly degrading the model's precision. We apply this method to a BOSS-like survey and extend a model covariance to be valid at scales relevant for measurements of Redshift Space Distortions (8-40 Mpc/h)…
We use the Fisher-matrix formalism to investigate whether the galaxy bispectrum in redshift space, $B$, contains additional cosmological information with respect to the power spectrum, $P$. We focus on a $Euclid$-like survey and consider cosmological models dominated by dark energy and cold dark matter with Gaussian primordial perturbations. After discussing the phenomenology of redshift-space distortions for the bispectrum, we derive an expression for the cross-covariance between $B$ and $P$ at leading order in perturbation theory. Our equation generalizes previous results that did not consid…
Covariance matrices are important tools for obtaining reliable parameter constraints. Advancements in cosmological surveys lead to larger data vectors and, consequently, increasingly complex covariance matrices, whose number of elements grows as the square of the size of the data vector. The most straightforward way of comparing these matrices, in terms of their ability to produce parameter constraints, involves a full cosmological analysis, which can be very computationally expensive. Using the concept and construction of compression schemes, which have become increasingly popular, we propose…
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…
The forthcoming generation of galaxy redshift surveys will sample the large-scale structure of the Universe over unprecedented volumes with high-density tracers. This advancement will make robust measurements of three-point clustering statistics possible. In preparation for this improvement, we investigate how several methodological choices can influence inferences based on the bispectrum about galaxy bias and shot noise. We first measure the real-space bispectrum of dark-matter haloes extracted from 298 N-body simulations covering a volume of approximately $1000 h^{-3} \mathrm{Gpc}^3$. We the…
We derive analytic covariance matrices for the $N$-Point Correlation Functions (NPCFs) of galaxies in the Gaussian limit. Our results are given for arbitrary $N$ and projected onto the isotropic basis functions of Cahn & Slepian (2020), recently shown to facilitate efficient NPCF estimation. A numerical implementation of the 4PCF covariance is compared to the sample covariance obtained from a set of lognormal simulations, Quijote dark matter halo catalogues, and MultiDark-Patchy galaxy mocks, with the latter including realistic survey geometry. The analytic formalism gives reasonable predictio…
We show how consistency relations can be used to robustly extract the amplitude of local primordial non-Gaussianity ($f_{\rm NL}$) from the squeezed limit of the matter bispectrum, well into the non-linear regime. First, we derive a non-perturbative relation between primordial non-Gaussianity and the leading term in the squeezed bispectrum, revising some results present in the literature. This relation is then used to successfully measure $f_{\rm NL}$ from $N$-body simulations. We discuss the dependence of our results on different scale cuts and redshifts. Specifically, the analysis is strongl…
The forthcoming generation of wide-field galaxy surveys will probe larger volumes and galaxy densities, thus allowing for a much larger signal-to-noise ratio for higher-order clustering statistics, in particular the galaxy bispectrum. Extracting this information, however, is more challenging than using the power spectrum due to more complex theoretical modeling, as well as significant computational cost of evaluating the bispectrum signal and the error budget. To overcome these challenges, several proxy statistics have been proposed in the literature, which partially or fully capture the infor…
In order to best improve constraints on cosmological parameters and on models of modified gravity using current and future galaxy surveys it is necessary maximally exploit the available data. As redshift-space distortions mean statistical translation invariance is broken for galaxy observations, this will require measurement of the monopole, quadrupole and hexadecapole of not just the galaxy power spectrum, but also the galaxy bispectrum. A recent (2015) paper by Scoccimarro demonstrated how the standard bispectrum estimator may be expressed in terms of Fast Fourier Transforms (FFTs) to afford…
