We present a Fisher information study of the statistical impact of galaxy bias and selection effects on the estimation of key cosmological parameters from galaxy redshift surveys; in particular, the angular diameter distance, Hubble parameter, and linear growth rate at a given redshift, the cold dark matter density, and the tilt and running of the primordial power spectrum. The line-of-sight-dependent selection contributions we include here are known to exist in real galaxy samples. We determine the maximum wavenumber included in the analysis by requiring that the next-order corrections to the galaxy power spectrum or bispectrum, treated here at next-to-leading and leading order, respectively, produce shifts of $\lesssim 0.25σ$ on each of the six cosmological parameters. With the galaxy power spectrum alone, selection effects can deteriorate the constraints severely, especially on the linear growth rate. Adding the galaxy bispectrum helps break parameter degeneracies significantly. We find that a joint power spectrum-bispectrum analysis of a Euclid-like survey can still measure the linear growth rate to 10% precision after complete marginalization over selection bias. We also discuss systematic parameter shifts arising from ignoring selection effects and/or other bias parameters, and emphasize that it is necessary to either control selection effects at the percent level or marginalize over them. We obtain similar results for the Roman Space Telescope and HETDEX.
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…
We extend the modal decomposition method, previously applied to compress the information in the real-space bispectrum, to the anisotropic redshift-space galaxy bispectrum. In the modal method approach, the bispectrum is expanded on a basis of smooth functions of triangles and their orientations, such that a set of modal expansion coefficients can capture the information in the bispectrum. We assume a reference survey and compute Fisher forecasts for the compressed modal bispectrum and two other basis decompositions of the redshift-space bispectrum in the literature, one based on (single) spher…
We present an analytic formula for the galaxy bispectrum in redshift space on the basis of the halo approach description with the halo occupation distribution of central galaxies and satellite galaxies. This work is an extension of a previous work on the galaxy power spectrum, which illuminated the significant contribution of satellite galaxies to the higher multipole spectrum through the non-linear redshift space distortions of their random motions. Behaviors of the multipoles of the bispectrum are compared with results of numerical simulations assuming a halo occupation distribution of the L…
The anisotropy of the redshift space bispectrum contains a wealth of cosmological information. This anisotropy depends on the orientation of three vectors ${\bf k_1,k_2,k_3}$ with respect to the line of sight. Here we have decomposed the redshift space bispectrum in spherical harmonics which completely quantify this anisotropy. To illustrate this we consider linear redshift space distortion of the bispectrum arising from primordial non-Gaussianity. In the plane parallel approximation only the first four even $\ell$ multipoles have non-zero values, and we present explicit analytical expressions…
As a generalization of our previous work [Phys. Rev. D 95 043528 (2017)], in which an analytic model for the galaxy bispectrum in redshift space was developed on the basis of the halo approach, we here investigate its higher multipoles that have not been known so far. The redshift-space bispectrum includes the two variables $ω$ and $ϕ$ for the line-of-sight direction, and the higher multipole bispectra are defined by the coefficients in the expansion of the redshift-space bispectrum using the spherical harmonics. We find 6 new nonvanishing components out of $25$ total components up to $\ell=4$…
The redshift-space bispectrum (three point statistics) of galaxies depends on the expansion rate, the growth rate, and geometry of the Universe, and hence can be used to measure key cosmological parameters. In a homogeneous Universe the bispectrum is a function of five variables and unlike its two point statistics counterpart -- the power spectrum, which is a function of only two variables -- is difficult to analyse unless the information is somehow reduced. The most commonly considered reduction schemes rely on computing angular integrals over possible orientations of the bispectrum triangle,…
The large-scale matter distribution in the late-time Universe exhibits gravity-induced non-Gaussianity, and the bispectrum, three-point cumulant is expected to contain significant cosmological information. In particular, the measurement of the bispectrum helps to tighten the constraints on dark energy and modified gravity through the redshift-space distortions (RSD). In this paper, extending the work by Taruya, Nishimichi & Saito (2010, Phys.Rev.D 82, 063522), we present a perturbation theory (PT) based model of redshift-space matter bispectrum that can keep the non-perturbative damping effect…
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…
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 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 present the complete expression for the next-to-leading (1-loop) order galaxy power spectrum and the leading-order galaxy bispectrum in redshift space in the general bias expansion, or equivalently the effective field theory of biased tracers. We consistently include all line-of-sight dependent selection effects. These are degenerate with many, but not all, of the redshift-space distortion contributions, and have not been consistently derived before. Moreover, we show that, in the framework of effective field theory, a consistent bias expansion in redshift space must include these selection…
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）
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…
The bispectrum can quantify the non-Gussianity present in the redshifted 21-cm signal produced by the neutral hydrogen (HI) during the epoch of reionization (EoR). Motivated by this, we perform a comprehensive study of the EoR 21-cm bispectrum using simulated signals. Given a model of reionization, we demonstrate the behaviour of the bispectrum for all unique triangles in $k$ space. For ease of identification of the unique triangles, we parametrize the $k$-triangle space with two parameters, namely the ratio of the two arms of the triangle ($n=k_2/k_1$) and the cosine of the angle between them…
We study the halo bispectrum from non-Gaussian initial conditions. Based on a set of large $N$-body simulations starting from initial density fields with local type non-Gaussianity, we find that the halo bispectrum exhibits a strong dependence on the shape and scale of Fourier space triangles near squeezed configurations at large scales. The amplitude of the halo bispectrum roughly scales as $f_nl^2$. The resultant scaling on the triangular shape is consistent with that predicted by Jeong & Komatsu based on perturbation theory. We systematically investigate this dependence with varying redshif…
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）
We present a phenomenological modification of the standard perturbation theory prediction for the bispectrum in redshift space that allows us to extend the model to mildly non-linear scales over a wide range of redshifts, $z\leq1.5$. We find that we can describe the bispectrum of dark matter particles with $\sim5%$ accuracy for $k_i\lesssim0.10\,h/{\rm Mpc}$ at $z=0$, for $k_i\lesssim0.15\,h/{\rm Mpc}$ at $z=0.5$, for $k_i\lesssim0.17\,h/{\rm Mpc}$ at $z=1.0$ and for $k_i\lesssim0.20\,h/{\rm Mpc}$ at $z=1.5$. We also test that the fitting formula is able to describe with similar accuracy the b…
The redshift space anisotropy of the bispectrum is generally quantified using multipole moments. The possibility of measuring these multipoles in any survey depends on the level of statistical fluctuations. We present a formalism to compute the statistical fluctuations in the measurement of bispectrum multipoles for galaxy surveys. We consider specifications of a {\it Euclid} like galaxy survey and present two quantities: the signal-to-noise ratio (SNR) which quantifies the detectability of a multipole, and the rank correlation which quantifies the correlation in measurement errors between any…
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 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…
The Signature of Strong High-Redshift Radio Backgrounds on the Cosmic Dawn 21-cm Bispectrum
Tel-Aviv University（特拉维夫大学）；National Institute of Technology Calicut（卡利卡特国家理工学院）；University of Cambridge（剑桥大学）；Kavli Institute for Cosmology（卡弗里宇宙学研究所）
We study the matter bispectrum of the large-scale structure by comparing different perturbative and phenomenological models with measurements from $N$-body simulations obtained with a modal bispectrum estimator. Using shape and amplitude correlators, we directly compare simulated data with theoretical models over the full three-dimensional domain of the bispectrum, for different redshifts and scales. We review and investigate the main perturbative methods in the literature that predict the one-loop bispectrum: standard perturbation theory, effective field theory, resummed Lagrangian and renorm…
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…
To fully extract cosmological information from nonlinear galaxy distribution in redshift space, it is essential to include higher-order statistics beyond the two-point correlation function. In this paper, we propose a new decomposition formalism for computing the anisotropic bispectrum in redshift space and for measuring it from galaxy samples. Our formalism uses tri-polar spherical harmonic decomposition with zero total angular momentum to compress the 3D modes distribution in the redshift-space bispectrum. This approach preserves three fundamental properties of the Universe: statistical homo…
We compute the redshift-dependent angular bispectrum of galaxy number counts at tree-level, including nonlinear clustering bias and estimating numerically for the first time the effect of redshift space distortions (RSD). We show that for narrow redshift bins the amplitude of nonlinear RSD is comparable with the matter density perturbations. While our numerical results only include terms relevant on sub-horizon scales, the formalism can readily be extended to the full tree-level bispectrum. Our approach does not rely on the flat-sky approximation and it can be easily generalized to different s…
Accurate modeling of nonlinearities in the galaxy bispectrum, the Fourier transform of the galaxy three-point correlation function, is essential to fully exploit it as a cosmological probe. In this paper, we present numerical and theoretical challenges in modeling the nonlinear bispectrum. First, we test the robustness of the matter bispectrum measured from N-body simulations using different initial conditions generators. We run a suite of N-body simulations using the Zel'dovich approximation and second-order Lagrangian perturbation theory (2LPT) at different starting redshifts, and find that …
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…
We forecast constraints on primordial non-Gaussianity (PNG) and bias parameters from measurements of galaxy power spectrum and bispectrum in future radio continuum and optical surveys. In the galaxy bispectrum, we consider a comprehensive list of effects, including the bias expansion for non-Gaussian initial conditions up to second order, redshift space distortions, redshift uncertainties and theoretical errors. These effects are all combined in a single PNG forecast for the first time. Moreover, we improve the bispectrum modelling over previous forecasts, by accounting for trispectrum contrib…
Intensity maps of the 21cm emission line of neutral hydrogen are lensed by intervening large-scale structure, similar to the lensing of the cosmic microwave background temperature map. We extend previous work by calculating the lensing contribution to the full-sky 21cm bispectrum in redshift space. The lensing contribution tends to peak when equal-redshift fluctuations are lensed by a lower redshift fluctuation. At high redshift, lensing effects can become comparable to the contributions from density and redshift-space distortions.
The Fourier-space galaxy bispectrum is complex, with the imaginary part arising from leading-order relativistic corrections, due to Doppler, gravitational redshift and related line-of-sight effects in redshift space. The detection of the imaginary part of the bispectrum is potentially a smoking gun signal of relativistic contributions. We investigate whether next-generation spectroscopic surveys could make such a detection. For a Stage IV spectroscopic $Hα$ survey similar to Euclid, we find that the cumulative signal to noise of this relativistic signature is $\mathcal{O}(10)$. Long-mode relat…
We present measurements of the dark matter bispectrum in N-body simulations with non-Gaussian initial conditions of the local kind for a large variety of triangular configurations and compare them with predictions from Eulerian Perturbation Theory up to one-loop corrections. We find that the effects of primordial non-Gaussianity at large scales, when compared to Perturbation Theory, are well described by the initial component of the matter bispectrum, linearly extrapolated at the redshift of interest. In addition, we find that, for f_NL=100, the nonlinear corrections due to non-Gaussian initia…
We investigate how much can be learnt about four types of primordial non-Gaussianity (PNG) from small-scale measurements of the halo field. Using the QUIJOTE-PNG simulations, we quantify the information content accessible with measurements of the halo power spectrum monopole and quadrupole, the matter power spectrum, the halo-matter cross spectrum and the halo bispectrum monopole. This analysis is the first to include small, non-linear scales, up to $k_\mathrm{max}=0.5 \mathrm{h/Mpc}$, and to explore whether these scales can break degeneracies with cosmological and nuisance parameters making u…
We re-examine a genuine power of weak lensing bispectrum tomography for constraining cosmological parameters, when combined with the power spectrum tomography, based on the Fisher information matrix formalism. To account for the full information at two- and three-point levels, we include all the power spectrum and bispectrum information built from all-available combinations of tomographic redshift bins, multipole bins and different triangle configurations over a range of angular scales (up to lmax=2000 as our fiducial choice). For the parameter forecast, we use the halo model approach in Kayo,…
Massive neutrinos suppress the growth of structure on small scales and leave an imprint on large-scale structure that can be measured to constrain their total mass, $M_ν$. With standard analyses of two-point clustering statistics, $M_ν$ constraints are severely limited by parameter degeneracies. Hahn et al.(2020) demonstrated that the bispectrum, the next higher-order statistic, can break these degeneracies and dramatically improve constraints on $M_ν$ and other cosmological parameters. In this paper, we present the constraining power of the redshift-space galaxy bispectrum, $B_0^g$. We constr…
Next-generation galaxy and 21cm intensity mapping surveys will rely on a combination of the power spectrum and bispectrum for high-precision measurements of primordial non-Gaussianity. In turn, these measurements will allow us to distinguish between various models of inflation. However, precision observations require theoretical precision at least at the same level. We extend the theoretical understanding of the galaxy bispectrum by incorporating a consistent general relativistic model of galaxy bias at second order, in the presence of local primordial non-Gaussianity. The influence of primord…
The radiations from the first luminous sources drive the fluctuations in the 21-cm signal at Cosmic Dawn (CD) via two dominant astrophysical processes i.e. the Ly$α$ coupling and X-ray heating, making this signal highly non-Gaussian. The impact of these processes on the 21-cm signal and its non-Gaussianity vary depending on the properties of these first sources of light. In this work, we consider different CD scenarios by varying two major source parameters i.e. the minimum halo mass $M_{\rm h,\, min}$ and X-ray photon production efficiency $f_{\rm X}$ in a 1D radiative transfer code GRIZZLY. …
We perform a detailed study of the bispectrum of the Sunyaev-Zel'dovich effect. Using an analytical model for the pressure profiles of the intracluster medium, we demonstrate the SZ bispectrum to be a sensitive probe of the amplitude of the matter power spectrum parameter sigma_8. We find that the bispectrum amplitude scales as B_SZ ~ sigma_8^{11-12}, compared to that of the power spectrum, which scales as A_tSZ ~ sigma_8^{7-9}. We show that the SZ bispectrum is principally sourced by massive clusters at redshifts around z~0.4, which have been well-studied observationally. This is in contrast …
Gravity-induced non-Gaussianity can provide important clues to Modified Gravity (MG) Theories. Several recent studies have suggested using the {\it Integrated Bispectrum} (IB) as a probe for squeezed configuration of bispectrum. Extending previous studies on the IB, we include redshift-space distortions to study a class of (parametrised) MG theories that include the string-inspired Dvali, Gabadadze \& Porrati (DGP) model. Various contributions from redshift-space distortions are derived in a transparent manner, and squeezed contributions from these terms are derived separately. Results are obt…
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）
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 …
We present a study of the 21-cm signal bispectrum (which quantifies the non-Gaussianity in the signal) from the Cosmic Dawn (CD). For our analysis, we have simulated the 21-cm signal using radiative transfer code GRIZZLY, while considering two types of sources (mini-QSOs and HMXBs) for Ly$α$ coupling and the X-ray heating of the IGM. Using this simulated signal, we have, for the first time, estimated the CD 21-cm bispectra for all unique $k$-triangles and for a range of $k$ modes. We observe that the redshift evolution of the bispectra magnitude and sign follow a generic trend for both source …
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.
Large surveys for Lyman-alpha emitting (LAE) galaxies have been proposed as a new method for measuring clustering of the galaxy population at high redshift with the goal of determining cosmological parameters. However, Lyman-alpha radiative transfer effects may modify the observed clustering of LAE galaxies in a way that mimics gravitational effects, potentially reducing the precision of cosmological constraints. For example, the effect of the linear redshift-space distortion on the power spectrum of LAE galaxies is potentially degenerate with Lyman-alpha radiative transfer effects owing to th…
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…
The amplitude of redshifted 21 cm fluctuations during the Epoch of Reionization (EoR) is expected to show a distinctive "rise and fall" behavior with decreasing redshift as reionization proceeds. On large scales (k <~ 0.1 Mpc^{-1}) this can mostly be characterized by evolution in the product of the mean 21 cm brightness temperature and a bias factor, b_21(z). This quantity evolves in a distinctive way that can help in determining the average ionization history of the intergalactic medium (IGM) from upcoming 21 cm fluctuation data sets. Here we consider extracting <T_21> b_21(z) using a combina…
Measurements of the non-Gaussianity of the primordial density field have the power to considerably improve our understanding of the physics of inflation. Indeed, if we can increase the precision of current measurements by an order of magnitude, a null-detection would rule out many classes of scenarios for generating primordial fluctuations. Large-scale galaxy redshift surveys represent experiments that hold the promise to realise this goal. Thus, we model the galaxy bispectrum and forecast the accuracy with which it will probe the parameter $f_{\rm NL}$, which represents the degree of primordi…
This is part two in a series of papers in which we investigate an approach based on Lagrangian perturbation theory (LPT) to study the non-linear evolution of the large-scale structure distribution in the universe. Firstly, we compute the matter bispectrum in real space using LPT up one-loop order, for both Gaussian and non-Gaussian initial conditions. In the initial position limit, we find that the one-loop bispectrum computed in this manner is identical to its counterpart obtained from standard Eulerian perturbation theory (SPT). Furthermore, the LPT formalism allows for a simple reorganisati…
The anisotrpy of the redshift space bispectrum $B^s(\mathbf{k_1},\mathbf{k_2},\mathbf{k_3})$, which contains a wealth of cosmological information, is completely quantified using multipole moments $\bar{B}^m_{\ell}(k_1,μ,t)$ where $k_1$, the length of the largest side, and $(μ,t)$ respectively quantify the size and shape of the triangle $(\mathbf{k_1},\mathbf{k_2},\mathbf{k_3})$. We present analytical expressions for all the multipoles which are predicted to be non-zero ($\ell \le 8, m \le 6$ ) at second order perturbation theory. The multipoles also depend on $β_1,b_1$ and $γ_2$, which quantif…
Massive neutrinos suppress the growth of structure below their free-streaming scale and leave an imprint on large-scale structure. Measuring this imprint allows us to constrain the sum of neutrino masses, $M_ν$, a key parameter in particle physics beyond the Standard Model. However, degeneracies among cosmological parameters, especially between $M_ν$ and $σ_8$, limit the constraining power of standard two-point clustering statistics. In this work, we investigate whether we can break these degeneracies and constrain $\smnu$ with the next higher-order correlation function --- the bispectrum. We …
We discuss the dominant terms of the relativistic galaxy number counts to second order in cosmological perturbation theory on sub-Hubble scales and on intermediate to large redshifts. In particular, we determine their contribution to the bispectrum. In addition to the terms already known from Newtonian second order perturbation theory, we find that there are a series of additional `lensing-like' terms which contribute to the bispectrum. We derive analytical expressions for the full leading order bispectrum and we evaluate it numerically for different configurations, indicating how they can be …
We address the amount of information in the non-Gaussian regime of weak lensing surveys by modelling all relevant covariances of the power spectra and bispectra, using 1000 ray-tracing simulation realizations for a Lambda-CDM model and an analytical halo model. We develop a formalism to describe the covariance matrices of power spectra and bispectra of all triangle configurations. In addition to the known contributions which extend up to six-point correlation functions, we propose a new contribution `the halo sample variance (HSV)' arising from the coupling of the lensing Fourier modes with la…
Several statistics have been proposed for measuring the kSZ effect by combining the small-scale CMB with galaxy surveys. We review five such statistics, and show that they are all mathematically equivalent to the optimal bispectrum estimator of type $\langle ggT \rangle$. Reinterpreting these kSZ statistics as special cases of bispectrum estimation makes many aspects transparent, for example optimally weighting the estimator, or incorporating photometric redshift errors. We analyze the information content of the bispectrum and show that there are two observables: the small-scale galaxy-electro…
