We use a recently introduced statistic called {\em Integrated Bispectrum} (IB) to probe the gravity-induced non-Gaussianity at the level of the bispectrum from weak lensing convergence or $κ$ maps. We generalize the concept of the IB to spherical coordinates. This result is next connected to the response function approach. Finally, we use the Euclid Flagship simulations to compute the IB as a function of redshift and wave number. We also outline how the IB can be computed using a variety of analytical approaches including the ones based on Effective Field Theory (EFT), {\em Halo models} and models based on the {\em Separate Universe approach} in projection or two-dimension (2D). Comparing these results against simulations we find that the existing theoretical models tend to over-predict the numerical value of the IB. We emphasize the role of the finite volume effect in the numerical estimation of the IB. We introduced the concept of squeezed and collapsed tripsectrum for 2D $κ$ maps. We derive the IB for many parameterized theories of modified gravity including the Horndeskii and beyond-Horndeskii theories specifically for the non-degenerate scenarios that are also known as the Gleyzes-Langlois-Piazza-Venizzi or GPLV theories. In addition, the cosmological models with clustering quintessence and models involving massive neutrinos are also derived.
We discuss detectability of the nonlinear growth of the large-scale structure in the cosmic microwave background (CMB) lensing. Lensing signals involved in CMB anisotropies have been measured from multiple CMB experiments, such as Atacama Cosmology Telescope (ACT), Planck, POLARBEAR, and South Pole Telescope (SPT). Reconstructed lensing signals are useful to constrain cosmology via their angular power spectrum, while detectability and cosmological application of their bispectrum induced by the nonlinear evolution are not well studied. Extending the analytic estimate of the galaxy lensing bispe…
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 explore the effect of massive neutrinos on the weak lensing shear bispectrum using the Cosmological Massive Neutrino Simulations. We find that the primary effect of massive neutrinos is to suppress the amplitude of the bispectrum with limited effect on the bispectrum shape. The suppression of the bispectrum amplitude is a factor of two greater than the suppression of the small scale power-spectrum. For an LSST-like weak lensing survey that observes half of the sky with five tomographic redshift bins, we explore the constraining power of the bispectrum on three cosmological parameters: the s…
Cosmic Microwave Background experiments from COBE to Planck, have launched cosmology into an era of precision science, where many cosmological parameters are now determined to the percent level. Next generation telescopes, focussing on the cosmological 21cm signal from neutral hydrogen, will probe enormous volumes in the low-redshift Universe, and have the potential to determine dark energy properties and test modifications of Einstein's gravity. We study the 21cm bispectrum due to gravitational collapse as well as the contribution by line of sight perturbations in the form of the lensing-ISW …
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.
We estimate uncertainties of cosmological parameters for phenomenological interacting dark energy models using weak lensing convergence power spectrum and bispectrum. We focus on the bispectrum tomography and examine how well the weak lensing bispectrum with tomography can constrain the interactions between dark sectors, as well as other cosmological parameters. Employing the Fisher matrix analysis, we forecast parameter uncertainties derived from weak lensing bispectra with a two-bin tomography and place upper bounds on strength of the interactions between the dark sectors. The cosmic shear w…
We characterize the Cosmic Infrared Background (CIB)-lensing bispectrum which is one of the contributions to the three-point functions of Cosmic Microwave Background (CMB) maps in harmonic space. We show that the CIB-lensing bispectrum has a considerable strength and that it can be detected with high significance in the Planck high-frequency maps. We also present forecasts of the contamination on different shapes of the primordial non-Gaussianity $f_{nl}$ parameter produced by the CIB-lensing bispectrum and by the extragalactic point sources bispectrum in the Planck high-resolution CMB anisotr…
The rapidly improving precision of measurements of gravitational lensing of the Cosmic Microwave Background (CMB) also requires a corresponding increase in the precision of theoretical modeling. A commonly made approximation is to model the CMB deflection angle or lensing potential as a Gaussian random field. In this paper, however, we analytically quantify the influence of the non-Gaussianity of large-scale structure lenses, arising from nonlinear structure formation, on CMB lensing measurements. In particular, evaluating the impact of the non-zero bispectrum of large-scale structure on the r…
Cross-correlating the lensing signals of galaxies and comic microwave background (CMB) fluctuations is expected to provide valuable cosmological information. In particular it may help tighten constraints on parameters describing the properties of intrinsically aligned galaxies at high redshift. To access the information conveyed by the cross-correlation signal its accurate theoretical description is required. We compute the bias to CMB lensing-galaxy shape cross-correlation measurements induced by nonlinear structure growth. Using tree-level perturbation theory for the large-scale structure bi…
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…
Recent studies have demonstrated that {\em secondary} non-Gaussianity induced by gravity will be detected with a high signal-to-noise (S/N) by future and even by on-going weak lensing surveys. One way to characterise such non-Gaussianity is through the detection of a non-zero three-point correlation function of the lensing convergence field, or of its harmonic transform, the bispectrum. A recent study analysed the properties of the squeezed configuration of the bispectrum, when two wavenumbers are much larger than the third one. We extend this work by estimating the amplitude of the (reduced) …
We present the first detection of a correlation between the Lyman-$α$ forest and cosmic microwave background (CMB) lensing. For each Lyman-$α$ forest in SDSS-III/BOSS DR12, we correlate the one-dimensional power spectrum with the CMB lensing convergence on the same line of sight from Planck. This measurement constitutes a position-dependent power spectrum, or a squeezed bispectrum, and quantifies the non-linear response of the Lyman-$α$ forest power spectrum to a large-scale overdensity. The signal is measured at 5~$σ$ and is consistent with the $Λ$CDM expectation. We measure the linear bias o…
The significant increase in precision that will be achieved by Stage IV cosmic shear surveys means that several currently used theoretical approximations may cease to be valid. An additional layer of complexity arises from the fact that many of these approximations are interdependent; the procedure to correct for one involves making another. Two such approximations that must be relaxed for upcoming experiments are the reduced shear approximation and the effect of neglecting magnification bias. Accomplishing this involves the calculation of the convergence bispectrum; typically subject to the L…
We investigate the prospects for using the weak lensing bispectrum alongside the power spectrum to control systematic uncertainties in a Euclid-like survey. Three systematic effects are considered: the intrinsic alignment of galaxies, uncertainties in the means of tomographic redshift distributions, and multiplicative bias in the measurement of the shear signal. We find that the bispectrum is very effective in mitigating these systematic errors. Varying all three systematics simultaneously, a joint power spectrum and bispectrum analysis reduces the area of credible regions for the cosmological…
Future Parameter Constraints from Weak Lensing CMB and Galaxy Lensing Power- and Bispectra
Institute for Theoretical Physics, Utrecht University（乌得勒支大学理论物理研究所）；Van Swinderen Institute for Particle Physics and Gravity, University of Groningen（格罗宁根大学范斯温德恩粒子物理与引力研究所）
Halo models and halo occupation distributions (HODs) are important tools to model the galaxy and matter distribution. We present and assess a new method for constraining the parameters of HODs using the gravitational lensing shear around galaxy pairs, galaxy-galaxy-galaxy-lensing (G3L). In contrast to galaxy-galaxy-lensing, G3L is sensitive to correlations between the per-halo numbers of galaxies from different populations. We use G3L to probe these correlations and test the default hypothesis that they are negligible. We derive a halo model for G3L and validate it with realistic mock data fro…
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…
We study the effect of weak lensing by cosmic (super-)strings on the higher-order statistics of the cosmic microwave background (CMB). A cosmic string segment is expected to cause weak lensing as well as an integrated Sachs-Wolfe (ISW) effect, the so-called Gott-Kaiser-Stebbins (GKS) effect, to the CMB temperature fluctuation, which are thus naturally cross-correlated. We point out that, in the presence of such a correlation, yet another kind of the post-recombination CMB temperature bispectra, the ISW-lensing bispectra, will arise in the form of products of the auto- and cross-power spectra. …
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 …
The Squeezed Bispectrum from CHIME HI Emission and Planck CMB Lensing: Current Sensitivity and Forecasts
McGill University（麦吉尔大学）；Arizona State University（亚利桑那州立大学）；University of British Columbia（不列颠哥伦比亚大学）；National Research Council Canada（加拿大国家研究委员会）；Massachusetts Institute of Technology（麻省理工学院）
Upcoming cosmic microwave background (CMB) lensing measurements and tomographic galaxy surveys are expected to provide us with high-precision data sets in the coming years, thus paving the way for fruitful cross-correlation analyses. In this paper we study the information content of the weighted skew-spectrum, a nearly-optimal estimator of the angular bispectrum amplitude, as a means to extract non-Gaussian information on both bias and cosmological parameters from the bispectra of galaxies cross-correlated with CMB lensing, while gaining significantly on speed. Our results show that for the co…
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 provide a new fitting formula of the matter bispectrum in the nonlinear regime calibrated by high-resolution cosmological $N$-body simulations of $41$ cold dark matter ($w$CDM, $w=$ constant) models around the Planck 2015 best-fit parameters. As the parameterization in our fitting function is similar to that in Halofit, our fitting is named BiHalofit. The simulation volume is sufficiently large ($> 10 \, {\rm Gpc}^3$) to cover almost all measurable triangle bispectrum configurations in the universe. The function is also calibrated using one-loop perturbation theory at large scales ($k<0.3 \…
Analytic expressions for the statistics of peaks of random fields with weak non-Gaussianity are provided. Specifically, the abundance and spatial correlation of peaks are represented by formulas which can be evaluated only by virtually one-dimensional integrals. We assume the non-Gaussianity is weak enough such that it is represented by linear terms of the bispectrum. The formulas are formally given in $N$-dimensional space, and explicitly given in the case of $N=1,2,3$. Some examples of peak statistics in cosmological fields are calculated for the cosmic density field and weak lensing field, …
