Accurate covariance matrices for two-point functions are critical for inferring cosmological parameters in likelihood analyses of large-scale structure surveys. Among various approaches to obtaining the covariance, analytic computation is much faster and less noisy than estimation from data or simulations. However, the transform of covariances from Fourier space to real space involves integrals with two Bessel integrals, which are numerically slow and easily affected by numerical uncertainties. Inaccurate covariances may lead to significant errors in the inference of the cosmological parameters. In this paper, we introduce a 2D-FFTLog algorithm for efficient, accurate and numerically stable computation of non-Gaussian real space covariances for both 3D and projected statistics. The 2D-FFTLog algorithm is easily extended to perform real space bin-averaging. We apply the algorithm to the covariances for galaxy clustering and weak lensing for a Dark Energy Survey Year 3-like and a Rubin Observatory's Legacy Survey of Space and Time Year 1-like survey, and demonstrate that for both surveys, our algorithm can produce numerically stable angular bin-averaged covariances with the flat sky approximation, which are sufficiently accurate for inferring cosmological parameters. The code CosmoCov for computing the real space covariances with or without the flat sky approximation is released along with this paper.
Angular two-point statistics of large-scale structure observables are important cosmological probes. To reach the high accuracy required by the statistical precision of future surveys, some of these statistics may need to be computed without the commonly employed Limber approximation; the exact computation however requires integration over Bessel functions, and a brute-force evaluation is slow to converge. We present a new method based on our generalized FFTLog algorithm for the efficient computation of angular power spectra beyond the Limber approximation. The new method significantly simplif…
We introduce two kurt-spectra to probe fourth-order statistics of weak lensing convergence maps. Using state-of-the-art numerical simulations, we study the shapes of these kurt-spectra as a function of source redshifts and smoothing angular scales. We employ a pseudo-$C_{\ell}$ approach to estimate the spectra from realistic convergence maps in the presence of an observational mask and noise for stage-IV large-scale structure surveys. We compare these results against theoretical predictions calculated using the FFTLog formalism, and find that a simple nonlinear clustering model-the hierarchica…
We study the impact of lensing corrections on modeling cross correlations between CMB lensing and galaxies, cosmic shear and galaxies, and galaxies in different redshift bins. Estimating the importance of these corrections becomes necessary in the light of anticipated high-accuracy measurements of these observables. While higher order lensing corrections (sometimes also referred to as post Born corrections) have been shown to be negligibly small for lensing auto correlations, they have not been studied for cross correlations. We evaluate the contributing four-point functions without making use…
We develop a method to simulate galaxy-galaxy weak lensing by utilizing all-sky, light-cone simulations and their inherent halo catalogs. Using the mock catalog to study the error covariance matrix of galaxy-galaxy weak lensing, we compare the full covariance with the "jackknife" (JK) covariance, the method often used in the literature that estimates the covariance from the resamples of the data itself. We show that there exists the variation of JK covariance over realizations of mock lensing measurements, while the average JK covariance over mocks can give a reasonably accurate estimation of …
We investigate correlations induced by gravitational lensing on simulated cosmic microwave background data of experiments with an incomplete sky coverage and their effect on inferences from the South Pole Telescope data. These correlations agree well with the theoretical expectations, given by the sum of super-sample and intra-sample lensing terms, with only a typically negligible $\sim$ 5% discrepancy in the amplitude of the super-sample lensing effect. Including these effects we find that lensing constraints are in $3.0σ$ or $2.1σ$ tension between the SPT polarization measurements and Planck…
Angular cosmological correlators are infamously difficult to compute due to the highly oscillatory nature of the projection integrals. Motivated by recent development on analytic approaches to cosmological perturbation theory, in this paper we present an efficient method for computing cosmological four-point correlations in angular space, generalizing previous works on lower-point functions. This builds on the FFTLog algorithm that approximates the matter power spectrum as a sum over power-law functions, which makes certain momentum integrals analytically solvable. The computational complexity…
CMB and lensing reconstruction power spectra are powerful probes of cosmology. However they are correlated, since the CMB power spectra are lensed and the lensing reconstruction is constructed using CMB multipoles. We perform a full analysis of the auto- and cross-covariances, including polarization power spectra and minimum variance lensing estimators, and compare with simulations of idealized future CMB-S4 observations. Covariances sourced by fluctuations in the unlensed CMB and instrumental noise can largely be removed by using a realization-dependent subtraction of lensing reconstruction n…
We study two key issues militating against the use of the anisotropic three-point correlation function (3PCF) for cosmological parameter inference: difficulties with its computational estimation and high-dimensionality. We show how high-dimensionality may be reduced significantly by multipole decompositions of all angular dependence. This allows deriving the full expression for the multipole moments of the anisotropic 3PCF and its covariance matrix in a basis where the dimensionality reduces from nine to two at each multipole in the plane-parallel limit. We use 2D FFTLog formalism to show how …
Next-generation optical imaging surveys will revolutionise the observations of weak gravitational lensing by galaxy clusters and provide stringent constraints on growth of structure and cosmic acceleration. In these experiments, accurate modelling of covariance matrices of cluster weak lensing plays the key role in obtaining robust measurements of the mean mass of clusters and cosmological parameters. We use a combination of analytical calculations and high-resolution N-body simulations to derive accurate covariance matrices that span from the virial regime to linear scales of the cluster-matt…
Weak gravitational lensing is one of the most promising tools to investigate the equation-of-state of dark energy. In order to obtain reliable parameter estimations for current and future experiments, a good theoretical understanding of dark matter clustering is essential. Of particular interest is the statistical precision to which weak lensing observables, such as cosmic shear correlation functions, can be determined. We construct a fitting formula for the non-Gaussian part of the covariance of the lensing power spectrum. The Gaussian contribution to the covariance, which is proportional to …
The observable universe contains density perturbations on scales larger than any finite volume survey. Perturbations on scales larger than a survey can measure degrade its power to constrain cosmological parameters. The dependence of survey observables such as the weak lensing power spectrum on these long-wavelength modes results in super-sample covariance. Accurately forecasting parameter constraints for future surveys requires accurately accounting for the super-sample effects. If super-sample covariance is in fact a major component of the survey error budget, it may be necessary to investig…
We derive the complete super-sample covariance (SSC) of the matter and weak lensing convergence power spectra using the power spectrum response formalism to accurately describe the coupling of super- to sub-survey modes. The SSC term is completely characterized by the survey window function, the nonlinear matter power spectrum and the full first-order nonlinear power spectrum response function, which describes the response to super-survey density and tidal field perturbations. Generalized separate universe simulations can efficiently measure these responses in the nonlinear regime of structure…
We study the covariance properties of real space correlation function estimators -- primarily galaxy-shear correlations, or galaxy-galaxy lensing -- using SDSS data for both shear catalogs and lenses (specifically the BOSS LOWZ sample). Using mock catalogs of lenses and sources, we disentangle the various contributions to the covariance matrix and compare them with a simple analytical model. We show that not subtracting the lensing measurement around random points from the measurement around the lens sample is equivalent to performing the measurement using the lens density field instead of the…
With the advent of a new generation of cosmological experiments that will provide high-precision measurements of the cosmic microwave background (CMB) and galaxies in the large-scale structure, it is pertinent to examine the potential of performing a joint analysis of multiple cosmological probes. In this paper, we study the cosmological information content contained in the one-loop power spectra and tree bispectra of galaxies cross-correlated with CMB lensing. We use the FFTLog method to compute angular correlations in spherical harmonic space, applicable for wide angles that can be accessed …
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…
Gravitational lensing surveys have now become large and precise enough that the interpretation of the lensing signal has to take into account an increasing number of theoretical limitations and observational biases. Since the lensing signal is the strongest at small angular scales, only numerical simulations can reproduce faithfully the non-linear dynamics and secondary effects at play. This work is the first of a series in which all gravitational lensing corrections known so far will be implemented in the same set of simulations, using realistic mock catalogues and non-Gaussian statistics. In…
In this paper we show how intrinsic alignments can be incorporated consistently in the formalism of 3d weak lensing. We use two different descriptions of the intrinsic galaxy ellipticities, the so-called linear and quadratic model, respectively. For both models we derive the covariance matrix of the intrinsic alignment signal (II-alignments) and GI-alignments (the cross correlation of intrinsic and lensing induced ellipticities). Evaluating the covariance matrices for the linear model numerically and comparing the results to the cosmic shear signal we find that for a low redshift survey the to…
Stacked lensing is a powerful means of measuring the average mass distribution around large-scale structure tracers. There are two stacked lensing estimators used in the literature, denoted as $ΔΣ$ and $γ_+$, which are related as $ΔΣ=Σ_{\rm cr}γ_+$, where $Σ_{\rm cr}(z_l,z_s)$ is the critical surface mass density for each lens-source pair ($z_l$ and $z_s$ are lens and source redshifts, respectively). In this paper we derive a formula for the covariance matrix of $ΔΣ$-estimator focusing on `weight' function to improve the signal-to-noise ($S/N$). We assume that the lensing fields and the distri…
We study how well the Gaussian approximation is valid for computing the covariance matrices of the convergence power and bispectrum in weak gravitational lensing analyses. We focus on its impact on the cosmological parameter estimations by comparing the results with and without non-Gaussian error contribution in the covariance matrix. We numerically derive the covariance matrix as well as the cosmology dependence of the spectra from a large set of N-body simulations performed for various cosmologies and carry out Fisher matrix forecasts for tomographic weak lensing surveys with three source re…
The combination of galaxy-galaxy lensing and galaxy clustering data has the potential to simultaneously constrain both the cosmological and galaxy formation models. In this paper we perform a comprehensive exploration of these signals and their covariances through a combination of analytic and numerical approaches. First, we derive analytic expressions for the projected galaxy correlation function and stacked tangential shear profile and their respective covariances, which include Gaussian and discreteness noise terms. Secondly, we measure these quantities from mock galaxy catalogues obtained …
Weak gravitational lensing is one of the few direct methods to map the dark-matter distribution on large scales in the Universe, and to estimate cosmological parameters. We study a Bayesian inference problem where the data covariance $\mathbf{C}$, estimated from a number $n_{\textrm{s}}$ of numerical simulations, is singular. In a cosmological context of large-scale structure observations, the creation of a large number of such $N$-body simulations is often prohibitively expensive. Inference based on a likelihood function often includes a precision matrix, $Ψ= \mathbf{C}^{-1}$. The covariance …
Using 1000 ray-tracing simulations for a Λ-dominated cold dark model in Sato et al. (2009), we study the covariance matrix of cosmic shear correlation functions, which is the standard statistics used in the previous measurements. The shear correlation function of a particular separation angle is affected by Fourier modes over a wide range of multipoles, even beyond a survey area, which complicates the analysis of the covariance matrix. To overcome such obstacles we first construct Gaussian shear simulations from the 1000 realizations, and then use the Gaussian simulations to disentangle the Ga…
A coherent over- or under-density contrast across a finite survey volume causes an upward- or downward-fluctuation in the observed number of halos. This fluctuation in halo number adds a significant co-variant scatter in the observed amplitudes of weak lensing power spectrum at nonlinear, small scales -- the so-called super-sample variance or the halo sample variance. In this paper, we show that by measuring both the number counts of clusters and the power spectrum in the same survey region, we can mitigate this loss of information and significantly enhance the scientific return from the upcom…
Upcoming weak lensing surveys will probe large fractions of the sky with unprecedented accuracy. To infer cosmological constraints, a large ensemble of survey simulations are required to accurately model cosmological observables and their covariances. We develop a parallelized multi-lens-plane pipeline called UFalcon, designed to generate full-sky weak lensing maps from lightcones within a minimal runtime. It makes use of L-PICOLA, an approximate numerical code, which provides a fast and accurate alternative to cosmological $N$-Body simulations. The UFalcon maps are constructed by nesting 2 si…
Baryonic feedback effects lead to a suppression of the weak lensing angular power spectrum on small scales. The poorly constrained shape and amplitude of this suppression is an important source of uncertainties for upcoming cosmological weak lensing surveys such as Euclid or LSST. In this first paper in a series of two, we use simulations to build a Euclid-like tomographic mock data-set for the cosmic shear power spectrum and the corresponding covariance matrix, which are both corrected for baryonic effects following the baryonification method of Schneider et al. (2019). In addition, we develo…
The thermal Sunyaev-Zel'dovich (tSZ) effect signal is widely recognized as a robust mass proxy of galaxy clusters with small intrinsic scatter. However, recent observational calibration of the tSZ scaling relation using weak lensing (WL) mass exhibits considerably larger scatter than the intrinsic scatter predicted from numerical simulations. This raises a question as to whether we can realize the full statistical power of ongoing and upcoming tSZ-WL observations of galaxy clusters. In this work, we investigate the origin of observed scatter in the tSZ-WL scaling relation, using mock maps of g…
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…
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…
In this study, we measure the response of matter and halo projected power spectra $P^{\rm 2D}_{\rm XY}(k)$ (X, Y are matter and/or halos), to a large-scale density contrast, $δ_{\rm b}$, using separate universe simulations. We show that the fractional response functions, i.e., $\mathrm{d}\ln P^{\rm 2D}_{\rm XY}(k)/\mathrm{d}δ_{\rm b}$, are identical to their respective three-dimensional power spectra within simulation measurement errors. Then, using various $N$-body simulation combinations (small-box simulations with periodic boundary conditions and sub-volumes of large-box simulations) to con…
Gravitational lensing information from the two and higher point statistics of the CMB temperature and polarization fields are intrinsically correlated because they are lensed by the same realization of structure between last scattering and observation. Using an analytic model for lens sample covariance, we show that there is one mode, separately measurable in the lensed CMB power spectra and lensing reconstruction, that carries most of this correlation. Once these measurements become lens sample variance dominated, this mode should provide a useful consistency check between the observables tha…
We present the application of the pseudo-spectrum method to galaxy-galaxy lensing. We derive explicit expressions for the pseudo-spectrum analysis of the galaxy-shear cross spectrum, which is the Fourier space counterpart of the stacked galaxy-galaxy lensing profile. The pseudo-spectrum method corrects observational issues such as the survey geometry, masks of bright stars and their spikes, and inhomogeneous noise, which distort the spectrum and also mix the E-mode and the B-mode signals. Using ray-tracing simulations in N-body simulations including realistic masks, we confirm that the pseudo-…
We present here the cosmo-SLICS, a new suite of simulations specially designed for the analysis of current and upcoming weak lensing data beyond the standard two-point cosmic shear. We sample the $[Ω_{\rm m}, σ_8, h, w_0]$ parameter space at 25 points organised in a Latin hyper-cube, spanning a range that contains most of the $2σ$ posterior distribution from ongoing lensing surveys. At each of these nodes we evolve a pair of $N$-body simulations in which the sampling variance is highly suppressed, and ray-trace the volumes 800 times to further increase the effective sky coverage. We extract a …
Upcoming wide-area weak lensing surveys are expensive both in time and cost and require an optimal survey design in order to attain maximum scientific returns from a fixed amount of available telescope time. The super-sample covariance (SSC), which arises from unobservable modes that are larger than the survey size, significantly degrades the statistical precision of weak lensing power spectrum measurement even for a wide-area survey. Using the 1000 mock realizations of the log-normal model, which approximates the weak lensing field for a $Λ$-dominated cold dark matter model, we study an optim…
(Abridged) We investigate and quantify the impact of finite simulation volume on weak lensing two- and four-point statistics. These {\it finite support} (FS) effects are modelled for several estimators, simulation box sizes and source redshifts, and validated against a new large suite of 500 $N$-body simulations. The comparison reveals that our theoretical model is accurate to better than 5 per cent for the shear correlation function $ξ_{+}(θ)$ and its error. We find that the most important quantities for FS modelling is the ratio between the measured angle $θ$ and the angular size of the simu…
An accurate covariance matrix is essential for obtaining reliable cosmological results when using a Gaussian likelihood. In this paper we study the covariance of pseudo-$C_\ell$ estimates of tomographic cosmic shear power spectra. Using two existing publicly available codes in combination, we calculate the full covariance matrix, including mode-coupling contributions arising from both partial sky coverage and non-linear structure growth. For three different sky masks, we compare the theoretical covariance matrix to that estimated from publicly available N-body weak lensing simulations, finding…
We study weak gravitational lensing by the cosmic large-scale structure of the 21-cm radiation background in the 3d-weak lensing formalism. The interplay between source distance measured at finite resolution, visibility and lensing terms is analysed in detail and the resulting total covariance $C_{\ell}(k,k')$ is derived. The effect of lensing correlates different multipoles through convolution, breaking the statistical homogeneity of the 21-cm radiation background. This homogeneity breaking can be exploited to reconstruct the lensing field $\hatϕ_{\ell m}(κ)$ and noise lensing reconstruction …
We investigate whether a Gaussian likelihood, as routinely assumed in the analysis of cosmological data, is supported by simulated survey data. We define test statistics, based on a novel method that first destroys Gaussian correlations in a dataset, and then measures the non-Gaussian correlations that remain. This procedure flags pairs of datapoints which depend on each other in a non-Gaussian fashion, and thereby identifies where the assumption of a Gaussian likelihood breaks down. Using this diagnostic, we find that non-Gaussian correlations in the CFHTLenS cosmic shear correlation function…
We present a public suite of weak lensing mock data, extending the Scinet Light Cone Simulations (SLICS) to simulate cross-correlation analyses with different cosmological probes. These mocks include KiDS-450- and LSST-like lensing data, cosmic microwave background lensing maps and simulated spectroscopic surveys that emulate the GAMA, BOSS and 2dFLenS galaxy surveys. With 844 independent realisations, our mocks are optimised for combined-probe covariance estimation, which we illustrate for the case of a joint measurement involving cosmic shear, galaxy-galaxy lensing and galaxy clustering from…
The likelihood function for cosmological parameters, given by e.g. weak lensing shear measurements, depends on contributions to the covariance induced by the nonlinear evolution of the cosmic web. As nonlinear clustering to date has only been described by numerical $N$-body simulations in a reliable and sufficiently precise way, the necessary computational costs for estimating those covariances at different points in parameter space are tremendous. In this work we describe the change of the matter covariance and of the weak lensing covariance matrix as a function of cosmological parameters by …
We explore a variety of statistics of clusters selected with cosmic shear measurement by utilizing both analytic models and large numerical simulations. We first develop a halo model to predict the abundance and the clustering of weak lensing selected clusters. Observational effects such as galaxy shape noise are included in our model. We then generate realistic mock weak lensing catalogs to test the accuracy of our analytic model. To this end, we perform full-sky ray-tracing simulations that allow us to have multiple realizations of a large continuous area. We model the masked regions on the …
We examine cosmological constraints from high precision weak lensing surveys including super-sample covariance (SSC) due to the finite survey volume. Specifically, we focus on the contribution of {\it beat coupling} in the intrinsic alignments as a part of full cosmic shear signal under flat sky approximation. The SSC-effect grows by going to lower redshift bin and indicates considerable footprint on the intermediate and high multipoles for cumulative signal to noise ratio (SNR). The SNR is reduced by $\approx 10\%$ as a consequence of including the intrinsic alignments super-sample covariance…
The disconnected part of the power spectrum covariance matrix (also known as the "Gaussian" covariance) is the dominant contribution on large scales for galaxy clustering and weak lensing datasets. The presence of a complicated sky mask causes non-trivial correlations between different Fourier/harmonic modes, which must be accurately characterized in order to obtain reliable cosmological constraints. This is particularly relevant for galaxy survey data. Unfortunately, an exact calculation of these correlations involves $O(\ell_{\rm max}^6)$ operations that become computationally impractical ve…
The one-point probability distribution function (PDF) is a powerful summary statistic for non-Gaussian cosmological fields, such as the weak lensing (WL) convergence reconstructed from galaxy shapes or cosmic microwave background (CMB) maps. Thus far, no analytic model has been developed that successfully describes the high-convergence tail of the WL convergence PDF for small smoothing scales from first principles. Here, we present a halo-model formalism to compute the WL convergence PDF, building upon our previous results for the thermal Sunyaev-Zel'dovich field. Furthermore, we extend our fo…
We study the lensing convergence power spectrum and its covariance for a standard LCDM cosmology. We run 400 cosmological N-body simulations and use the outputs to perform a total of 1000 independent ray-tracing simulations. We compare the simulation results with analytic model predictions. The semi-analytic model based on Smith et al.(2003) fitting formula underestimates the convergence power by ~30% at arc-minute angular scales. For the convergence power spectrum covariance, the halo model reproduces the simulation results remarkably well over a wide range of angular scales and source redshi…
To combine information from measurements of the redshift-space power spectrum from spectroscopic data with angular weak lensing, galaxy clustering and galaxy-galaxy lensing power spectra from photometric surveys (i.e. the $3 \times 2$ point statistics), we must account for the covariance between the two probes. Currently any covariance between the two types of measurements is neglected as existing photometric and spectroscopic surveys largely probe different cosmological volumes. This will cease to be the case as data arrives from Stage-IV surveys. In this paper we derive an analytic expressio…
We present a combined cosmic shear analysis of the modeling of line-of-sight distortions on strongly lensed extended arcs and galaxy shape measurements in the COSMOS field. We develop a framework to predict the covariance of strong lensing and galaxy shape measurements of cosmic shear on the basis of the small scale matter power-spectrum. The weak lensing measurement is performed using data from the COSMOS survey calibrated with a cloning scheme using the Ultra Fast Image Generator UFig (Berge 2013). The strong lensing analysis is performed by forward modeling the lensing arcs with a main lens…
We measure the cross-correlation between Fermi-LAT gamma-ray photons and over 1000 deg$^2$ of weak lensing data from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), the Red Cluster Sequence Lensing Survey (RCSLenS), and the Kilo Degree Survey (KiDS). We present the first measurement of tomographic weak lensing cross-correlations and the first application of spectral binning to cross-correlations between gamma rays and weak lensing. The measurements are performed using an angular power spectrum estimator while the covariance is estimated using an analytical prescription. We verify…
The generation of simulated convergence maps is of key importance in fully exploiting weak lensing by Large Scale Structure (LSS) from which cosmological parameters can be derived. In this paper we present an extension of the PINOCCHIO code which produces catalogues of dark matter haloes so that it is capable of simulating weak lensing by LSS. Like WL-MOKA, the method starts with a random realisation of cosmological initial conditions, creates a halo catalogue and projects it onto the past-light-cone, and paints in haloes assuming parametric models for the mass density distribution within them…
Gravitational lensing of the Cosmic Microwave Background (CMB) encodes cosmological information in the observed anisotropies of temperature and polarization. Accurate extraction of this additional information requires precise modeling of the covariance matrix of the power spectra of observed CMB fields. We introduce a new analytical model to describe the non-Gaussian structure of this covariance matrix and display the importance of second-order terms that were previously neglected. When compared with direct numerical simulations our model captures parameter errors to better than a few percent …
We report the weak lensing measurement of filaments between Sloan Digital Sky Survey (SDSS) III/Baryon Oscillation Spectroscopic Survey (BOSS) CMASS galaxy pairs at $z\sim0.55$, using the Subaru Hyper Suprime-Cam (HSC) first-year galaxy shape catalogue. Despite of the small overlap of $140$ deg$^2$ between these surveys we detect the filament lensing signal at 3.9$σ$ significance, which is the highest signal-to-noise lensing measurement of filaments between galaxy-scale halos at this redshift range. We derive a theoretical prediction and covariance using mock catalogues based on full-sky ray-t…
We have investigated a recently proposed halo-based model, Camelus, for predicting weak-lensing peak counts, and compared its results over a collection of 162 cosmologies with those from N-body simulations. While counts from both models agree for peaks with $\mathcal{S/N}>1$ (where $\mathcal{S/N}$ is the ratio of the peak height to the r.m.s. shape noise), we find $\approx 50\%$ fewer counts for peaks near $\mathcal{S/N}=0$ and significantly higher counts in the negative $\mathcal{S/N}$ tail. Adding shape noise reduces the differences to within $20\%$ for all cosmologies. We also found larger …
Gravitational lensing provides a significant source of cosmological information in modern CMB parameter analyses. It is measured in both the power spectrum and trispectrum of the temperature fluctuations. These observables are often treated as independent, although as they are both determined from the same map this is impossible. In this paper, we perform a rigorous analysis of the covariance between lensing power spectrum and trispectrum analyses. We find two dominant contributions coming from: (i) correlations between the disconnected noise bias in the trispectrum measurement and sample vari…
Recently, it has been shown that cross-correlating CMB lensing and 3D cosmic shear allows to considerably tighten cosmological parameter constraints. We investigate whether similar improvement can be achieved in a conventional tomographic setup. We present Fisher parameter forecasts for a Euclid-like galaxy survey in combination with different ongoing and forthcoming CMB experiments. In contrast to a fully three-dimensional analysis we find only marginal improvement. Assuming Planck-like CMB data we show that including the full covariance of the combined CMB and cosmic shear data improves the …
