Minkowski Functionals (MFs) are topological statistics that have become one of many standard tools used for investigating the statistical properties of cosmological random fields. They have found regular use in studies of departures from Gaussianity in a number of important cosmological scenarios. Important examples include the Cosmic Microwave Background (CMB), weak lensing studies, 21cm surveys and large scale structure (LSS). To lowest order the MFs depend on three generalised skewness parameters that can be shown to probe the bispectrum with differing weights. Recent studies have advocated the use of a power spectrum associated with the bispectrum, called the skew-spectrum, that has more power to distinguish between various contributions to the bispectrum than the conventional formalism adopted when using the Minkowski Functionals. In this article we review the motivations for studying non-Gaussianity and emphasize the importance of the momentum dependence of higher order correlators in investigating both inflationary and early Universe models as well as analytical models for gravitational instability. We then introduce the skew-spectra, applied to galaxy surveys, as a tool for investigating various models for primordial and gravitationally induced non-Gaussianities. We present analytical expressions for the skew-spectra for the density field and divergence of the velocity field in 3D and for projected surveys as a function of redshift and a smoothing angular scale. A Gaussian window function is assumed throughout this paper. Analytical results are derived for the case of gravitationally induced non-Gaussianity. These results can be generalised to incorporate redshift space effects. This will be useful in probing primordial and gravitationally induced non-Gaussianity from ongoing and future galaxy surveys.
Analytic formulas of Minkowski functionals in two-dimensional random fields are derived, including effects of second-order non-Gaussianity in the presence of both the bispectrum and trispectrum. The set of formulas provides a promising method to constrain the primordial non-Gaussianity of the universe by temperature fluctuations in the cosmic microwave background radiation. In a case of local-type non-Gaussianity, the Minkowski functionals are analytically given by powers of quadratic and cubic parameters, $f_{\rm NL}$ and $g_{\rm NL}$. Our formulas are not restricted to this particular model,…
Two of the most commonly used tools to constrain the primordial non-Gaussianity are the bispectrum and the Minkowski functionals of CMB temperature anisotropies. These two measures of non-Gaussianity in principle provide distinct (though correlated) information, but in the past constraints from them have only been loosely compared, and not statistically combined. In this work we evaluate, for the first time, the covariance matrix between the local non-Gaussianity coefficient fnl estimated through the bispectrum and Minkowski functionals. We find that the estimators are positively correlated, w…
The Minkowski functionals are useful statistics to quantify the morphology of various random fields. They have been applied to numerous analyses of geometrical patterns, including various types of cosmic fields, morphological image processing, etc. In some cases, including cosmological applications, small deviations from the Gaussianity of the distribution are of fundamental importance. Analytic formulas for the expectation values of Minkowski functionals with small non-Gaussianity have been derived in limited cases to date. We generalize these previous works to derive an analytic expression f…
We analyze non-Gaussianity (NG) due to the primordial bispectrum and trispectrum using CMB temperature maps of WMAP 7-year data. We first apply the perturbative formulae of Minkowski functionals up to second-order NG derived by Matsubara (2010), which enable us to give limits on cubic NG parametrized with tau_NL and g_NL as well as various types of quadratic NG parametrized with f_NL. We find no signature of primordial NG in WMAP 7-year data, but give constraints on the local-type, equilateral-type, orthogonal-type f_NL: f_NL(loc)=20+-42, f_NL(eq)=-121+-208, f_NL(ort)=-129+-171, respectively, …
Both WMAP and PLANCK missions reported the extremely Cold Spot (CS) centered at Galactic coordinate ($l=209^{\circ}$, $b=-57^{\circ}$) in CMB map. In this paper, we study the local non-Gaussianity of CS by defining the local Minkowski functions. We find that the third Minkowski function $ν_2$ is quite sensitive to the non-Gaussianity caused by CS. Compared with the random Gaussian simulations, WMAP CS deviates from Gaussianity at more than 99% confident level at the scale $R\sim10^{\circ}$. Meanwhile, we find that cosmic texture provides an excellent explanation for these anomalies related to …
We study the cosmological information contained in the Minkowski Functionals (MFs) of weak gravitational lensing convergence maps. We show that the MFs provide strong constraints on the local type primordial non-Gaussianity parameter f_NL. We run a set of cosmological N-body simulations and perform ray-tracing simulations of weak lensing, to generate 100 independent convergence maps of 25 deg^2 field-of-view for f_NL = -100, 0 and 100. We perform a Fisher analysis to study the degeneracy among other cosmological parameters such as the dark energy equation of state parameter w and the fluctuati…
We present a new harmonic-domain approach for extracting morphological information, in the form of Minkowski Functionals (MFs), from weak lensing (WL) convergence maps. Using a perturbative expansion of the MFs, which is expected to be valid for the range of angular scales probed by most current weak-lensing surveys, we show that the study of three generalized skewness parameters is equivalent to the study of the three MFs defined in two dimensions. We then extend these skewness parameters to three associated skew-spectra which carry more information about the convergence bispectrum than their…
We study Minkowski Functionals as probes of primordial non-Gaussianity in the Cosmic Microwave Background, specifically for the estimate of the primordial `local' bi-spectrum parameter f_NL, with instrumental parameters which should be appropriate for the Planck experiment. We use a maximum likelihood approach, which we couple with various filtering methods and test thoroughly for convergence. We included the effect of inhomogeneous noise as well as astrophysical biases induced by point sources and by the contamination from the Galaxy. We find that, when Wiener filtered maps are used (rather t…
We use Minkowski Functionals (MF) to constrain a primordial non-Gaussian contribution to the CMB intensity field as observed in the 150 GHz and 145 GHz BOOMERanG maps from the 1998 and 2003 flights, respectively, performing for the first time a joint analysis of the two datasets. A perturbative expansion of the MF formulae in the limit of a weakly non-Gaussian field yields analytical formulae, derived by Hikage et al. (2006), which can be used to constrain the coupling parameter f_NL without the need for non-Gaussian simulations. We find -1020<f_NL<390 at 95% CL, significantly improving the pr…
CMB polarization data is usually analyzed using $E$ and $B$ modes because they are scalars quantities under rotations along the lines of sight and have distinct physical origins. We explore the possibility of using the Stokes parameters $Q$ and $U$ for complementary analysis and consistency checks in the context of searches for non-Gaussianity. We show that the Minkowski Functionals (MFs) of $Q,U$ are invariant under local rotations along the lines of sight even though $Q,U$ are spin-2 variables, for full sky analysis. The invariance does not hold for incomplete sky. For local type primordial …
In this work we effectively calculated the two-dimensional Minkowski functionals for cosmic microwave background (CMB) temperature maps generated by single field models of inflation with a standard kinetic term. We started with calculation of the bispectrum of initial perturbations and then calculated the two-dimensional configuration space cubic moments for temperature fluctuations. These cubic moments give rise to first order non-Gaussian correction terms to the Minkowski functionals. Thus, we developed a robust mechanism to predict the amount of non-Gaussianity generated by inflation in the…
We generalize the concept of the ordinary skew-spectrum to probe the effect of non-Gaussianity on the morphology of Cosmic Microwave Background (CMB) maps in several domains: in real-space (where they are commonly known as cumulant-correlators), and in harmonic and needlet bases. The essential aim is to retain more information than normally contained in these statistics, in order to assist in determining the source of any measured non-Gaussianity, in the same spirit as Munshi & Heavens (2010) skew-spectra were used to identify foreground contaminants to the CMB bispectrum in Planck data. Using…
Despite the wealth of $Planck$ results, there are difficulties in disentangling the primordial non-Gaussianity of the Cosmic Microwave Background (CMB) from the secondary and the foreground non-Gaussianity (NG). For each of these forms of NG the lack of complete data introduces model-dependencies. Aiming at detecting the NGs of the CMB temperature anisotropy $δT$, while paying particular attention to a model-independent quantification of NGs, our analysis is based upon statistical and morphological univariate descriptors, respectively: the probability density function $P(δT)$, related to ${\ma…
We study the signatures of local type primordial non-Gaussianity, parametrized by $\fnl$, of scalar perturbations in CMB polarization using the probability distribution functions, Minkowski Functionals and Betti numbers. We show that the lowest order non-Gaussian deviation of the PDF of the total polarization intensity is at order $(\fnlσ)^2$. We calculate the non-Gaussian deviations of Minkowski Functionals and Betti numbers from simulated polarization maps. We find that $E$ mode polarization provides independent and equally strong constraint on $\fnl$ as temperature fluctuations. The non-Gau…
We study the impact of correlated instrumental noise and non-circular antenna beam patterns on primordial non-Gaussianity analysis. The two systematic effects are reproduced in the case of the Planck mission, using Planck-like realistic simulations. The non-Gaussian analysis is conducted with different approaches. First we adopt a blind approach, using the Spherical Mexican Hat Wavelet and the Minkowski functionals, and then a fNL estimator. We look respectively for false primordial non-Gaussian detections and for bias or variance increase in the estimated fNL value. Even if some slight effect…
Accurate component separation of full-sky maps in the radio and microwave frequencies, such as the cosmic microwave background (CMB), relies on a thorough understanding of the statistical properties of the Galactic foreground emissions. Using scalar Minkowski functionals and their tensorial generalization known as Minkowski tensors, we analyze the statistical properties of one of the major foreground components, namely the Galactic synchrotron given by the full sky 408 MHz Haslam map. We focus on understanding the nature of non-Gaussianity and statistical isotropy of the cooler regions of the …
We introduce the numbers of hot and cold spots, $n_h$ and $n_c$, of excursion sets of the CMB temperature anisotropy maps as statistical observables that can discriminate different non-Gaussian models. We numerically compute them from simulations of non-Gaussian CMB temperature fluctuation maps. The first kind of non-Gaussian model we study is the local type primordial non-Gaussianity. The second kind of models have some specific form of the probability distribution function from which the temperature fluctuation value at each pixel is drawn, obtained using HEALPIX. We find the characteristic …
We analyze whether there is any residual foreground contamination in the cleaned WMAP 7 years data for the differential assemblies, Q, V and W. We calculate the correlation between the foreground map, from which long wavelength correlations have been subtracted, and the foreground reduced map for each differential assembly after applying the Galaxy and point sources masks. We find positive correlations for all the differential assemblies, with high statistical significance. For Q and V, we find that a large fraction of the contamination comes from pixels where the foreground maps have positive…
We generalize the translation invariant tensor-valued Minkowski Functionals which are defined on two-dimensional flat space to the unit sphere. We apply them to level sets of random fields. The contours enclosing boundaries of level sets of random fields give a spatial distribution of random smooth closed curves. We obtain analytic expressions for the ensemble expectation values for the matrix elements of the tensor-valued Minkowski Functionals for isotropic Gaussian and Rayleigh fields. We elucidate the way in which the elements of the tensor Minkowski Functionals encode information about the…
The second-order formula of Minkowski functionals in weakly non-Gaussian fields is compared with the numerical $N$-body simulations. Recently, weakly non-Gaussian formula of Minkowski functionals is extended to include the second-order effects of non-Gaussianity in general dimensions. We apply this formula to the three-dimensional density field in the large-scale structure of the Universe. The parameters of the second-order formula include several kinds of skewness and kurtosis parameters. We apply the tree-level nonlinear perturbation theory to estimate these parameters. First we compare the …
We present an upgraded combined estimator, based on Minkowski Functionals and Neural Networks, with excellent performance in detecting primordial non-Gaussianity in simulated maps that also contain a weighted mixture of Galactic contaminations, besides real pixel's noise from Planck cosmic microwave background radiation data. We rigorously test the efficiency of our estimator considering several plausible scenarios for residual non-Gaussianities in the foreground-cleaned Planck maps, with the intuition to optimize the training procedure of the Neural Network to discriminate between contaminati…
The detection of the magnetic type $B$-mode polarization is the main goal of future cosmic microwave background (CMB) experiments. In the standard model, the $B$-mode map is a strongly non-gaussian field due to the lensed component. Besides the two-point correlation function, the other statistics are also very important to dig the information of the polarization map. In this paper, we employ the Minkowski functionals to study the morphological properties of the lensed $B$-mode maps. We find that the deviations from Gaussianity are very significant for both full and partial-sky surveys. As an a…
The extensive search for deviations from Gaussianity in cosmic microwave background radiation (CMB) data is very important due to the information about the very early moments of the universe encoded there. Recent analyses from Planck CMB data do not exclude the presence of non-Gaussianity of small amplitude, although they are consistent with the Gaussian hypothesis. The use of different techniques is essential to provide information about types and amplitudes of non-Gaussianities in the CMB data. In particular, we find interesting to construct an estimator based upon the combination of two pow…
The general expression for the second order large scale curvature perturbation in the form of a functional over a background solution is derived. The explicit expressions was obtained for two special forms of the inflationary potential. In the considered cases, it is shown that a significant level of non-Gaussianity can be generated during the super-Hubble evolution only if nonadiabatic perturbations are non-negligible at the end of inflation.
Galaxy clusters exhibit a rich morphology during the early and intermediate stages of mass assembly, especially beyond their boundary. A classification scheme based on shapefinders deduced from the Minkowski functionals is examined to fully account for the morphological diversity of galaxy clusters, including relaxed and merging clusters, clusters fed by filamentary structures, and cluster-pair bridges. These configurations are conveniently treated with idealised geometric models and analytical formulae, some of which are novel. Examples from CLASH and LC$^2$ clusters and observed cluster-pair…
Minkowski functionals (MFs) quantify the topological properties of a given field probing its departure from Gaussianity. We investigate their use on lensing convergence maps in order to see whether they can provide further insights on the underlying cosmology with respect to the standard second-order statistics, i.e., cosmic shear tomography. To this end, we first present a method to match theoretical predictions with measured MFs taking care of the shape noise, imperfections in the map reconstruction, and inaccurate description of the nonlinearities in the matter power spectrum and bispectrum…
In order to test for non-Gaussianities with respect to scale-dependencies we use so-called surrogate maps, in which possible phase correlations of the Fourier phases of the original WMAP data and simulations, respectively, are destroyed by applying a shuffling scheme to the maps. A statistical comparison of the original maps with the surrogate maps then allows to test for the existence of higher order correlations in the original maps, also and especially on well-defined Fourier modes. Using Minkowski functionals as an image analysis technique we calculate the deviation between the original da…
We present measurements of the Minkowski functionals extracted from the SDSS-III BOSS catalogs. After defining the Minkowski functionals, we describe how an unbiased reconstruction of these statistics can be obtained from a field with masked regions and survey boundaries, validating our methodology with Gaussian random fields and mock galaxy snapshot data. From the BOSS galaxy data we generate a set of four density fields in three dimensions corresponding to the northern and southern skies of LOWZ and CMASS catalogs, smoothing over large scales such that the field is perturbatively non-Gaussia…
The act of projecting data sampled on the surface of the celestial sphere onto a regular grid on the plane can introduce error and a loss of information. This paper evaluates the effects of different planar projections on non-Gaussian statistics of weak lensing convergence maps. In particular we investigate the effect of projection on peak counts and Minkowski Functionals (MFs) derived from convergence maps and the suitability of a number of projections at matching the peak counts and MFs obtained from a sphere. We find that the peak counts derived from planar projections consistently overesti…
In this paper, we introduce the topological persistence diagram as a statistic for Cosmic Microwave Background (CMB) temperature anisotropy maps. A central concept in `Topological Data Analysis' (TDA), the idea of persistence is to represent a data set by a family of topological spaces. One then examines how long topological features `persist' as the family of spaces is traversed. We compute persistence diagrams for simulated CMB temperature anisotropy maps featuring various levels of primordial non-Gaussianity of local type. Postponing the analysis of observational effects, we show that persi…
Cosmic shear - the weak gravitational lensing effect generated by fluctuations of the gravitational tidal fields of the large-scale structure - is one of the most promising tools for current and future cosmological analyses. The spherical-Bessel decomposition of the cosmic shear field ("3D cosmic shear") is one way to maximise the amount of redshift information in a lensing analysis and therefore provides a powerful tool to investigate in particular the growth of cosmic structure that is crucial for dark energy studies. However, the computation of simulated 3D cosmic shear covariance matrices …
We have calculated the third order moments of scalar curvature perturbations in configuration space for different inflationary models. We developed a robust numerical technique to compute the bispectrum for different models that have some features in the inflationary potential. From the bispectrum we evaluated moments analytically in the slow roll regime while we devised a numerical mechanism to calculated these moments for non slow roll single field inflationary models with standard kinetic term that are minimally coupled to gravity. With help of these third order moments one can directly pre…
In the conference presentation we have reviewed the theory of non-Gaussian geometrical measures for the 3D Cosmic Web of the matter distribution in the Universe and 2D sky data, such as Cosmic Microwave Background (CMB) maps that was developed in a series of our papers. The theory leverages symmetry of isotropic statistics such as Minkowski functionals and extrema counts to develop post- Gaussian expansion of the statistics in orthogonal polynomials of invariant descriptors of the field, its first and second derivatives. The application of the approach to 2D fields defined on a spherical sky w…
We present a novel method for computing the Minkowski Functionals from isodensity surfaces extracted directly from the Delaunay tessellation of a point distribution. This is an important step forward compared to the previous cosmological studies when the isodensity surface was built in the field on a uniform cubic grid and therefore having a uniform spatial resolution. The density field representing a particular interest in cosmology is the density of galaxies which is obtained from the highly nonuniform distribution of the galaxy positions. Therefore, the constraints caused by the spatially u…
We explore the Minkowski functionals of weak lensing convergence map to distinguish between $f(R)$ gravity and the general relativity (GR). The mock weak lensing convergence maps are constructed with a set of high-resolution simulations assuming different gravity models. It is shown that the lensing MFs of $f(R)$ gravity can be considerably different from that of GR because of the environmentally dependent enhancement of structure formation. We also investigate the effect of lensing noise on our results, and find that it is likely to distinguish F5, F6 and GR gravity models with a galaxy surve…
In the context of upcoming large-scale structure surveys such as Euclid, it is of prime importance to quantify the effect of peculiar velocities on geometric probes. Hence the formalism to compute in redshift space the geometrical and topological one-point statistics of mildly non-Gaussian 2D and 3D cosmic fields is developed. Leveraging the partial isotropy of the target statistics, the Gram-Charlier expansion of the joint probability distribution of the field and its derivatives is reformulated in terms of the corresponding anisotropic variables. In particular, the cosmic non-linear evolutio…
The morphological properties of large scale structure of the Universe can be fully described by four Minkowski functionals (MFs), which provide important complementary information to other statistical observables such as the widely used 2-point statistics in configuration and Fourier spaces. In this work, for the first time, we present the differences in the morphology of large scale structure caused by modifications to general relativity (to address the cosmic acceleration problem), by measuring the MFs from N-body simulations of modified gravity and general relativity. We find strong statist…
We compare the efficiency of moments and Minkowski functionals (MFs) in constraining the subset of cosmological parameters (Omega_m,w,sigma_8) using simulated weak lensing convergence maps. We study an analytic perturbative expansion of the MFs in terms of the moments of the convergence field and of its spatial derivatives. We show that this perturbation series breaks down on smoothing scales below 5', while it shows a good degree of convergence on larger scales (15'). Most of the cosmological distinguishing power is lost when the maps are smoothed on these larger scales. We also show that, on…
Weak gravitational lensing is a powerful cosmological probe, with non--Gaussian features potentially containing the majority of the information. We examine constraints on the parameter triplet $(Ω_m,w,σ_8)$ from non-Gaussian features of the weak lensing convergence field, including a set of moments (up to $4^{\rm th}$ order) and Minkowski functionals, using publicly available data from the 154deg$^2$ CFHTLenS survey. We utilize a suite of ray--tracing N-body simulations spanning 91 points in $(Ω_m,w,σ_8)$ parameter space, replicating the galaxy sky positions, redshifts and shape noise in the C…
We investigate the inclusion of clustering maps in a weak lensing Minkowski functional (MF) analysis of DES-like and LSST-like simulations to constrain cosmological parameters. The standard 3x2pt approach to lensing and clustering data uses two-point correlations as its primary statistic; MFs, morphological statistics describing the shape of matter fields, provide additional information for non-Gaussian fields. Previous analyses have studied MFs of lensing convergence maps; in this project we explore their simultaneous application to clustering maps. We employ a simplified linear galaxy bias m…
As deeper galaxy catalogues are soon to come, it becomes even more importantto measure large-scale fluctuations in the catalogues with robust statistics that cover all moments of the galaxy distribution.In this paper we reinforce a direct analysis of galaxy data by employing the Germ-Grain method to calculate thefamily of Minkowski Functionals. We introduce a new code, suitable for the analysis of large data sets without smoothingand without the construction of excursion sets. We provide new tools to measure correlation properties, putting emphasis onexplicitly isolating non-Gaussian correlati…
We probe the higher-order galaxy clustering in the final data release (DR12) of the Sloan Digital Sky Survey Baryon Oscillation Spectroscopic Survey (BOSS) using germ-grain Minkowski Functionals (MFs). Our data selection contains $979,430$ BOSS galaxies from both the northern and southern galactic caps over the redshift range $z=0.2 - 0.6$. We extract the higher-order part of the MFs, detecting the deviation from the purely Gaussian case with $χ^2 \sim \mathcal{O}(10^3)$ on 24 degrees of freedom across the entire data selection. We measure significant redshift evolution in the higher-order fun…
The brightness temperature of the redshifted 21cm line brings rich information on the Inter Galactic Medium (IGM) from the Cosmic Dawn and Epoch of Reionization (EoR). While the power spectrum is a useful tool to statistically investigate the 21cm signal, the 21cm brightness temperature field is highly non-Gaussian, and the power spectrum is inadequate to characterize the non-Gaussianity. The Minkowski Functionals (MFs) are promising tools to extract non-gaussian features of the 21cm signal and give topological information such as morphology of ionized bubbles. In this work, we study the 21cm …
Secondary contributions to the anisotropy of the Cosmic Microwave Background (CMB), such as the integrated Sachs-Wolfe (ISW) effect, the thermal Sunyaev-Zel'dovich effect (tSZ), and the effect of gravitational lensing, have distinctive non-Gaussian signatures, and full descriptions therefore require information beyond that contained in their power spectra. In this paper we use the recently introduced skew-spectra associated with the Minkowski Functionals (MF) to probe the topology of CMB maps to probe the secondary non-Gaussianity as a function of beam-smoothing in order to separate various co…
We probe the higher-order clustering of the galaxies in the final data release (DR12) of the Sloan Digital Sky Survey Baryon Oscillation Spectroscopic Survey (BOSS) using the method of germ-grain Minkowski Functionals (MFs). Our sample consists of 410,615 BOSS galaxies from the northern Galactic cap in the redshift range 0.450--0.595. We show the MFs to be sensitive to contributions up to the six-point correlation function for this data set. We ensure with a custom angular mask that the results are more independent of boundary effects than in previous analyses of this type. We extract the high…
The presence of massive neutrinos affects structure formation, leaving imprints on large-scale structure observables such as the weak lensing field. The common lensing analyses with two-point statistics are insensitive to the large amount of non-Gaussian information in the density field. We investigate non-Gaussian tools, in particular the Minkowski Functionals (MFs)---morphological descriptors including area, perimeter, and genus---in an attempt to recover the higher-order information. We use convergence maps from the Cosmological Massive Neutrino Simulations (\texttt{MassiveNus}) and assume …
Tensor Minkowski Functionals (TMFs) are tensorial generalizations of the usual Minkowski Functionals which are scalar quantities. We introduce them here for use in cosmological analysis, in particular to analyze CMB maps. They encapsulate information about the shapes and the orientation of structures. We focus on one of the TMFs, namely $W_2^{1,1}$, which is the generalization of the genus. The ratio of the eigenvalues of the average of $W_2^{1,1}$ over all structures, $α$, encodes the net orientation; and the average of the ratios of the eigenvalues of $W_2^{1,1}$ for each structure, $β$, enc…
We study the evolution of the hydrogen ionization field during the epoch of reionization (EoR) using semi-numerical simulations. By calculating the Minkowski functionals (MFs) of the 21cm brightness temperature field, which provides a quantitative description of topology of the neutral and ionized regions, we find that the reionization process can be divided into five stages, each with different topological structures, corresponding to isolated ionized regions ("bubbles"); connected ionized region ("ionized fibers") which percolate through the cosmic volume; a sponge-like configuration with in…
Minkowski Functionals (MF) are excellent tools to investigate the statistical properties of the cosmic background radiation (CMB) maps. Between their notorious advantages is the possibility to use them efficiently in patches of the CMB sphere, which allow studies in masked skies, inclusive analyses of small sky regions. Then, possible deviations from Gaussianity are investigated by comparison with MF obtained from a set of Gaussian isotropic simulated CMB maps to which are applied the same cut-sky masks. These analyses are sensitive enough to detect contaminations of small intensity like prima…
The measurement of cosmic shear using weak gravitational lensing is a challenging task that involves a number of complicated procedures. We study in detail the systematic errors in the measurement of weak lensing Minkowski Functionals (MFs). Specifically, we focus on systematics associated with galaxy shape measurements, photometric redshift errors, and shear calibration correction. We first generate mock weak-lensing catalogs that directly incorporate the actual observational characteristics of the Canada-France-Hawaii Lensing Survey (CFHTLenS). We then perform a Fisher analysis using the lar…
Minkowski functionals (MFs) are a set of statistics that characterise the geometry and topology of the cosmic density field and contain complementary information to the standard two-point analyses. We present MEDUSA, an implementation of an accurate method for estimating the MFs of three-dimensional point distributions. These estimates are inferred from triangulated isodensity surfaces that are constructed from the Delaunay tessellation of the input point sample. Contrary to previous methods, MEDUSA can account for periodic boundary conditions, which is crucial for the analysis of N-body simul…
We use the binned bispectrum estimator to determine the bispectra of the dust, free-free, synchrotron, and AME galactic foregrounds using maps produced by the Commander component separation method from Planck 2015 data. We find that all of these peak in the squeezed configuration, allowing for potential confusion with in particular the local primordial shape. Applying an additional functionality implemented in the binned bispectrum estimator code, we then use these galactic bispectra as templates in an $f_\mathrm{NL}$ analysis of other maps. After testing and validating the method and code wit…
