arXiv subjects

Dipak Munshi

Publications and source records attributed to Dipak Munshi.

At least 19 recordsLinked to original sources

arXiv2022

Weak Lensing Trispectrum and Kurt-Spectra

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 hierarchical ansatz-can reproduce the numerical trends for the kurt-spectra in the nonlinear regime. In addition, we provide estimators for beyond fourth-order spectra where no definitive analytical results are available, and present corresponding results from numerical simulations.

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arXiv2021

The integrated angular bispectrum of weak lensing

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 how accurate are theoretical formulae for both the integrated bispectrum and its covariance, finding that there a small inaccuracies in the theoretical signal, and more serious deviations in the covariance matrix, which may need to be estimated using simulations.

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arXiv2017

Symmetries, Invariants and Generating Functions: Higher-order Statistics of Biased Tracers

Gravitationally collapsed objects are known to be biased tracers of an underlying density contrast. Using symmetry arguments, generalised biasing schemes have recently been developed to relate the halo density contrast $δ_h$ with the underlying density contrast $δ$, divergence of velocity $θ$ and their higher-order derivatives. This is done by constructing invariants such as $s, t, ψ,η$. We show how the generating function formalism in Eulerian standard perturbation theory (SPT) can be used to show that many of the additional terms based on extended Galilean and Lifshitz symmetry actually do not make any contribution to the higher-order statistics of biased tracers. Other terms can also be drastically simplified allowing us to write the vertices associated with $δ_h$ in terms of the vertices of $δ$ and $θ$, the higher-order derivatives and the bias coefficients. We also compute the cumulant correlators (CCs) for two different tracer populations. These perturbative results are valid for tree-level contributions but at an arbitrary order. We also take into account the stochastic nature bias in our analysis. Extending previous results of a local polynomial model of bias, we express the one-point cumulants ${\cal S}_N$ and their two-point counterparts, the CCs i.e. ${\cal C}_{pq}$, of biased tracers in terms of that of their underlying density contrast counterparts. As a by-product of our calculation we also discuss the results using approximations based on Lagrangian perturbation theory (LPT).

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arXiv2017

Stable Clustering Ansatz, Consistency Relations and Gravity Dual of Large-Scale Structure

Gravitational clustering in the nonlinear regime remains poorly understood. Gravity dual of gravitational clustering has recently been proposed as a means to study the nonlinear regime. The stable clustering ansatz remains a key ingredient to our understanding of gravitational clustering in the highly nonlinear regime. We study certain aspects of violation of the stable clustering ansatz in the gravity dual of Large Scale Structure (LSS). We extend the recent studies of gravitational clustering using AdS gravity dual to take into account possible departure from the stable clustering ansatz and to arbitrary dimensions. Next, we extend the recently introduced consistency relations to arbitrary dimensions. We use the consistency relations to test the commonly used models of gravitational clustering including the halo models and hierarchical ansätze. In particular we establish a tower of consistency relations for the hierarchical amplitudes: $Q, R_a, R_b, S_a,S_b,S_c$ etc. as a functions of the scaled peculiar velocity $h$. We also study the variants of popular halo models in this context. In contrast to recent claims, none of these models, in their simplest incarnation, seem to satisfy the consistency relations in the soft limit.

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arXiv2017

Consistency Relations in Effective Field Theory

The consistency relations in large scale structure relate the lower-order correlation functions with their higher-order counterparts. They are direct outcome of the underlying symmetries of a dynamical system and can be tested using data from future surveys such as Euclid. Using techniques from standard perturbation theory (SPT), previous studies of consistency relation have concentrated on continuity-momentum (Euler)-Poisson system of an ideal fluid. We investigate the consistency relations in effective field theory (EFT) which adjusts the SPT predictions to account for the departure from the ideal fluid description on small scales. We provide detailed results for the 3D density contrast $δ$ as well as the {\em scaled} divergence of velocity $\barθ$. Assuming a $Λ$CDM background cosmology, we find the correction to SPT results becomes important at $k \gtrsim 0.05 \rm h/Mpc$ and that the suppression from EFT to SPT results that scales as square of the wave number $k$, can reach $40\%$ of the total at $k \approx 0.25\rm h/Mpc$ at $z=0$. We have also investigated whether effective field theory corrections to models of primordial non-Gaussianity can alter the squeezed limit behaviour, finding the results to be rather insensitive to these counterterms. In addition, we present the EFT corrections to the squeezed limit of the bispectrum in redshift space which may be of interest for tests of theories of modified gravity.

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arXiv2016

The Integrated Bispectrum in Modified Gravity Theories

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 obtained using the Zel'dovich Approximation (ZA). Results are also presented for projected surveys (2D). We use the Press-Schechter (PS) and Sheth-Torman (ST) mass functions to compute the IB for collapsed objects that can readily be extended to peak-theory based approaches. The {\em cumulant correlators} (CCs) generalise the ordinary {\em cumulants} and are known to probe collapsed configurations of higher order correlation functions. We generalise the concept of CCs to halos of different masses. We also introduce a generating function based approach to analyse more general non-local biasing models. The Fourier representations of the CCs, the skew-spectrum, or the kurt-spctra are discussed in this context. The results are relevant for the study of the Minkowski Functionals (MF) of collapsed tracers in redshift-space.} \keywords {Cosmology, Large Scale Structure, Modified Theories of Gravity

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arXiv2016

The Integrated Bispectrum and Beyond

The position-dependent power spectrum has been recently proposed as a descriptor of gravitationally induced non-Gaussianity in galaxy clustering, as it is sensitive to the "soft limit" of the bispectrum (i.e. when one of the wave number tends to zero). We generalise this concept to higher order and clarify their relationship to other known statistics such as the skew-spectrum, the kurt-spectra and their real-space counterparts the cumulants correlators. Using the {\em Hierarchical Ansatz} (HA) as a toy model for the higher order correlation hierarchy, we show how in the soft limit, polyspectra at a given order can be identified with lower order polyspectra with the same geometrical dependence but with {\em renormalised} amplitudes expressed in terms of amplitudes of the original polyspectra. We extend the concept of position-dependent bispectrum to bispectrum of the divergence of the velocity field $Θ$ and mixed multispectra involving $δ$ and $Θ$ in the 3D perturbative regime. To quantify the effects of transients in numerical simulations, we also present results for lowest order in Lagrangian perturbation theory (LPT) or the Zel'dovich approximation (ZA). Finally, we discuss how to extend the position-dependent spectrum concept to encompass cross-spectra. And finally study the application of this concept to two dimensions (2D), for projected galaxy maps, convergence $κ$ maps from weak-lensing surveys or maps of CMB secondaries e.g. the frequency cleaned $y$ - parameter maps of thermal Sunyaev-Zel'dovich (tSZ) effect from CMB surveys.

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arXiv2016

3D Weak Lensing: Modified Theories of Gravity

Weak lensing (WL) promises to be a particularly sensitive probe of both the growth of large scale structure (LSS) as well as the fundamental relation between matter density perturbations and metric perturbations, thus providing a powerful tool with which we may constrain modified theories of gravity (MG) on cosmological scales. Future deep, wide-field WL surveys will provide an unprecedented opportunity to constrain deviations from General Relativity (GR). Employing a three-dimensional (3D) analysis based on the spherical Fourier-Bessel (sFB) expansion, we investigate the extent to which MG theories will be constrained by a typical 3D WL survey configuration including noise from the intrinsic ellipticity distribution $σ_ε$ of source galaxies. Here we focus on two classes of screened theories of gravity: i) $f(R)$ chameleon models and ii) environmentally dependent dilaton models. We use one-loop perturbation theory combined with halo models in order to accurately model the evolution of matter power-spectrum with redshift in these theories. Using a Fisher information matrix based approach, we show that for an all-sky spectroscopic survey, the parameter $f_{R_0}$ can be constrained in the range $f_{R_0}< 5\times 10^{-6}(9\times 10^{-6})$ for $n=1(2)$ with a 3$σ$ confidence level. This can be achieved by using relatively low order angular harmonics $\ell<100$. Including higher order harmonics $\ell>100$ can further tighten the constraints, making them comparable to current solar-system constraints. We also employ a Principal Component Analysis (PCA) in order to study the parameter degeneracies in the MG parameters. Our results can trivially be extended to other MG theories, such as the K-mouflage models. The confusion from intrinsic ellipticity correlation and modification of the matter power-spectrum at small scale due to feedback mechanisms is briefly discussed.

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arXiv2015

Galaxy Clustering in 3D and Modified Gravity Theories

We study Modified Gravity (MG) theories by modelling the redshifted matter power spectrum in a spherical Fourier-Bessel (sFB) basis. We use a fully non-linear description of the real-space matter power-spectrum and include the lowest-order redshift-space correction (Kaiser effect), taking into account some additional non-linear contributions. Ignoring relativistic corrections, which are not expected to play an important role for a shallow survey, we analyse two different modified gravity scenarios, namely the generalised Dilaton scalar-tensor theories and the $f({R})$ models in the large curvature regime. We compute the 3D power spectrum ${\cal C}^s_{\ell}(k_1,k_2)$ for various such MG theories with and without redshift space distortions, assuming precise knowledge of background cosmological parameters. Using an all-sky spectroscopic survey with Gaussian selection function $φ(r)\propto \exp(-{r^2 / r^2_0})$, $r_0 = 150 \, h^{-1} \, {\textrm{Mpc}}$, and number density of galaxies $\bar {\textrm{N}} =10^{-4}\;{\textrm{Mpc}}^{-3}$, we use a $χ^2$ analysis, and find that the lower-order $(\ell \leq 25)$ multipoles of ${\cal C}^s_\ell(k,k')$ (with radial modes restricted to $k < 0.2 \, h \,{\textrm{Mpc}}^{-1}$) can constraint the parameter $f_{R_0}$ at a level of $2\times 10^{-5} (3\times 10^{-5})$ with $3 σ$ confidence for $n=1(2)$. Combining constraints from higher $\ell > 25$ modes can further reduce the error bars and thus in principle make cosmological gravity constraints competitive with solar system tests. However this will require an accurate modelling of non-linear redshift space distortions. Using a tomographic $β(a)$-$m(a)$ parameterization we also derive constraints on specific parameters describing the Dilaton models of modified gravity.

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arXiv2015

Testing Modified Gravity with Cosmic Shear

We use the cosmic shear data from the Canada-France-Hawaii Telescope Lensing Survey to place constraints on $f(R)$ and {\it Generalized Dilaton} models of modified gravity. This is highly complimentary to other probes since the constraints mainly come from the non-linear scales: maximal deviations with respects to the General-Relativity + $Λ$CDM scenario occurs at $k\sim1 h \mbox{Mpc}^{-1}$. At these scales, it becomes necessary to account for known degeneracies with baryon feedback and massive neutrinos, hence we place constraints jointly on these three physical effects. To achieve this, we formulate these modified gravity theories within a common tomographic parameterization, we compute their impact on the clustering properties relative to a GR universe, and propagate the observed modifications into the weak lensing $ξ_{\pm}$ quantity. Confronted against the cosmic shear data, we reject the $f(R)$ $\{ |f_{R_0}|=10^{-4}, n=1\}$ model with more than 99.9% confidence interval (CI) when assuming a $Λ$CDM dark matter only model. In the presence of baryonic feedback processes and massive neutrinos with total mass up to 0.2eV, the model is disfavoured with at least 94% CI in all different combinations studied. Constraints on the $\{ |f_{R_0}|=10^{-4}, n=2\}$ model are weaker, but nevertheless disfavoured with at least 89% CI. We identify several specific combinations of neutrino mass, baryon feedback and $f(R)$ or Dilaton gravity models that are excluded by the current cosmic shear data. Notably, universes with three massless neutrinos and no baryon feedback are strongly disfavoured in all modified gravity scenarios studied. These results indicate that competitive constraints may be achieved with future cosmic shear data.

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arXiv2015

Principal Components of CMB non-Gaussianity

The skew-spectrum statistic introduced by Munshi & Heavens (2010) has recently been used in studies of non-Gaussianity from diverse cosmological data sets including the detection of primary and secondary non-Gaussianity of Cosmic Microwave Background (CMB) radiation. Extending previous work, focussed on independent estimation, here we deal with the question of joint estimation of multiple skew-spectra from the same or correlated data sets. We consider the optimum skew-spectra for various models of primordial non-Gaussianity as well as secondary bispectra that originate from the cross-correlation of secondaries and lensing of CMB: coupling of lensing with the Integrated Sachs-Wolfe (ISW) effect, coupling of lensing with thermal Sunyaev-Zeldovich (tSZ), as well as from unresolved point-sources (PS). For joint estimation of various types of non-Gaussianity, we use the PCA to construct the linear combinations of amplitudes of various models of non-Gaussianity, e.g. $f^{\rm loc}_{\rm NL},f^{\rm eq}_{\rm NL},f^{\rm ortho}_{\rm NL}$ that can be estimated from CMB maps. Bias induced in the estimation of primordial non-Gaussianity due to secondary non-Gaussianity is evaluated. The PCA approach allows one to infer approximate (but generally accurate) constraints using CMB data sets on any reasonably smooth model by use of a lookup table and performing a simple computation. This principle is validated by computing constraints on the DBI bispectrum using a PCA analysis of the standard templates.

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arXiv2014

Reconstructing the Thermal Sunyaev-Zel'dovich Effect in 3D

The thermal Sunyaev-Zel'dovich (tSZ) effect measures the line-of-sight projection of the thermal pressure of free electrons and lacks any redshift information. By cross correlating the tSZ effect with an external cosmological tracer we can recover a good fraction of this lost information. Weak lensing (WL) is thought to provide an unbiased probe of the dark Universe, with many WL surveys having sky coverage that overlaps with tSZ surveys. Generalising the tomographic approach, we advocate the use of the spherical Fourier-Bessel (sFB) expansion to perform an analysis of the cross-correlation between the projected (2D) tSZ Compton $y$-parameter maps and 3D weak lensing convergence maps. We use redshift dependent linear biasing and the halo model as a tool to investigate the tSZ-WL cross-correlations in 3D. We use the Press-Schechter (PS) and the Sheth-Tormen (ST) mass-functions in our calculations, finding that the results are quite sensitive to detailed modelling. We provide detailed analysis of surveys with photometric and spectroscopic redshifts. The signal-to-noise (S/N) of the cross-spectra $\mathcal{C}_{\ell} (k)$ for individual 3D modes, defined by the radial and tangential wave numbers $(k;\ell)$, remains comparable to, but below, unity though optimal binning is expected to improve this. The results presented can be generalised to analyse other CMB secondaries, such as the kinetic Sunyaev-Zel'dovich (kSZ) effect.

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arXiv2014

Cross-correlating Sunyaev-Zel'dovich and Weak Lensing Maps

We present novel statistical tools to cross-correlate frequency cleaned thermal Sunyaev-Zel'dovich (tSZ) maps and tomographic weak lensing (wl) convergence maps. Moving beyond the lowest order cross-correlation, we introduce a hierarchy of mixed higher-order statistics, the cumulants and cumulant correlators, to analyze non-Gaussianity in real space, as well as corresponding polyspectra in the harmonic domain. Using these moments, we derive analytical expressions for the joint two-point probability distribution function (2PDF) for smoothed tSZ (y_s) and convergence (κ_s) maps. The presence of tomographic information allows us to study the evolution of higher order {\em mixed} tSZ-weak lensing statistics with redshift. We express the joint PDFs p_{κy}(κ_s,y_s) in terms of individual one-point PDFs (p_κ(κ_s), p_y(y_s)) and the relevant bias functions (b_κ(κ_s), b_y(y_s)). Analytical results for two different regimes are presented that correspond to the small and large angular smoothing scales. Results are also obtained for corresponding {\em hot spots} in the tSZ and convergence maps. In addition to results based on hierarchical techniques and perturbative methods, we present results of calculations based on the lognormal approximation. The analytical expressions derived here are generic and applicable to cross-correlation studies of arbitrary tracers of large scale structure including e.g. that of tSZ and soft X-ray background.

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arXiv2013

Effects of Linear Redshift Space Distortions and Perturbation Theory on BAOs: A 3D Spherical Analysis

The Baryon Acoustic Oscillations (BAO) are features in the matter power spectrum on scales of order 100-150 h^{-1} Mpc that promise to be a powerful tool to constrain and test cosmological models. The BAO have attracted such attention that future upcoming surveys have been designed with the BAO at the forefront of the primary science goals. Recent studies have advocated the use of a spherical-Fourier Bessel (sFB) expansion for future wide field surveys that cover both wide and deep regions of the sky necessitating the simultaneous treatment of the spherical sky geometry as well as the extended radial coverage. Ignoring the possible effects of growth, which is not expected to be significant at low redshifts, we present an extended analysis of the BAOs using the sFB formalism by taking into account the role of non-linearities and linear redshift distortions in the oscillations observed in the galaxy power spectrum. The sFB power spectrum has both radial and tangential dependence and it has been shown that in the limit that we approach a deep survey the sFB power spectrum is purely radial and collapses to the Cartesian Fourier power spectrum. This radialisation of information is shown to hold even in the presence of redshift space distortions (RSD) and 1-loop corrections to the galaxy power spectrum albeit with modified tangential and radial dependence. As per previous studies we find that the introduction of non-linearities leads to a damping of the oscillations in the matter power spectrum.

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arXiv2013

New Approaches to Probing Minkowski Functionals

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 a perturbative series to construct the Minkowski Functionals (MFs), we provide a pseudo-Cl based approach in both harmonic and needlet representations to estimate these spectra in the presence of a mask and inhomogeneous noise. Assuming homogeneous noise we present approx- imate expressions for error covariance for the purpose of joint estimation of these spectra. We present specific results for four different models of primordial non-Gaussianity local, equilateral, orthogonal and enfolded models, as well as non-Gaussianity caused by unsubtracted point sources. Closed form results of next-order corrections to MFs too are obtained in terms of a quadruplet of kurt-spectra. We also use the method of modal decomposition of the bispectrum and trispectrum to reconstruct the MFs as an alternative method of reconstruction of morphological properties of CMB maps. Finally, we introduce the odd-parity skew-spectra to probe the odd-parity bispectrum and its impact on the morphology of the CMB sky. Although developed for the CMB, the generic results obtained here can be useful in other areas of cosmology.

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arXiv2012

Statistical Properties of Thermal Sunyaev-Zel'dovich Maps

At high angular frequencies, beyond the damping tail of the primary power spectrum, the dominant contribution to the power spectrum of cosmic microwave background (CMB) temperature fluctuations is the thermal Sunyaev-Zel'dovich (tSZ) effect. We investigate various important statistical properties of the Sunyaev-Zel'dovich maps, using well-motivated models for dark matter clustering to construct statistical descriptions of the tSZ effect to all orders enabling us to determine the entire probability distribution function (PDF). Any generic deterministic biasing scheme can be incorporated in our analysis and the effects of projection, biasing and the underlying density distribution can be analysed separately and transparently in this approach. We introduce the cumulant correlators as tools to analyse tSZ catalogs and relate them to corresponding statistical descriptors of the underlying density distribution. The statistics of hot spots in frequency-cleaned tSZ maps are also developed in a self-consistent way to an arbitrary order, to obtain results complementary to those found using the halo model. We also consider different beam sizes, to check the extent to which the PDF can be extracted from various observational configurations. The formalism is presented with two specific models for underlying matter clustering: (1) the hierarchical ansatz; and (2) the lognormal distribution. We find both models to be in very good agreement with the simulation results, though the lognormal model has an edge over the hierarchical model.

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arXiv2012

Probing CMB Secondary Anisotropies through Minkowski Functionals

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 contributions. We devise estimators for these spectra in the presence of a realistic observational masks and present expressions for their covariance as a function of instrumental noise. Specific results are derived for the mixed ISW-lensing and tSZ-lensing bispectra as well as contamination due to point sources for noise levels that correspond to the Planck (143 GHz channel) and EPIC (150 GHz channel) experiments. The cumulative signal to noise ration $S/N$ for one-point generalized skewness-parameters can reach an order of ${\cal O}(10)$ for Planck and two orders of magnitude higher for EPIC, i.e. ${\cal O}(10^3)$. We also find that these three spectra skew-spectra are correlated, having correlation coefficients $r \sim 0.5-1.0$; higher $l$ modes are more strongly correlated. Though the values of $S/N$ increase with decreasing noise, the triplets of skew-spectra that determine the MFs bcome more correlated; the $S/N$ ratios of lensing-induced skew-spectra are smaller compared to that of a frequency-cleaned tSZ map.

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arXiv2012

Non-Gaussianity in Large Scale Structure and Minkowski Functionals

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.

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