The cosmic microwave background (CMB) bispectrum is a well-known probe of the non-Gaussianity of primordial perturbations. Just as the intervening large-scale structure modifies the CMB angular power spectrum through weak gravitational lensing, the CMB primary bispectrum generated at the last scattering surface is also modified by lensing. We discuss the lensing modification to the CMB bispectrum and show that lensing leads to an overall decrease in the amplitude of the primary bispectrum at multipoles of interest between 100 and 2000 through additional smoothing introduced by lensing. Since weak lensing is not accounted for in current estimators of the primordial non-Gaussianity parameter, the existing measurements of $f_{\rm NL}$ of the local model with WMAP out to $l_{\rm max} \sim 750$ is biased low by about 6%. For a high resolution experiment such as Planck, the lensing modification to the bispectrum must be properly included when attempting to estimate the primordial non-Gaussianity or the bias will be at the level of 30%. For Planck, weak lensing increases the minimum detectable value for the non-Gaussianity parameter of the local type $f_{\rm NL}$ to 7 from the previous estimate of about 5 without lensing. The minimum detectable value of $f_{\rm NL}$ for a cosmic variance limited experiment is also increased from less than 3 to $\sim$ 5.
For those angular multipoles where cosmic variance is an issue, non-Gaussianities in the Cosmic Microwave Background (CMB) anisotropies will be hard to detect. Here, we construct explicitly the best unbiased estimator for the CMB angular bispectrum.
We present a new formalism, together with efficient numerical methods, to directly calculate the CMB bispectrum today from a given primordial bispectrum using the full linear radiation transfer functions. Unlike previous analyses which have assumed simple separable ansatze for the bispectrum, this work applies to a primordial bispectrum of almost arbitrary functional form, for which there may have been both horizon-crossing and superhorizon contributions. We employ adaptive methods on a hierarchical triangular grid and we establish their accuracy by direct comparison with an exact analytic sol…
We consider the CMB bispectrum signal induced by structure formation through the correlation between the Integrated Sachs-Wolfe and the weak lensing effect. We investigate how the bispectrum knowledge can improve our knowledge of the most important cosmological parameters, focusing on the dark energy ones. Preliminary results suggest a consistent improvement on the estimation of dark energy abundance and on dynamical properties of the equation of state.
We present a set of formalisms for comparing, evolving and constraining primordial non-Gaussian models through the CMB bispectrum. We describe improved methods for efficient computation of the full CMB bispectrum for any general (non-separable) primordial bispectrum, incorporating a flat sky approximation and a new cubic interpolation. We review all the primordial non-Gaussian models in the present literature and calculate the CMB bispectrum up to l <2000 for each different model. This allows us to determine the observational independence of these models by calculating the cross-correlation of…
Weak gravitational lensing of background galaxies offers an excellent opportunity to study the intervening distribution of matter. While much attention to date has focused on the two-point function of the cosmic shear, the three-point function, the {\it bispectrum}, also contains very useful cosmological information. Here, we compute three corrections to the bispectrum which are nominally of the same order as the leading term. We show that the corrections are small, so they can be ignored when analyzing present surveys. However, they will eventually have to be included for accurate parameter e…
We use simulated maps of the cosmic microwave background anisotropy to quantify the ability of different statistical tests to discriminate between Gaussian and non-Gaussian models. Despite the central limit theorem on large angular scales, both the genus and extrema correlation are able to discriminate between Gaussian models and a semi-analytic texture model selected as a physically motivated non-Gaussian model. When run on the COBE 4-year CMB maps, both tests prefer the Gaussian model. Although the bispectrum has comparable statistical power when computed on the full sky, once a Galactic cut…
We examine how lensing tomography with the bispectrum and power spectrum can constrain cosmological parameters and the equation of state of dark energy. Our analysis uses the full information at the two- and three-point level from angular scales of a few degrees to 5 arcminutes (50 < l < 3000), which will be probed by lensing surveys. We use all triangle configurations, cross-power spectra and bispectra constructed from up to three redshift bins with photometric redshifts, and relevant covariances in our analysis. We find that the parameter constraints from bispectrum tomography are comparable…
All the analyses of Cosmic Microwave Background (CMB) temperature maps up--to--date show that CMB anisotropies follow a Gaussian distribution. On the other hand, astrophysical foregrounds which hamper the detection of the CMB angular power spectrum, are not Gaussian distributed on the sky. Therefore, they should give a sizeable contribution to the CMB bispectrum. In fact, the first year data of the Wilkinson Microwave Anisotropy Probe (WMAP) mission have allowed the {\it first} detection of the extragalactic source contribution to the CMB bispectrum at 41 GHz and, at the same time, much tighte…
It is now well known that mode-coupling effects associated with certain secondary effects generate higher order correlations in cosmic microwave background (CMB) temperature anisotropies, beyond the two-point function. In order to extract the non-Gaussian signal at the three-point level, we suggest a two-point statistic in the form of an angular power spectrum involving correlations between squared temperature and temperature anisotropies. This power spectrum contains compressed information from the bispectrum and can be easily measured in data with the same techniques that have been considere…
We study contributions to the cosmic microwave background (CMB) bispectrum from non-Gaussianity induced by secondary anisotropies during reionization. Large-scale structure in the reionized epoch both gravitational lenses CMB photons and produces Doppler shifts in their temperature from scattering off electrons in infall. The resulting correlation is potentially observable through the CMB bispectrum. The second-order Ostriker-Vishniac also couples to a variety of linear secondary effects to produce a bispectrum. For the currently favored flat cosmological model with a low matter content and sm…
If the primordial fluctuations are non-Gaussian, then this non-Gaussianity will be apparent in the cosmic microwave background (CMB) sky. With their sensitive all-sky observation, MAP and Planck satellites should be able to detect weak non-Gaussianity in the CMB sky. On large angular scale, there is a simple relationship between the CMB temperature and the primordial curvature perturbation. On smaller scales; however, the radiation transfer function becomes more complex. In this paper, we present the angular bispectrum of the primary CMB anisotropy that uses the full transfer function. We find…
Weak gravitational lensing observations probe the spectrum and evolution of density fluctuations and the cosmological parameters which govern them. The non-linear evolution of large scale structure produces a non-Gaussian signal which is potentially observable in galaxy shear data. We study the three-point statistics of the convergence, specifically the bispectrum, using the dark matter halo approach which describes the density field in terms of correlations between and within dark matter halos. Our approach allows us to study the effect of the mass distribution in observed fields, in particul…
We propose a new method for a numerical computation of the angular bispectrum of the CMB anisotropies arising from active models such as cosmic topological defects, using a modified Boltzmann code based on CMBFAST. The method does not use CMB sky maps and requires moderate computational power. As a first implementation, we apply our method to a recently proposed model of simulated cosmic strings and estimate the observability of the non-Gaussian bispectrum signal. A comparison with the cosmic variance of the bispectrum estimator shows that the bispectrum for the simulated string model we used …
We consider a phenomenological model for a coupling between the dark matter and dark energy fluids and investigate the sensitivity of a weak lensing measurement for constraining the size of this coupling term. Physically, the functional form of the coupling term in our model describes the decay of dark matter into dark energy. We present forecasts for tomographic measurements of the weak shear bispectrum for the DUNE experiment in a Fisher-matrix formalism, where we describe the nonlinearities in structure formation by hyper-extended perturbation theory. Physically, CDM decay tends to increase…
After the precise observations of the Cosmic Microwave Background (CMB) anisotropy power spectrum, attention is now being focused on the higher order statistics of the CMB anisotropies. Since linear evolution preserves the statistical properties of the initial conditions, observed non-Gaussianity of the CMB will mirror primordial non-Gaussianity. Single field slow-roll inflation robustly predicts negligible non-Gaussianity so an indication of non-Gaussianity will suggest alternative scenarios need to be considered. In this paper we calculate the information on primordial non-Gaussianity encode…
We propose a fast and efficient bispectrum statistic for Cosmic Microwave Background (CMB) temperature anisotropies to constrain the amplitude of the primordial non-Gaussian signal measured in terms of the non-linear coupling parameter f_NL. We show how the method can achieve a remarkable computational advantage by focussing on subsets of the multipole configurations, where the non-Gaussian signal is more concentrated. The detection power of the test, increases roughly linearly with the maximum multipole, as shown in the ideal case of an experiment without noise and gaps. The CPU-time scales a…
In this paper, we discuss the potential importance of measuring the CMB anisotropy bispectrum. We develop a formalism for computing the bispectrum and for measuring it from microwave background maps. As an example, we compute the bispectrum resulting from the 2nd order Rees-Sciama effect, and find that is undetectable with current and upcoming missions.
We investigate what the lensing information contained in high resolution, low noise CMB temperature maps can teach us about cluster mass profiles. We create lensing fields and Sunyaev-Zel'dovich effect maps from N-body simulations and apply them to primary CMB anisotropies modeled as a Gaussian random field. We examine the success of several techniques of cluster mass reconstruction using CMB lensing information, and make an estimate of the observational requirements necessary to achieve a satisfactory result.
Gravitational lensing can be used to directly constrain the projected density profile of galaxy clusters. We discuss possible future constraints from lensing of the CMB temperature and polarization, and compare to results from galaxy weak lensing. We model the moving lens and kinetic SZ signals that confuse the temperature CMB lensing when cluster velocities and angular momenta are unknown, and show how they degrade parameter constraints. The CMB polarization cluster lensing signal is ~1 micro-Kelvin for massive clusters and challenging to detect; however it should be significantly cleaner tha…
We measure the angular bispectrum of the cosmic microwave background (CMB) radiation anisotropy from the COBE Differential Microwave Radiometer (DMR) four-year sky maps. The angular bispectrum is the harmonic transform of the three-point correlation function, analogous to the angular power spectrum, the harmonic transform of the two-point correlation function. First, we study statistical properties of the bispectrum and the normalized bispectrum. We find the latter more useful for statistical analysis; the distribution of the normalized bispectrum is very much Gaussian, while the bare bispectr…
Recent tentative findings of non-Gaussian structure in the COBE-DMR dataset have triggered renewed attention to candidate models from which such intrinsic signature could arise. In the framework of slow roll inflation with built-in non linearities in the inflaton field evolution we present expressions for both the cosmic microwave background (CMB) skewness and the full angular bispectrum ${\cal C}_{\ell_1 \ell_2 \ell_3}$ in terms of the slow roll parameters. We use an estimator for the angular bispectrum recently proposed in the literature and calculate its variance for an arbitrary $\ell_i$ m…
Inflationary cosmologies predict Gaussian primordial fluctuations, but subsequent gravitational lensing of the CMB disturbs its Gaussianity. Knowledge of the specific signature of lensing is necessary to distinguish a lensed Gaussian sky from an intrinsically non-Gaussian one. In this paper we investigate the pattern of non-Gaussian features in the CMB resulting from gravitational lensing, both analytically and numerically. We describe the lensed CMB temperature distribution using the formalism of generating functionals and obtain the complete picture of emerging non-Gaussian effects. To test …
The detection of a "Cold Spot" in the CMB sky could be explained by the presence of an anomalously large spherical underdense region (with radius of a few hundreds Mpc/h) located between us and the Last Scattering Surface. Modeling such an underdensity with an LTB metric, we investigate whether it could produce significant signals on the CMB power spectrum and bispectrum, via the Rees-Sciama effect. We find that this leads to a bump on the power spectrum, that corresponds to an O(5%-25%) correction at multipoles 5 < l < 50; in the cosmological fits, this would modify the χ^2 by an amount of or…
We derive an expression for the non-Gaussian cosmic-microwave-background (CMB) statistic $I_l^3$ defined recently by Ferreira, Magueijo, and Górski in terms of the slow-roll-inflation parameters $ε$ and $η$. This result shows that a nonzero value of $I_l^3$ in COBE would rule out single-field slow-roll inflation. A sharp change in the slope of the inflaton potential could increase the predicted value of $I_l^3$, but not significantly. This further suggests that it will be difficult to account for such a detection in multiple-field models in which density perturbations are produced by quantum f…
Gravitational lensing of the cosmic microwave background by large-scale structure in the late universe is both a source of cosmological information and a potential contaminant of primordial gravity waves. Because lensing imprints growth of structure in the late universe on the CMB, measurements of CMB lensing will constrain parameters to which the CMB would not otherwise be sensitive, such as neutrino mass. If the instrumental noise is sufficiently small (<~ 5 uK-arcmin), the gravitational lensing contribution to the large-scale B-mode will be the limiting source of contamination when constrai…
Weak gravitational lensing by intervening large-scale structure induces a distinct signature in the cosmic microwave background (CMB) that can be used to reconstruct the weak-lensing displacement map. Estimators for individual Fourier modes of this map can be combined to produce an estimator for the lensing-potenial power spectrum. The naive estimator for this quantity will be biased upwards by the uncertainty associated with reconstructing individual modes; we present an iterative scheme for removing this bias. The variance and covariance of the lensing-potenial power spectrum estimator are c…
We present a fast, arbitrarily accurate method to simulate the effect of gravitational lensing of the Cosmic Microwave Background anisotropies and polarization fields by large scale structures. We demonstrate the efficiency and accuracy of the method and exhibit their dependence on the algorithm parameters.
We discuss the real-space moments of temperature anisotropies in the cosmic microwave background (CMB) due to weak gravitational lensing by intervening large-scale structure. We show that if the probability distribution function of primordial temperature anisotropies is Gaussian, then it remains unchanged after gravitational lensing. With finite resolution, however, non-zero higher-order cumulants are generated both by lensing autocorrelations and by cross-correlations between the lensing potential and secondary anisotropies in the CMB such as the Sunayev-Zel'dovich (SZ) effect. Skewness is pr…
Since cosmic-microwave-background (CMB) and large-scale-structure (LSS) data will shortly improve dramatically with the Microwave Anisotropy Probe (MAP) and Planck Surveyor, and the Anglo-Australian 2-Degree Field (2dF) and Sloan Digital Sky Survey (SDSS), respectively, it is timely to ask which of the CMB or LSS will provide a better probe of primordial non-gaussianity. In this paper we consider this question, using the bispectrum as a discriminating statistic. We consider several non-gaussian models and find that in each case the CMB will provide a better probe of primordial non-gaussianity.…
Cosmologists have suggested a number of intriguing hypotheses for the origin of the "WMAP cold spot", the coldest extended region seen in the CMB sky, including a very large void and a collapsing texture. Either hypothesis predicts a distinctive CMB lensing signal. We show that the upcoming generation of high resolution CMB experiments such as ACT and SPT should be able to detect the signatures of either textures or large voids. If either signal is detected, it would have profound implications for cosmology.
A long-standing problem in astrophysics is to measure the mass associated with galaxies. Gravitational lensing provides one of the cleanest ways to make this measurement. To date, the most powerful lensing probes of galactic mass have been multiply imaged QSO's (strong lensing of a background point source) and galaxy-galaxy lensing (weak deformation of many background galaxies). Here we point out that the mass associated with galaxies also lenses the Cosmic Microwave Background (CMB) and this effect is potentially detectable in small scale experiments. The signal is small (roughly a few tenths…
The intervening large--scale structure distorts cosmic microwave background (CMB) anisotropies via gravitational lensing. The same large--scale structure, traced by dusty star--forming galaxies, also induces anisotropies in the far--infrared background (FIRB). We investigate the resulting inter--dependence of the FIRB and CMB with a halo model for the FIRB. In particular, we calculate the cross--correlation between the lensing potential and the FIRB. The lensing potential can be quadratically estimated from CMB temperature and/or polarization maps. We show that the cross--correlation can be me…
Power spectra and cross-correlation measurements from the weak gravitational lensing of the cosmic microwave background (CMB) and the cosmic shearing of faint galaxies images will help shed light on quantities hidden from the CMB temperature anisotropies: the dark energy, the end of the dark ages, and the inflationary gravitational wave amplitude. Even with modest surveys, both types of lensing power spectra break CMB degeneracies and they can ultimately improve constraints on the dark energy equation of state w by over an order of magnitude. In its cross correlation with the integrated Sachs-…
Weak gravitational lensing has several important effects on the cosmic microwave background (CMB): it changes the CMB power spectra, induces non-Gaussianities, and generates a B-mode polarization signal that is an important source of confusion for the signal from primordial gravitational waves. The lensing signal can also be used to help constrain cosmological parameters and lensing mass distributions. We review the origin and calculation of these effects. Topics include: lensing in General Relativity, the lensing potential, lensed temperature and polarization power spectra, implications for c…
The metric around straight arbitrarily-oriented cosmic strings forming a stationary junction is obtained at the linearized level. It is shown that the geometry is flat. The sum rules for lensing by this configuration and the anisotropies of the CMB are obtained.
