non-Gaussian Cosmic Microwave Background Research Articles

Observations of the Corona Borealis supercluster with the superextended Very Small Array: further constraints on the nature of the non-Gaussian cosmic microwave background cold spot

We present interferometric imaging at 33 GHz, with the new superextended configuration of the Very Small Array (VSA), of a very deep decrement in the cosmic microwave background (CMB) temperature. This decrement is located in the direction of the Corona Borealis supercluster, at a position with no known galaxy clusters, and was discovered by a previous VSA survey (Genova-Santos et al.). A total area of 3 sq.deg. has now been imaged, with an angular resolution of 7 arcmin and a flux sensitivity of 5 mJy/beam. These observations confirm the presence of this strong and resolved negative spot at -41+/-5 mJy/beam (-258+/-29 muK), with a signal to noise level of 8. This structure is also present in the WMAP 5-year data. The temperature of the W-band (94 GHz) data at the position of the decrement agrees within 1.2-sigma with that observed by the VSA at 33 GHz, and within 0.2-sigma with the Sunyaev-Zel'dovich (SZ) spectrum. Our analyses show that it is a non-Gaussian feature in the CMB at a level of 4.8-sigma. The probability of finding such a deviation or larger in CMB Gaussian simulations is only 0.19 per cent. Therefore, an explanation other than primordial CMB is required. We have considered the possibility of an SZ effect generated in a diffuse, extended warm/hot gas distribution. This hypothesis is especially relevant, as the presence of such structures, if confirmed, could provide the location for a significant fraction of the missing baryons in the Local Universe.

Temperature and polarization CMB maps from primordial non-Gaussianities of the local type

The forthcoming Planck experiment will provide high sensitivity polarization measurements that will allow us to further tighten the ${f}_{\mathrm{NL}}$ bounds from the temperature data. Monte Carlo simulations of non-Gaussian cosmic microwave background maps have been used as a fundamental tool to characterize non-Gaussian signatures in the data, as they allow us to calibrate any statistical estimators and understand the effect of systematics, foregrounds and other contaminants. We describe an algorithm to generate high-angular resolution simulations of non-Gaussian cosmic microwave background maps in temperature and polarization. We consider non-Gaussianities of the local type, for which the level of non-Gaussianity is defined by the dimensionless parameter, ${f}_{\mathrm{NL}}$. We then apply the temperature and polarization fast cubic statistics recently developed by Yadav et al. to a set of non-Gaussian temperature and polarization simulations. We compare our results to theoretical expectations based on a Fisher matrix analysis, test the unbiasedness of the estimator, and study the dependence of the error bars on ${f}_{\mathrm{NL}}$. All our results are in very good agreement with theoretical predictions, thus confirming the reliability of both the simulation algorithm and the fast cubic temperature and polarization estimator.

Testing models of inflation with cosmic microwave background non-Gaussianity

Two different predictions for the primordial curvature fluctuation bispectrum arecompared through their effects on the cosmic microwave background temperaturefluctuations. The first has a local form described with a single parameterfNL. The second is based on a prediction from the warm inflationaryscenario, with a different dependence on wavenumber and a parameterfWI. New expressions are obtained for the angular bispectra of thetemperature fluctuations and for the estimators used to determinefNL and fWI. The standard deviation of the estimators in an ideal experiment is roughly5 timeslarger for fWI than for fNL. Using three-year WMAP (Wilkinson Microwave Anisotropy Probe) data gives limits−375<fWI<36.8, but there is a possibility of detecting a signal forfWI from the Planck satellite.

Scalar quantities as detectors of non-Gaussianity in cosmic microwave background maps

We study the power of several scalar quantities constructed on the sphere (presented in Monteserin et al.) to detect non-Gaussianity in the temperature distribution of the cosmic microwave background (CMB). The test has been performed using non-Gaussian CMB simulations with injected skewness or kurtosis generated through the Edgeworth expansion. We have also taken into account in the analysis the effect of anisotropic noise and the presence of a Galactic mask. We find that the best scalars to detect an excess of skewness in the simulations are the derivative of the gradient, the fractional isotropy, the Laplacian and the shape index. For the kurtosis case, the fractional anisotropy, the Laplacian and the determinant are the quantities that perform better.

The integrated bispectrum as a test of cosmic microwave background non-Gaussianity: detection power and limits on fNL with WMAP data

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 focusing 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 as l$^3$$_max$ instead of l$^5$$_max$ for the full bispectrum, which for Planck resolution l$_max$ \~{} 3000 means an improvement in speed of a factor of 10$^7$ compared with the full bispectrum analysis with minor loss in precision. This approach is complementary to the fast method introduced by Komatsu, Spergel \amp Wandelt using a reconstruction of the primordial fluctuation field. We find that the introduction of a galactic cut partially destroys the optimality of the configuration, which will then need to be dealt with in the future. We find for an ideal experiment with l$_max$ = 2000 that upper limits of f$_NL$ \lt 8 can be obtained at 1$\sigma$. For the case of the WMAP experiment, we would be able to put limits of |f$_NL$| \lt 40 if no galactic cut were present. Using the real data with a galactic cut, we obtain an estimate of -80 \lt f$_NL$ \lt 80 and -160 \lt f$_NL$ \lt 160 at 1 and 2$\sigma$, respectively. }

What can be learned from the lensed cosmic microwave background B-mode polarization power spectrum?

The effect of weak gravitational lensing on the cosmic microwave background (CMB) temperature anisotropies and polarization will provide access to cosmological information that cannot be obtained from the primary anisotropies alone. We compare the information content of the lensed B-mode polarization power spectrum, properly accounting for the non-Gaussian correlations between the power on different scales, with that of the unlensed CMB fields and the lensing potential. The latter represent the products of an (idealised) optimal analysis that exploits the lens-induced non-Gaussianity to reconstruct the fields. Compressing the non-Gaussian lensed CMB into power spectra is wasteful and leaves a tight degeneracy between the equation of state of dark energy and neutrino mass that is much stronger than in the more optimal analysis. Despite this, a power spectrum analysis will be a useful first step in analysing future B-mode polarization data. For this reason, we also consider how to extract accurate parameter constraints from the lensed B-mode power spectrum. We show with simulations that for cosmic-variance-limited measurements of the lensed B-mode power, including the non-Gaussian correlations in existing likelihood approximations gives biased parameter results. We develop a more refined likelihood approximation that performs significantly better. This new approximation should also be of more general interest in the wider context of parameter estimation from Gaussian CMB data.

Effect of component separation on the temperature distribution of the cosmic microwave background

We present a study of the effect of component separation on the recovered cosmic microwave background (CMB) temperature distribution, considering Gaussian and non-Gaussian input CMB maps. In particular, the non-Gaussian maps have been generated as a mixture of a Gaussian CMB map and a cosmic strings map in different proportions. First, we extract the CMB component from simulated multifrequency Planck data (in small patches of the sky) using the maximum-entropy method (MEM), Wiener filter (WF) and a method based on the subtraction of foreground templates plus a linear combination of frequency channels (LCFC). We then apply a wavelet-based method to study the Gaussianity of the recovered CMB and compare it with the same analysis for the input map. When the original CMB map is Gaussian (and assuming that point sources have been removed), we find that neither MEM nor WF introduce non-Gaussianity in the CMB reconstruction. Regarding the LCFC, the Gaussian character is also preserved provided that the appropriate combination of frequency channels is used. On the contrary, if the input CMB map is non-Gaussian, all the studied methods produce a reconstructed CMB with lower detections of non-Gaussianity than the original map. This effect is mainly due to the presence of instrumental noise in the data, which clearly affects the quality of the reconstructions. In this case, MEM tends to produce slightly higher non-Gaussian detections in the reconstructed map than WF whereas the detections are lower for the LCFC. We have also studied the effect of point sources in the MEM reconstruction. If no attempt to remove point sources is performed, they clearly contaminate the CMB reconstruction, introducing spurious non-Gaussianity. When the brightest point sources are removed from the data using the Mexican Hat Wavelet, the Gaussian character of the CMB is preserved. However, when analysing larger regions of the sky, the variance of our estimators will be appreciably reduced and, in this case, we expect the point source residuals to introduce spurious non-Gaussianity in the CMB distribution. Therefore, a careful subtraction (or masking) of point source emission is crucial in order to be able to perform Gaussian analysis of the CMB.

Primordial non-Gaussianity: local curvature method and statistical significance of constraints onfNLfromWMAPdata

We test the consistency of estimates of the non-linear coupling constant f$_{NL$ using non-Gaussian cosmic microwave background (CMB) maps generated by the method described in the work of Liguori, Matarrese \amp Moscardini. This procedure to obtain non-Gaussian maps differs significantly from the method used in previous works on the estimation of f$_NL$. Nevertheless, using spherical wavelets, we find results in very good agreement with Mukherjee \amp Wang, showing that the two ways of generating primordial non-Gaussian maps give equivalent results. Moreover, we introduce a new method for estimating the non-linear coupling constant from CMB observations by using the local curvature of the temperature fluctuation field. We present both Bayesian credible regions (assuming a flat prior) and proper (frequentist) confidence intervals on f$_NL$, and discuss the relation between the two approaches. The Bayesian approach tends to yield lower error bars than the frequentist approach, suggesting that a careful analysis of the different interpretations is needed. Using this method, we estimate f$_NL$=-10$^+270$$_-260$ at the 2$\sigma$ level (Bayesian) and f$_NL$=-10$^+310$$_-270$ (frequentist). Moreover, we find that the wavelet and the local curvature approaches, which provide similar error bars, yield approximately uncorrelated estimates of f$_NL$ and therefore, as advocated in the work of Cabella et al., the estimates may be combined to reduce the error bars. In this way, we obtain f$_NL$=-5 +/- 85 and f$_NL$=-5 +/- 175 at the 1$\sigma$ and 2$\sigma$ level respectively using the frequentist approach. }

High‐Resolution Simulations of Non‐Gaussian Cosmic Microwave Background Maps in Spherical Coordinates

We describe a new numerical algorithm for obtaining high-resolution simulated maps of the cosmic microwave background (CMB) for a broad class of non-Gaussian models. The kind of non-Gaussianity we account for is based on the simple idea that the primordial gravitational potential is obtained by a nonlinear but local mapping from an underlying Gaussian random field, as results from a variety of inflationary models. Our technique, which is based on a direct realization of the potential in spherical coordinates and fully accounts for the radiation transfer function, allows us to simulate non-Gaussian CMB maps down to the Planck resolution (lmax ~ 3000) with reasonable memory storage and computational time.

CMB non-Gaussianities from the “local” universe

The present and future cosmic microwave background (CMB) experiments allow us to go beyond the information contained in the power spectrum. In particular, the non-Gaussian signatures in the CMB represent a very promising tool to probe the early universe. However, the secondary anisotropies, the galactic emission and the instrumental effects also induce non-Gaussian distributed anisotropies. It is therefore important not only to develop non-Gaussian estimators, but also to understand the physics of these effects to better disentangle between them.

Digital deblurring of CMB maps: Performance and efficient implementation

Digital deblurring of images is an important problem that arises in multifrequency observations of the Cosmic Microwave Background (CMB) where, because of the width of the point spread functions (PSF), maps at different frequencies suffer a different loss of spatial resolution. Deblurring is useful for various reasons: first, it helps to restore high frequency components lost through the smoothing effect of the instrument's PSF; second, emissions at various frequencies observed with different resolutions can be better studied on a comparable resolution; third, some map-based component separation algorithms require maps with similar level of degradation. Because of computational efficiency, deblurring is usually done in the frequency domain. But this approach has some limitations as it requires spatial invariance of the PSF, stationarity of the noise, and is not flexible in the selection of more appropriate boundary conditions. Deblurring in real space is more flexible but usually not used because of its high computational cost. In this paper (the first in a series on the subject) we present new algorithms that allow the use of real space deblurring techniques even for very large images. In particular, we consider the use of Tikhonov deblurring of noisy maps with applications to {\it PLANCK}. We provide details for efficient implementations of the algorithms. Their performance is tested on Gaussian and non-Gaussian simulated CMB maps, and PSFs with both circular and elliptical symmetry. Matlab code is made available.

COBE—DMR constraints on the non-linear coupling parameter: a wavelet based method

Non-linearity introduced in slow-roll inflation will produce weakly non-Gaussian cosmic microwave background (CMB) temperature fluctuations. We have simulated non-Gaussian large-scale CMB maps (including COBE—DMR constraints) introducing an additional quadratic term in the gravitational potential. The amount of non-linearity is controlled by the so-called non-linear coupling parameter fnl. An analysis based on the Spherical Mexican Hat wavelet was applied to these and to the COBE—DMR maps. Skewness values obtained at several scales were combined into a Fisher discriminant. Comparison of the Fisher discriminant distributions obtained for different non-linear coupling parameters with the COBE—DMR values sets a constraint of |fnl| < 1100 at the 68 per cent confidence level. This new constraint is tighter than the one previously obtained by using the bispectrum by Komatsu et al.

Non-Gaussian cosmic microwave background temperature fluctuations from peculiar velocities of clusters

We use numerical simulations of a (480 Mpc h−1)3 volume to show that the distribution of peak heights in maps of the temperature fluctuations from the kinematic and thermal Sunyaev–Zeldovich (SZ) effects will be highly non-Gaussian, and very different from the peak-height distribution of a Gaussian random field. We then show that it is a good approximation to assume that each peak in either SZ effect is associated with one and only one dark matter halo. This allows us to use our knowledge of the properties of haloes to estimate the peak-height distributions. At fixed optical depth, the distribution of peak heights resulting from the kinematic effect is Gaussian, with a width that is approximately proportional to the optical depth; the non-Gaussianity comes from summing over a range of optical depths. The optical depth is an increasing function of halo mass and the distribution of halo speeds is Gaussian, with a dispersion that is approximately independent of halo mass. This means that observations of the kinematic effect can be used to put constraints on how the abundance of massive clusters evolves, and on the evolution of cluster velocities. The non-Gaussianity of the thermal effect, on the other hand, comes primarily from the fact that, on average, the effect is larger in more massive haloes, and the distribution of halo masses is highly non-Gaussian. We also show that because haloes of the same mass may have a range of density and velocity dispersion profiles, the relation between halo mass and the amplitude of the thermal effect is not deterministic, but has some scatter.

Correlation of excursion sets for non-Gaussian cosmic microwave background temperature distributions

We present a method, based on the correlation function of excursion sets above a given threshold, to test the Gaussianity of the cosmic microwave background (CMB) temperature fluctuations in the sky. In particular, this method can be applied to discriminate between standard inflationary scenarios and those producing non-Gaussianity such as topological defects. We have obtained the normalized correlation of excursion sets, including different levels of noise, for two-point probability density functions constructed from the Gaussian, χ2n and Laplace one-point probability density functions in two different ways. Considering subdegree angular scales, we find that this method can distinguish between different distributions even if the corresponding marginal probability density functions and/or the radiation power spectra are the same.