A comprehensive overview of the Cold Spot

The report of a significant deviation of the CMB temperature anisotropies distribution from Gaussianity (soon after the public release of the WMAP data in 2003) has become one of the most solid WMAP anomalies. This detection grounds on an excess of the kurtosis of the Spherical Mexican Hat Wavelet coefficients at scales of around 10 degrees. At these scales, a prominent feature --located in the southern Galactic hemisphere-- was highlighted from the rest of the SMHW coefficients: the Cold Spot. This article presents a comprehensive overview related to the study of the Cold Spot, paying attention to the non-Gaussianity detection methods, the morphological characteristics of the Cold Spot, and the possible sources studied in the literature to explain its nature. Special emphasis is made on the Cold Spot compatibility with a cosmic texture, commenting on future tests that would help to give support or discard this hypothesis.Comment: 21 pages, 14 figures. Accepted for publication in the Advances in Astronomy special issue "Testing the Gaussianity and Statistical Isotropy of the Universe

Alignment and signed-intensity anomalies in WMAP data

Significant alignment and signed-intensity anomalies of local features of the cosmic microwave background (CMB) are detected on the three-year WMAP data, through a decomposition of the signal with steerable wavelets on the sphere. Firstly, an alignment analysis identifies two mean preferred planes in the sky, both with normal axes close to the CMB dipole axis. The first plane is defined by the directions toward which local CMB features are anomalously aligned. A mean preferred axis is also identified in this plane, located very close to the ecliptic poles axis. The second plane is defined by the directions anomalously avoided by local CMB features. This alignment anomaly provides further insight on recent results (Wiaux et al. 2006). Secondly, a signed-intensity analysis identifies three mean preferred directions in the southern galactic hemisphere with anomalously high or low temperature of local CMB features: a cold spot essentially identified with a known cold spot (Vielva et al. 2004), a second cold spot lying very close to the southern end of the CMB dipole axis, and a hot spot lying close to the southern end of the ecliptic poles axis. In both analyses, the anomalies are observed at wavelet scales corresponding to angular sizes around 10 degress on the celestial sphere, with global significance levels around 1%. Further investigation reveals that the alignment and signed-intensity anomalies are only very partially related. Instrumental noise, foreground emissions, as well as some form of other systematics, are strongly rejected as possible origins of the detections. An explanation might still be envisaged in terms of a global violation of the isotropy of the Universe, inducing an intrinsic statistical anisotropy of the CMB.Comment: 12 pages, 7 figures. Accepted for publication in MNRAS. Small changes made (including the new subsection 3.4) to match the final versio

Complex data processing: fast wavelet analysis on the sphere

In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the plane and on the sphere. Two fast algorithms are also presented for the analysis of signals on the sphere with steerable wavelets.Comment: 20 pages, 5 figures, JFAA style, paper invited to J. Fourier Anal. and Appli

Steerable wavelet analysis of CMB structures alignment

This paper reviews the application of a novel methodology for analysing the isotropy of the universe by probing the alignment of local structures in the CMB. The strength of the proposed methodology relies on the steerable wavelet filtering of the CMB signal. One the one hand, the filter steerability renders the computation of the local orientation of the CMB features affordable in terms of computation time. On the other hand, the scale-space nature of the wavelet filtering allows to explore the alignment of the local structures at different scales, probing possible different phenomena. We present the WMAP first-year data analysis recently performed by the same authors (Wiaux et al.), where an extremely significant anisotropy was found. In particular, a preferred plane was detected, having a normal direction with a northern end position close to the northern end of the CMB dipole axis. In addition, a most preferred direction was found in that plane, with a northern end direction very close to the north ecliptic pole. This result synthesised for the first time previously reported anomalies identified in the direction of the dipole and the ecliptic poles axes. In a forthcoming paper (Vielva et al.), we have extended our analysis to the study of individual frequency maps finding first indications for discarding foregrounds as the origin of the anomaly. We have also tested that the preferred orientations are defined by structures homogeneously distributed in the sky, rather than from localised regions. We have also analysed the WMAP 3-year data, finding the same anomaly pattern, although at a slightly lower significance level.Comment: 14 pages, 8 figures. Proceedings of the Fundamental Physics With CMB workshop, UC Irvine, March 23-25, 2006, to be published in New Astronomy Review

Cross-correlation of the CMB and radio galaxies in real, harmonic and wavelet spaces: detection of the integrated Sachs-Wolfe effect and dark energy constraints

We report the first detection of the ISW effect in wavelet space, at scales in the sky around 7 degrees with a significance of around 3.3 sigma, by cross-correlating the WMAP first-year data and the NRAO VLA Sky Survey (NVSS). In addition, we present a detailed comparison among the capabilities of three different techniques for two different objectives: to detect the ISW and to put constraints in the nature of the dark energy. The three studied techniques are: the cross-angular power spectrum (CAPS, harmonic space), the correlation function (CCF, real space) and the covariance of the Spherical Mexican Hat Wavelet (SMHW) coefficients (CSMHW, wavelet space). We prove that the CSMHW is expected to provide a higher detection of the ISW effect for a certain scale. This prediction has been corroborated by the analysis of the data. The SMHW analysis shows that the cross-correlation signal is caused neither by systematic effects nor foreground contamination. However, by taking into account the information encoded in all the multipoles/scales/angles, the CAPS provides slightly better constraints than the SMHW in the cosmological parameters that define the nature of the dark energy. The limits provided by the CCF are wider than for the other two methods. Two different cases have been studied: 1) a flat Lambda-CDM universe and 2) a flat universe with an equation of state parameter different from -1. In the first case, the CAPS provides (for a bias value of b = 1.6) 0.59 < Lambda density < 0.84 (at 1 sigma CL). Moreover, the CAPS rejects the range Lambda density < 0.1 at 3.5 sigma, which is the highest detection of the dark energy reported up to date. In the second case, the CAPS gives 0.50 < dark energy density < 0.82 and -1.16 < w < 0.43 (at 1 sigma CL).Comment: 12 pages, 7 figures, accepted for publication in MNRAS. Analysis redone. Changes in the estimation of the cosmological parametres. Additional comparison between wavelets and more standard technique

Fast directional correlation on the sphere with steerable filters

A fast algorithm is developed for the directional correlation of scalar band-limited signals and band-limited steerable filters on the sphere. The asymptotic complexity associated to it through simple quadrature is of order O(L^5), where 2L stands for the square-root of the number of sampling points on the sphere, also setting a band limit L for the signals and filters considered. The filter steerability allows to compute the directional correlation uniquely in terms of direct and inverse scalar spherical harmonics transforms, which drive the overall asymptotic complexity. The separation of variables technique for the scalar spherical harmonics transform produces an O(L^3) algorithm independently of the pixelization. On equi-angular pixelizations, a sampling theorem introduced by Driscoll and Healy implies the exactness of the algorithm. The equi-angular and HEALPix implementations are compared in terms of memory requirements, computation times, and numerical stability. The computation times for the scalar transform, and hence for the directional correlation, of maps of several megapixels on the sphere (L~10^3) are reduced from years to tens of seconds in both implementations on a single standard computer. These generic results for the scale-space signal processing on the sphere are specifically developed in the perspective of the wavelet analysis of the cosmic microwave background (CMB) temperature (T) and polarization (E and B) maps of the WMAP and Planck experiments. As an illustration, we consider the computation of the wavelet coefficients of a simulated temperature map of several megapixels with the second Gaussian derivative wavelet.Comment: Version accepted in APJ. 14 pages, 2 figures, Revtex4 (emulateapj). Changes include (a) a presentation of the algorithm as directly built on blocks of standard spherical harmonics transforms, (b) a comparison between the HEALPix and equi-angular implementation

On the recovery of ISW fluctuations using large-scale structure tracers and CMB temperature and polarization anisotropies

In this work we present a method to extract the signal induced by the integrated Sachs-Wolfe (ISW) effect in the cosmic microwave background (CMB). It makes use of the Linear Covariance-Based filter introduced by Barreiro et al., and combines CMB data with any number of large-scale structure (LSS) surveys and lensing information. It also exploits CMB polarization to reduce cosmic variance. The performance of the method has been thoroughly tested with simulations taking into account the impact of non-ideal conditions such as incomplete sky coverage or the presence of noise. In particular, three galaxy surveys are simulated, whose redshift distributions peak at low ($z \simeq 0.3$), intermediate ($z \simeq 0.6$) and high redshift ($z \simeq 0.9$). The contribution of each of the considered data sets as well as the effect of a mask and noise in the reconstructed ISW map is studied in detail. When combining all the considered data sets (CMB temperature and polarization, the three galaxy surveys and the lensing map), the proposed filter successfully reconstructs a map of the weak ISW signal, finding a perfect correlation with the input signal for the ideal case and around 80 per cent, on average, in the presence of noise and incomplete sky coverage. We find that including CMB polarization improves the correlation between input and reconstruction although only at a small level. Nonetheless, given the weakness of the ISW signal, even modest improvements can be of importance. In particular, in realistic situations, in which less information is available from the LSS tracers, the effect of including polarisation is larger. For instance, for the case in which the ISW signal is recovered from CMB plus only one survey, and taking into account the presence of noise and incomplete sky coverage, the improvement in the correlation coefficient can be as large as 10 per cent.Comment: 17 pages, 15 figures, accepted for publication in MNRA