Patricio Vielva Astrophysics Department (IFCA, Santander) Currently Astrophysics Group (Cavendish Lab., Cambridge) Wiaux, Vielva, Martínez-González & Vandergheynst, 2006, PRL Bernard’s Cosmic Stories June 2006, Valencia

Motivation Our approach: the CMB structures can "watch" Steerable wavelets Application to the WMAP data What next? Conclusions Outline of the talk Bernard’s Cosmic Stories June 2006, Valencia

(from Copi et al. 2005) (from Hansen et al. 2004) Motivation Our approach: the CMB structures can "watch" Steerable wavelets Application to the WMAP data What next? Conclusions Motivation Many works have analysed the WMAP data for studying whether it is consistent with the isotropy principle. Some works based on wavelets have detected a very large and very cold spot in the southern hemisphere showing a significant deviation from an isotropic GRF (Vielva et al. 2004, Cruz et al. 2005, 2006). Certain analyses find a strong evidence for a north-south asymmetry maximized in a coordinate system with the north pole close to the north ecliptic pole (e.g. Eriksen et al. 2004, Hansen et al. 2004, Land & Magueijo 2005a). Other works find an anomalous alignment between the low multipoles of the CMB, suggesting a preferred direction near the ecliptic plane and close to the axis of the dipole (e.g. Copi et al. 2004,2005, Schwarz et al. 2004, de Oliveira-Costa et al., Land & Magueijo 2005b). Some authors have not found any strong evidence for the isotropy violation (e.g. Hajian et al. 2005) Bernard’s Cosmic Stories June 2006, Valencia

Considering the previous results, we propose an alternative method for probing the statistical isotropy of the CMB it relies on the analysis of the alignment of structures on the CMB preferred directions in the universe are defined as the directions towards which local features of the CMB are mostly oriented the number of times a direction is “watched” represents a signal on the sphere, D(  ), allowing also for the analysis of its corresponding angular power spectrum the analysis is feasible thanks to the steerable wavelet decomposition of the data, which also allows to probe different scales of the features Motivation Our approach: the CMB structures can "watch" Steerable wavelets Application to the WMAP data What next? Conclusions Our approach: the CMB structures can "watch" Bernard’s Cosmic Stories June 2006, Valencia

Great circle Seen twice Motivation Our approach: the CMB structures can "watch" Steerable wavelets Application to the WMAP data What next? Conclusions Our approach: the CMB structures can "watch" An even signal is obtained Bernard’s Cosmic Stories June 2006, Valencia Modified from the Max Tegmark web site

The wavelet transform of a signal gives us information about: the scale of the structures presented in the signal the position in which those structures are located and (for the continuous case) it is obtained by convolving the signal with the wavelet. Steerable wavelets are the natural extension of isotropic and directional wavelets, which have been successfully and extensively applied to many different topics within the CMB data analysis. The steerable wavelets were introduced by Freeman & Adelson at the fall of the 80’s and the rise of the 90’s. They have been recently extended to the sphere by Wiaux et al They appear as a solution for the multi-directional image analysis: any direction can be explored through a linear combination of a given basis. Motivation Our approach: the CMB structures can "watch" Steerable wavelets Application to the WMAP data What next? Conclusions Steerable wavelets Bernard’s Cosmic Stories June 2006, Valencia

The wavelet coefficient at a given position (x, y), at a given scale (R) and at a particular orientation , can be expressed as: Their properties allows to explore possibilities that are (in practice) unfeasible by using standard techniques, like the one proposed in this work: the anisotropy analysis by studying the alignment of the CMB structures. Typical examples of steerable wavelets are the Nth-directional derivatives of a Gaussian function Motivation Our approach: the CMB structures can "watch" Steerable wavelets Application to the WMAP data What next? Conclusions Steerable wavelets Bernard’s Cosmic Stories June 2006, Valencia

Motivation Our approach: the CMB structures can "watch" Steerable wavelets Application to the WMAP data What next? Conclusions Steerable wavelets Bernard’s Cosmic Stories June 2006, Valencia

Orientation of the maximum value of the wavelet coefficients Orientation of the feature Orientation given the maximum of the wavelet coefficient: By computing three wavelet coefficient maps (for each scale), the local orientation that better matches that of the CMB features can be obtained Motivation Our approach: the CMB structures can "watch" Steerable wavelets Application to the WMAP data What next? Conclusions Steerable wavelets Bernard’s Cosmic Stories June 2006, Valencia

{,,...} Motivation Our approach: the CMB structures can "watch" Steerable wavelets Application to the WMAP data What next? Conclusions Steerable wavelets Bernard’s Cosmic Stories June 2006, Valencia

Wavelet coefficients matching the features orientations Number of times that a position is “watched” by the features Motivation Our approach: the CMB structures can "watch" Steerable wavelets Application to the WMAP data What next? Conclusions Steerable wavelets Bernard’s Cosmic Stories June 2006, Valencia

Motivation Our approach: the CMB structures can "watch" Steerable wavelets Application to the WMAP data What next? Conclusions Application to the WMAP data Bernard’s Cosmic Stories June 2006, Valencia WMAP web site

The analysed map is the one proposed by Komatsu et al (NG paper of WMAP-1st yr). The map is degraded down to N side =32. The Kp0 mask is applied. Scales from 5 to 30 degrees are explored. Motivation Our approach: the CMB structures can "watch" Steerable wavelets Application to the WMAP data What next? Conclusions Application to the WMAP data Bernard’s Cosmic Stories June 2006, Valencia

D R (  ) map for the co-added WMAP 8.3º angular size given in terms of the 1 – p-value (estimated from simulations) Motivation Our approach: the CMB structures can "watch" Steerable wavelets Application to the WMAP data What next? Conclusions Application to the WMAP data Bernard’s Cosmic Stories June 2006, Valencia

There are 20 anomalous directions in the sky, that have been “watched” more times than any of the analysed simulations. The probability of having, at least, this number of so “watched” positions is 0.01 % Best fit of a great circle passing by the anomalous directions Dipole direction Normal direction to the detected plane NEP This results synthesises previous anomalies !! Motivation Our approach: the CMB structures can "watch" Steerable wavelets Application to the WMAP data What next? Conclusions Application to the WMAP data Bernard’s Cosmic Stories June 2006, Valencia

Q bandV bandW band Co-added Motivation Our approach: the CMB structures can "watch" Steerable wavelets Application to the WMAP data What next? Conclusions Application to the WMAP data Bernard’s Cosmic Stories June 2006, Valencia D R (  ) map for the co-added WMAP 8.3º angular size given in terms of the #  (estimated from simulations)

Motivation Our approach: the CMB structures can "watch" Steerable wavelets Application to the WMAP data What next? Conclusions Application to the WMAP data Bernard’s Cosmic Stories June 2006, Valencia Are those anomalous directions due to an specific “watching” of certain structures located in specific places? Or, on the contrary, they come from positions on the sky homogenously distributed?

Motivation Our approach: the CMB structures can "watch" Steerable wavelets Application to the WMAP data What next? Conclusions Application to the WMAP data 1yr 3yr Bernard’s Cosmic Stories June 2006, Valencia Same structures are found, but signification decreases: from 0.01% to 0.42%

Current work is in progress to find the possible source of this anisotropy detection: the coincidence of the preferred directions detected with the EP and dipole axes suggest possible unknown systematics the angular size in which the preferred directions appear is compatible with topological defects (like textures) or secondary anisotropies due to the Rees-Sciama effect although the detected anisotropy seems to be the same at all the frequencies, it must be also considered that foregrounds could generate aligned structures of several degrees the analysis of the angular power spectrum of D(  ) could help to study the multipole distribution of the anomalies Motivation Our approach: the CMB structures can "watch" Steerable wavelets Application to the WMAP data What next? Conclusions What next? Bernard’s Cosmic Stories June 2006, Valencia

A new approach based on the alignment of the CMB structures has been proposed for studying the isotropic principle. The method relies in the application of steerable wavelets, that allows to identified the local orientation of the features at each scale. The application to the 1st yr-WMAP data shows that, at scales of 8.3º (multipole range between l=11 and l=27), 20 anomalous directions are detected. Those directions identified, first, a plane which perpendicular direction is close to the dipole axis, and second, a most prominent position on that plane that is extremely close to the NEP. This result has been confirmed with the second WMAP release. Further analysis is needed to identify the possible source of this anisotropy. Steerable wavelets open a door to fast oriented multi-scale analyses of the CMB Motivation Our approach: the CMB structures can "watch" Steerable wavelets Application to the WMAP data What next? Conclusions Bernard’s Cosmic Stories June 2006, Valencia Thank you for your attention!