A search for concentric rings with unusual variance in the 7-year WMAP temperature maps using a fast convolution approach

We present a method for the computation of the variance of cosmic microwave background (CMB) temperature maps on azimuthally symmetric patches using a fast convolution approach. As an example of the application of the method, we show results for the search for concentric rings with unusual variance in the 7-year Wilkinson Microwave Anisotropy Probe (WMAP) data. We re-analyse claims concerning the unusual variance profile of rings centred at two locations on the sky that have recently drawn special attention in the context of the conformal cyclic cosmology scenario proposed by Penrose. We extend this analysis to rings with larger radii and centred on other points of the sky. Using the fast convolution technique enables us to perform this search with higher resolution and a wider range of radii than in previous studies. We show that for one of the two special points rings with radii larger than 10 degrees have systematically lower variance in comparison to the concordance Lambda cold dark matter model predictions. However, we show that this deviation is caused by the multipoles up to order l = 7. Therefore, the deficit of power for concentric rings with larger radii is yet another manifestation of the well-known anomalous CMB distribution on large angular scales. Furthermore, low-variance rings can be easily found centred on other points in the sky. In addition, we show also the results of a search for extremely high-variance rings. As for the low-variance rings, some anomalies seem to be related to the anomalous distribution of the low-order multipoles of the WMAP CMB maps. As such our results are not consistent with the conformal cyclic cosmology scenario.