The Cold Spot as a Large Void: Lensing Effect on CMB Two and Three Point Correlation Functions

Abstract

The "Cold Spot" in the CMB sky could be due to the presence of an anomalous huge spherical underdense region - a "Void" - of a few hundreds Mpc/h radius. Such a structure would have an impact on the CMB two-point (power spectrum) and three-point (bispectrum) correlation functions not only at low-l, but also at high-l through Lensing, which is a unique signature of a Void. Modeling such an underdensity with an LTB metric, we show that for the power spectrum the effect should be visible already in the WMAP data only if the Void radius is at least L \gtrsim 1 Gpc/h, while it will be visible by the Planck satellite if L \gtrsim 500 Mpc/h. We also speculate that this could be linked to the high-l detection of an hemispherical power asymmetry in the sky. Moreover, there should be non-zero correlations in the non-diagonal two-point function. For the bispectrum, the effect becomes important for squeezed triangles with two very high l's: this signal can be detected by Planck if the Void radius is at least L \gtrsim 300 Mpc/h, while higher resolution experiments should be able to probe the entire parameter space. We have also estimated the contamination of the primordial non-Gaussianity f_NL due to this signal, which turns out to be negligible.