Detecting the cold spot as a void with the non-diagonal two-point function

Abstract

The anomaly in the Cosmic Microwave Background known as the "Cold Spot" could be due to the existence of an anomalously large spherical (few hundreds Mpc/h radius) underdense region, called a "Void" for short. Such a structure would have an impact on the CMB also at high multipoles ℓ through Lensing. This would then represent a unique signature of a Void. Modeling such an underdensity with an LTB metric, we show that the Lensing effect leads to a large signal in the non-diagonal two-point function, centered in the direction of the Cold Spot, such that the Planck satellite will be able to confirm or rule out the Void explanation for the Cold Spot, for any Void radius with a Signal-to-Noise ratio of at least O(10).

How sensitive is the CMB to a single lens?

“…Collecting both contributions, the diagonal of the previous section and off-diagonal calculated in [29], we find that S N…”

“…With this motivation in mind we study the CMB weak lensing signal associated with a single lens that breaks statistical isotropy. Our main goal is to determine under what JCAP06(2011)033 circumstances will such a lens leave a statistically significant imprint on the CMB, that is, a S/N larger than 1 (for previous works on the subject see [27][28][29]).…”

“…(1) lm;l 2 m (with l = l 2 ), are derived in [29] (eq. 13), and here we mainly examine the diagonal contribution to the S/N (A.1).…”

Two-point correlation functions in inhomogeneous and anisotropic cosmologies

“…As a final remark, we emphasize that expression (3.41) should be seen as containing anisotropies and inhomogeneities only from the initial conditions, after which we assume the universe to be pure FLRW. In particular, contributions resulting from integrated effects from the last scattering surface to us -like the effect induced by the lensing potential in anisotropic [18,38] and inhomogeneous [27,39] universes -cannot be extracted from this formalism in its present form. On the other hand, the multipolar features resulting from the coefficients in Table 1 would still be preserved -perhaps in an integrated version -as long as perturbations are functions of the background coordinates.…”

“…Since ξ 0 (r − , 0) = ξ F L (r − ), we finally find that 15) which is the desired result 4 . In order to extract the amplitude of the leading corrections one still needs the specific shape of the function ξ 0 (r − , r + ), which at this point can only be fixed from first physical principles [16,26,27]. Note however that, as far as the angular dependence is concerned, there is no new information in ξ 0 (r − , r + ) as compared to (2.22), since its angular dependence also comes from the angle between r 2 and r 1 .…”