How likely is such a large underdense region in a concordance cosmology? Suppose there is only one such large underdense region in the whole volume up to z=1. The corresponding void frequency is then the ratio of the comoving volume of the void to the comoving volume of the Universe to z=1, which is roughly 3 × 10−5. Is this consistent with LCDM? Void statistics have been done for a number of optical galaxy surveys, as well as numerical structure formation simulations. Taking the most optimistic void statistics (filled dots in Fig. 9 of Hoyle & Vogeley, 2004) which can be approximated by log P = −(r/Mpc)/15, a 140 Mpc void would occur with a probability of 5 × 10−10, considerably more rare than our estimate for our Universe (3×10−5) based on the existence of the cold spot. One must keep in mind, however, that observational and numerical void probability studies are limited to rc 30 Mpc; it is not yet clear how these should be extrapolated to rc > 100 Mpc.
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