Topology of large-scale underdense regions

We investigate the large-scale matter distribution adopting QSOs as matter tracer. The quasar catalogue based on the Sloan Digital Sky Survey DR7 is used. The void finding algorithm is presented and statistical properties of void sizes and shapes are determined. Number of large voids in the quasar distribution is greater than the number of the same size voids found in the random distribution. The largest voids with diameters exceeding 300 Mpc indicate an existence of comparable size areas of lower than the average matter density. No void-void space correlations have been detected, and no larger scale deviations from the uniform distribution are revealed. The average cosmic microwave background temperature in the directions of the largest voids is lower than in the surrounding areas by 0.0046 +/- 0.0028 mK. This figure is compared to the amplitude of the expected temperature depletion caused by the integrated Sachs-Wolfe effect.