Effect of Void Network on Cosmic Microwave Background Anisotropy

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Abstract
We study the effect of a void network on the cosmic microwave background (CMB) anisotropy in the Einstein-de Sitter background using Thompson & Vishniac's model. We consider comprehensively the Sachs-Wolfe effect, the Rees-Sciama effect, and the gravitational lensing effect. Our analysis includes the model of primordial voids existing at recombination, which is realized in some inflationary models associated with a first-order phase transition. If there exist primordial voids whose comoving radius is larger than ~10 h-1 Mpc at recombination, not only the Sachs-Wolfe effect but also the Rees-Sciama effect is appreciable even for multipoles l1000 of the anisotropy spectrum. The gravitational lensing effect, on the other hand, slightly smooths the primary anisotropy; quantitatively, our results for the void model are similar to the previous results for a cold dark matter model. All the effects together would give some constraints on the configuration or origin of voids with high-resolution data of the CMB anisotropy.