Effect of Void Network on CMB Anisotropy

We study the effect of a void network on the CMB anisotropy in the Einstein-de Sitter background using Thompson & Vishniac's model. We estimate both the Rees-Sciama effect and the gravitational lensing effect. As well as the Sachs-Wolfe effect, the Rees-Sciama effect can be appreciable even for multipoles $l\lsim1000$ of the anisotropy spectrum, if primordial voids exist at recombination, which is realized in some inflationary models associated with a first-order phase transition. The gravitational lensing effect, on the other hand, slightly smoothes the primary anisotropy; quantitatively, our results for the void model are similar to the previous results for a CDM model. Both effects, together, would give some constraints on the configuration or origin of voids with high-resolution data of the CMB anisotropy up to $l\sim1000$. Those effects, on the other hand, are negligible for $l\lsim500$, which does not obstruct the determination of the cosmological model from the anisotropy spectrum.