On the microwave background anisotropy produced by big voids in open universes

Abstract

The Tolman-Bondi solution of the Einstein equations is used in order to model the time evolution of the void observed in Bo\"otes. The present density contrast of the central region ($\sim -0.75$) and its radius ($\sim 30h^{-1} \ Mpc$) are fixed, while the density parameter of the Universe, the amplitude of the density contrast inside the void wall, the width of this wall and the distance from the void centre to the Local Group are appropriately varied. The microwave background anisotropy produced by Bo\"otes-like voids is estimated for a significant set of locations. All the voids are placed far from the last scattering surface. It is shown that the anisotropy generated by these voids strongly depends on the density parameter, the wall structure and the void location. The Doppler dipole and quadrupole are subtracted and the residual anisotropy is calculated. In the case of some isolated Bo\"otes-like voids placed at redshifts between 1 and 10 in an open universe with density parameter $\Omega_{0}=0.2$, the residual anisotropy appears to be a few times $10^{-6}$ on scales of a few degrees. This anisotropy is about one order of magnitude greater than previous estimates corresponding to other cases. The anisotropy produced by a distribution of voids is qualitatively studied in the light of this result. Comparisons with previous estimates are discussed.