Secondary gravitational anisotropies in open universes

Abstract

The applicability of the potential approximation in the case of open universes is tested. Great Attractor-like structures are considered in the test. Previous estimates of the Cosmic Microwave background anisotropies produced by these structures are analyzed and interpreted. The anisotropies corresponding to inhomogeneous ellipsoidal models are also computed. It is proved that, whatever the spatial symmetry may be, Great Attractor-like objects with extended cores (radius $\sim 10h^{-1}$),located at redshift $z=5.9$ in an open universe with density parameter $Ω_{0}=0.2$, produce secondary gravitational anisotropies of the order of $10^{-5}$ on angular scales of a few degrees. This anisotropy appears to be an integrated effect along the photon geodesics. Its angular scale is much greater than that subtended by the Great Attractor itself. This is understood taking into account that the integrated effect is produced by the variations of the gravitational potential, which seem to be important in large regions subtending angular scales of various degrees. As a result of the large size of these regions, the spatial curvature of the universe becomes important and, consequently, significant errors ($\sim 30$ per cent) arise in estimations based on the potential approximation.